From c5dbcf461037e604b2a564d384cdd86da627bbf0 Mon Sep 17 00:00:00 2001 From: Galigeigei-Z <213375167+Galigeigei-Z@users.noreply.github.com> Date: Sun, 9 Aug 2026 14:59:19 +0800 Subject: [PATCH 1/5] Add two-way fluidized-bed HGFD model --- HGD/fluid.py | 332 ++++++++++++++++++++++++++++++++++ HGD/initial.py | 2 +- HGD/main.py | 19 ++ HGD/motion/hgfd.py | 130 +++++++++++++ HGD/plotter.py | 112 +++++++++++- docs/examples.md | 35 +++- docs/images/fluidized_bed.png | Bin 0 -> 14273 bytes json/defaults.json5 | 11 ++ json/fluidized_bed.json5 | 40 ++++ test/test_fluid.py | 116 ++++++++++++ 10 files changed, 788 insertions(+), 9 deletions(-) create mode 100644 HGD/fluid.py create mode 100644 HGD/motion/hgfd.py create mode 100644 docs/images/fluidized_bed.png create mode 100644 json/fluidized_bed.json5 create mode 100644 test/test_fluid.py diff --git a/HGD/fluid.py b/HGD/fluid.py new file mode 100644 index 0000000..c023a5e --- /dev/null +++ b/HGD/fluid.py @@ -0,0 +1,332 @@ +"""Two-way fluid coupling utilities for heterarchical granular dynamics. + +The implementation follows the fluid-fraction-weighted formulation used by +Heterarchical Granular--Fluid Dynamics (HGFD). It is intentionally a compact +2-D, isothermal, laminar solver: particle velocities are relaxed with the +Gidaspow drag law and the equal-and-opposite drag is applied to an +incompressible fluid using a variable-porosity pressure projection. +""" + +from dataclasses import dataclass + +import numpy as np +from scipy import sparse +from scipy.sparse.linalg import spsolve + + +@dataclass +class FluidState: + """Eulerian fluid fields and coupling diagnostics on the HGD grid.""" + + u: np.ndarray + v: np.ndarray + pressure: np.ndarray + beta: np.ndarray + solid_u: np.ndarray + solid_v: np.ndarray + momentum_source_u: np.ndarray + momentum_source_v: np.ndarray + divergence: np.ndarray + fluidized: np.ndarray + pressure_drop: float = 0.0 + fluidization_ratio: float = 0.0 + + +def _void_fraction(solid_fraction, p): + minimum = getattr(p, "fluid_min_void_fraction", 0.05) + return np.clip(1.0 - solid_fraction, minimum, 1.0) + + +def initialize(p, s): + """Initialise a co-located gas field from a prescribed superficial inlet velocity.""" + + solid_fraction = 1.0 - np.mean(np.isnan(s), axis=2) + void_fraction = _void_fraction(solid_fraction, p) + superficial_velocity = getattr(p, "fluid_inlet_velocity", 0.0) + shape = solid_fraction.shape + + # n * u_f is the superficial velocity. This initial field therefore + # satisfies the one-dimensional variable-porosity continuity equation. + u = np.zeros(shape) + v = superficial_velocity / void_fraction + pressure = np.zeros(shape) + zeros = np.zeros(shape) + return FluidState( + u=u, + v=v, + pressure=pressure, + beta=zeros.copy(), + solid_u=zeros.copy(), + solid_v=zeros.copy(), + momentum_source_u=zeros.copy(), + momentum_source_v=zeros.copy(), + divergence=zeros.copy(), + fluidized=np.zeros(shape, dtype=bool), + ) + + +def drag_coefficients(s, particle_u, particle_v, fluid_u, fluid_v, p): + """Return layer and cell Gidaspow momentum-exchange coefficients. + + ``layer_beta`` is the coefficient used for particle relaxation. The + cell-level coefficient contains the heterarchical ``1 / M`` weighting and + is the quantity supplied to the fluid momentum equation. + """ + + occupied = np.isfinite(s) + solid_fraction = np.mean(occupied, axis=2) + void_fraction = _void_fraction(solid_fraction, p) + phi = solid_fraction[:, :, np.newaxis] + eps = void_fraction[:, :, np.newaxis] + + fluid_u_3d = fluid_u[:, :, np.newaxis] + fluid_v_3d = fluid_v[:, :, np.newaxis] + rel_u = fluid_u_3d - particle_u + rel_v = fluid_v_3d - particle_v + relative_speed = np.sqrt(rel_u**2 + rel_v**2) + + diameter_floor = getattr(p, "fluid_drag_min_particle_size", 1e-12) + diameter = np.where(occupied, np.maximum(s, diameter_floor), 1.0) + rho_f = p.gas_density + mu_f = p.gas_viscosity + reynolds = rho_f * relative_speed * diameter / mu_f + + # Written as Cd*|ur| to remain finite in the Stokes limit Re -> 0. + beta_wen_yu = 18.0 * mu_f / diameter**2 * (1.0 + 0.15 * reynolds**0.687) * phi * eps ** (-2.65) + beta_ergun = 150.0 * mu_f * phi**2 / (eps * diameter**2) + 1.75 * rho_f * phi * relative_speed / diameter + layer_beta = np.where(phi < 0.2, beta_wen_yu, beta_ergun) + layer_beta = np.where(occupied, layer_beta, 0.0) + cell_beta = np.sum(layer_beta, axis=2) / p.nm + return layer_beta, cell_beta + + +def update_particle_velocities(particle_u, particle_v, s, state, p): + """Advance layer-wise particle velocity using the analytic drag relaxation.""" + + layer_beta, _ = drag_coefficients(s, particle_u, particle_v, state.u, state.v, p) + occupied = np.isfinite(s) + relaxation_rate = layer_beta / p.solid_density + decay = np.exp(-relaxation_rate * p.dt) + + buoyancy = 1.0 - p.gas_density / p.solid_density + gravity_x = getattr(p, "fluid_gravity_x", 0.0) * buoyancy + gravity_y = -abs(p.g) * buoyancy + fluid_u = state.u[:, :, np.newaxis] + fluid_v = state.v[:, :, np.newaxis] + + with np.errstate(divide="ignore", invalid="ignore"): + terminal_u = fluid_u + np.divide( + gravity_x, + relaxation_rate, + out=np.zeros_like(relaxation_rate), + where=relaxation_rate > 0, + ) + terminal_v = fluid_v + np.divide( + gravity_y, + relaxation_rate, + out=np.zeros_like(relaxation_rate), + where=relaxation_rate > 0, + ) + + new_u = terminal_u + (particle_u - terminal_u) * decay + new_v = terminal_v + (particle_v - terminal_v) * decay + + # In cells where the drag coefficient is exactly zero, integrate gravity + # directly instead of using the singular terminal-velocity expression. + no_drag = relaxation_rate == 0 + new_u = np.where(no_drag, particle_u + gravity_x * p.dt, new_u) + new_v = np.where(no_drag, particle_v + gravity_y * p.dt, new_v) + return np.where(occupied, new_u, 0.0), np.where(occupied, new_v, 0.0) + + +def coupling_fields(s, particle_u, particle_v, state, p): + """Aggregate heterarchical drag fields for the fluid momentum equation.""" + + layer_beta, cell_beta = drag_coefficients(s, particle_u, particle_v, state.u, state.v, p) + beta_sum = np.sum(layer_beta, axis=2) + with np.errstate(divide="ignore", invalid="ignore"): + solid_u = np.divide( + np.sum(layer_beta * particle_u, axis=2), + beta_sum, + out=np.zeros_like(cell_beta), + where=beta_sum > 0, + ) + solid_v = np.divide( + np.sum(layer_beta * particle_v, axis=2), + beta_sum, + out=np.zeros_like(cell_beta), + where=beta_sum > 0, + ) + + # Equal and opposite to beta * (u_f - u_p), the drag on particles. + source_u = cell_beta * (solid_u - state.u) + source_v = cell_beta * (solid_v - state.v) + return cell_beta, solid_u, solid_v, source_u, source_v + + +def _laplacian(field, dx, dy): + return np.gradient(np.gradient(field, dx, axis=0), dx, axis=0) + np.gradient( + np.gradient(field, dy, axis=1), dy, axis=1 + ) + + +def _upwind_derivative(field, velocity, spacing, axis): + """First-order upwind derivative without periodic wraparound.""" + + backward = (field - np.roll(field, 1, axis=axis)) / spacing + forward = (np.roll(field, -1, axis=axis) - field) / spacing + lower = [slice(None)] * field.ndim + upper = [slice(None)] * field.ndim + lower[axis] = 0 + upper[axis] = -1 + backward[tuple(lower)] = forward[tuple(lower)] + forward[tuple(upper)] = backward[tuple(upper)] + return np.where(velocity >= 0, backward, forward) + + +def _face_fluxes(u, v, void_fraction, inlet_velocity=0.0): + """Interpolate superficial velocity to finite-volume cell faces.""" + + nx, ny = void_fraction.shape + qx = np.zeros((nx + 1, ny)) + qy = np.zeros((nx, ny + 1)) + qx[1:nx, :] = 0.5 * (void_fraction[:-1, :] * u[:-1, :] + void_fraction[1:, :] * u[1:, :]) + qy[:, 1:ny] = 0.5 * (void_fraction[:, :-1] * v[:, :-1] + void_fraction[:, 1:] * v[:, 1:]) + qy[:, 0] = inlet_velocity + qy[:, -1] = void_fraction[:, -1] * v[:, -1] + return qx, qy + + +def _flux_divergence(qx, qy, dx, dy): + return (qx[1:, :] - qx[:-1, :]) / dx + (qy[:, 1:] - qy[:, :-1]) / dy + + +def weighted_divergence(u, v, void_fraction, dx, dy, inlet_velocity=0.0): + """Calculate finite-volume ``div(n u_f)`` at cell centres.""" + + qx, qy = _face_fluxes(u, v, void_fraction, inlet_velocity) + return _flux_divergence(qx, qy, dx, dy) + + +def _pressure_matrix(void_fraction, dx, dy): + """Build ``-div(n grad(.))`` with wall Neumann and open-top Dirichlet BCs.""" + + nx, ny = void_fraction.shape + matrix = sparse.lil_matrix((nx * ny, nx * ny)) + + def flat(i, j): + return i * ny + j + + for i in range(nx): + for j in range(ny): + row = flat(i, j) + diagonal = 0.0 + for di, dj, spacing in ((-1, 0, dx), (1, 0, dx), (0, -1, dy), (0, 1, dy)): + ii, jj = i + di, j + dj + if ii < 0 or ii >= nx or jj < 0: + continue + if jj >= ny: + continue + face_void = 0.5 * (void_fraction[i, j] + void_fraction[ii, jj]) + coefficient = face_void / spacing**2 + diagonal += coefficient + matrix[row, flat(ii, jj)] = -coefficient + if j == ny - 1: + # Fixed pressure at the open top face, half a cell away. + diagonal += 2.0 * void_fraction[i, j] / dy**2 + matrix[row, row] = diagonal + return matrix.tocsr() + + +def project_velocity(u, v, pressure, void_fraction, p): + """Project a tentative velocity onto ``div(n u_f) = 0``.""" + + del pressure + inlet = getattr(p, "fluid_inlet_velocity", 0.0) + qx, qy = _face_fluxes(u, v, void_fraction, inlet) + divergence = _flux_divergence(qx, qy, p.dx, p.dy) + rhs = -(p.gas_density / p.dt) * divergence.ravel() + correction = spsolve(_pressure_matrix(void_fraction, p.dx, p.dy), rhs).reshape(void_fraction.shape) + + nx, ny = void_fraction.shape + void_x = 0.5 * (void_fraction[:-1, :] + void_fraction[1:, :]) + void_y = 0.5 * (void_fraction[:, :-1] + void_fraction[:, 1:]) + qx[1:nx, :] -= p.dt / p.gas_density * void_x * (correction[1:, :] - correction[:-1, :]) / p.dx + qy[:, 1:ny] -= p.dt / p.gas_density * void_y * (correction[:, 1:] - correction[:, :-1]) / p.dy + qy[:, -1] -= p.dt / p.gas_density * void_fraction[:, -1] * (0.0 - correction[:, -1]) / (0.5 * p.dy) + + # Reconstruct intrinsic cell-centred velocities for HGD coupling. + u = 0.5 * (qx[:-1, :] + qx[1:, :]) / void_fraction + v = 0.5 * (qy[:, :-1] + qy[:, 1:]) / void_fraction + # The tentative step does not include an old pressure gradient, so this is + # the new pressure rather than an incremental pressure correction. + pressure = correction + return u, v, pressure, _flux_divergence(qx, qy, p.dx, p.dy) + + +def minimum_fluidization_velocity(p, solid_fraction=None, particle_size=None): + """Estimate ``U_mf`` from the same dense Gidaspow/Ergun force balance.""" + + phi = p.nu_fill if solid_fraction is None else solid_fraction + diameter = p.s_m if particle_size is None else particle_size + eps = max(1.0 - phi, getattr(p, "fluid_min_void_fraction", 0.05)) + weight = phi * (p.solid_density - p.gas_density) * p.g + linear = 150.0 * p.gas_viscosity * phi**2 / (eps**2 * diameter**2) + quadratic = 1.75 * p.gas_density * phi / (eps**2 * diameter) + if quadratic == 0: + return weight / linear + return (-linear + np.sqrt(linear**2 + 4.0 * quadratic * weight)) / (2.0 * quadratic) + + +def _diagnostics(state, solid_fraction, p): + drag_on_solid_y = state.beta * (state.v - state.solid_v) + effective_weight = solid_fraction * (p.solid_density - p.gas_density) * p.g + occupied = solid_fraction > 0 + state.fluidized = occupied & (drag_on_solid_y >= effective_weight) + state.pressure_drop = float(np.mean(state.pressure[:, 0]) - np.mean(state.pressure[:, -1])) + bed_weight = float(np.mean(np.sum(effective_weight, axis=1) * p.dy)) + state.fluidization_ratio = state.pressure_drop / bed_weight if bed_weight > 0 else 0.0 + + +def advance(state, s, particle_u, particle_v, p): + """Advance the fluid one staggered explicit HGD--CFD coupling step.""" + + solid_fraction = 1.0 - np.mean(np.isnan(s), axis=2) + void_fraction = _void_fraction(solid_fraction, p) + beta, solid_u, solid_v, source_u, source_v = coupling_fields(s, particle_u, particle_v, state, p) + + adv_u = state.u * _upwind_derivative(state.u, state.u, p.dx, axis=0) + state.v * _upwind_derivative( + state.u, state.v, p.dy, axis=1 + ) + adv_v = state.u * _upwind_derivative(state.v, state.u, p.dx, axis=0) + state.v * _upwind_derivative( + state.v, state.v, p.dy, axis=1 + ) + viscosity = p.gas_viscosity / p.gas_density + transport_u = state.u + p.dt * (-adv_u + viscosity * _laplacian(state.u, p.dx, p.dy)) + transport_v = state.v + p.dt * (-adv_v + viscosity * _laplacian(state.v, p.dx, p.dy)) + + # Treat the stiff drag term analytically. This is the fluid analogue of + # the exponential particle relaxation and remains stable in a dense bed. + drag_rate = beta / (p.gas_density * void_fraction) + drag_decay = np.exp(-drag_rate * p.dt) + tentative_u = solid_u + (transport_u - solid_u) * drag_decay + tentative_v = solid_v + (transport_v - solid_v) * drag_decay + + state.u, state.v, state.pressure, state.divergence = project_velocity( + tentative_u, tentative_v, state.pressure, void_fraction, p + ) + state.beta = beta + state.solid_u = solid_u + state.solid_v = solid_v + state.momentum_source_u = source_u + state.momentum_source_v = source_v + _diagnostics(state, solid_fraction, p) + courant = np.max(np.abs(state.u) * p.dt / p.dx + np.abs(state.v) * p.dt / p.dy) + p.fluid_courant = float(courant) + if not np.all(np.isfinite(state.u)) or not np.all(np.isfinite(state.v)): + raise FloatingPointError("Non-finite fluid velocity produced by the HGFD solver") + if courant > getattr(p, "fluid_cfl_limit", 0.8): + raise FloatingPointError( + f"Fluid CFL={courant:.3g} exceeds fluid_cfl_limit; reduce defined_time_step_size" + ) + return state diff --git a/HGD/initial.py b/HGD/initial.py index 9202d78..613e408 100644 --- a/HGD/initial.py +++ b/HGD/initial.py @@ -11,7 +11,7 @@ def IC(p): Returns: The array of grain sizes. Values of `NaN` are voids. """ - rng = np.random.default_rng() + rng = np.random.default_rng(getattr(p, "random_seed", None)) # First step: Generate BOTH the grain size distribution and the void distribution diff --git a/HGD/main.py b/HGD/main.py index 1dd39e3..e06294e 100644 --- a/HGD/main.py +++ b/HGD/main.py @@ -14,11 +14,15 @@ from HGD import boundary from HGD import mask from HGD import operators +from HGD import fluid # from HGD import cycles def init(p, cycles=None): + if p.random_seed is not None: + np.random.seed(p.random_seed) + p.move_voids = importlib.import_module(f"HGD.motion.{p.motion_model}").move_voids if hasattr(importlib.import_module(f"HGD.motion.{p.motion_model}"), "stream"): @@ -56,6 +60,18 @@ def init(p, cycles=None): # initial.set_boundary(s, p.X, p.Y, p) p = mask.update(p, s) + if p.fluid_coupling: + if not p.inertia: + raise ValueError("fluid_coupling requires inertia=true") + if p.motion_model != "hgfd": + raise ValueError("fluid_coupling requires motion_model='hgfd'") + p.fluid_state = fluid.initialize(p, s) + p.minimum_fluidization_velocity = fluid.minimum_fluidization_velocity(p) + print( + f"Estimated minimum fluidization velocity: {p.minimum_fluidization_velocity:.4g} m/s; " + f"inlet: {p.fluid_inlet_velocity:.4g} m/s" + ) + if hasattr(p, "temperature"): T = p.temperature["inlet_temperature"] * np.ones_like(s) T[np.isnan(s)] = np.nan @@ -174,6 +190,9 @@ def time_step(p, state): u = u_new v = v_new + if p.fluid_coupling: + p.fluid_state = fluid.advance(p.fluid_state, s, u, v, p) + state = ( s, u, diff --git a/HGD/motion/hgfd.py b/HGD/motion/hgfd.py new file mode 100644 index 0000000..5bb8a18 --- /dev/null +++ b/HGD/motion/hgfd.py @@ -0,0 +1,130 @@ +"""Inertial, four-direction HGD transport for two-way fluid coupling.""" + +import numpy as np + +from HGD import fluid + + +def concentration_dependent_alpha(solid_fraction, p): + """HGFD mixing coefficient that vanishes when dilute and saturates when dense.""" + + alpha_max = getattr(p, "fluid_alpha_max", p.alpha) + epsilon = getattr(p, "fluid_alpha_epsilon", 0.01) + phi_c = float(np.min(p.nu_cs)) if isinstance(p.nu_cs, np.ndarray) else p.nu_cs + phi_ref = phi_c - epsilon + clipped = np.minimum(solid_fraction, phi_ref) + numerator = np.maximum(phi_c - clipped, epsilon) ** -0.5 - phi_c**-0.5 + denominator = epsilon**-0.5 - phi_c**-0.5 + return np.clip(alpha_max * numerator / denominator, 0.0, alpha_max) + + +def _valid_destination(s, solid_fraction, boundary, axis, step, p): + destination = np.roll(s, -step, axis=axis) + destination_void = np.isnan(destination) + destination_fraction = np.roll(solid_fraction, -step, axis=axis)[:, :, np.newaxis] + destination_boundary = np.roll(boundary, -step, axis=axis)[:, :, np.newaxis] + valid = destination_void & (destination_fraction < p.nu_cs) & ~destination_boundary + + edge = [slice(None)] * 3 + edge[axis] = -1 if step > 0 else 0 + valid[tuple(edge)] = False + return valid + + +def _conflict_free(sources, destinations): + if len(sources) == 0: + return sources, destinations + order = np.random.permutation(len(sources)) + sources = sources[order] + destinations = destinations[order] + _, first = np.unique(destinations, axis=0, return_index=True) + keep = np.sort(first) + return sources[keep], destinations[keep] + + +def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): + """Advance particles using force-derived velocities and stochastic swaps.""" + + del diag + if not getattr(p, "fluid_coupling", False): + raise ValueError("The 'hgfd' motion model requires fluid_coupling=true") + if last_swap is None: + last_swap = np.zeros_like(s) + + u, v = fluid.update_particle_velocities(u, v, s, p.fluid_state, p) + occupied = np.isfinite(s) + solid_fraction = np.mean(occupied, axis=2) + boundary = getattr(p, "boundary_mask", np.zeros((p.nx, p.ny), dtype=bool)) + alpha = concentration_dependent_alpha(solid_fraction, p)[:, :, np.newaxis] + diffusivity = alpha * np.nan_to_num(s) * np.abs(v) + horizontal_diffusion = diffusivity * p.dt / p.dx**2 + + probabilities = [] + directions = ((0, 1), (0, -1), (1, 1), (1, -1)) + for axis, step in directions: + velocity = u if axis == 0 else v + directional = np.maximum(step * velocity, 0.0) * p.dt / (p.dx if axis == 0 else p.dy) + if axis == 0: + directional = directional + horizontal_diffusion + valid = occupied & _valid_destination(s, solid_fraction, boundary, axis, step, p) + probabilities.append(np.where(valid, directional, 0.0)) + + total = np.sum(probabilities, axis=0) + max_probability = float(np.max(total)) if total.size else 0.0 + p.max_transition_probability = max_probability + limit = getattr(p, "P_stab", 0.5) + if max_probability > limit: + policy = getattr(p, "fluid_probability_policy", "error") + if policy == "scale": + scale = np.minimum(1.0, limit / np.maximum(total, 1e-30)) + probabilities = [probability * scale for probability in probabilities] + else: + raise ValueError( + f"HGFD transition probability {max_probability:.3g} exceeds P_stab={limit}; " + "reduce defined_time_step_size or set fluid_probability_policy='scale'" + ) + + draw = np.random.random(s.shape) + cumulative = np.zeros_like(s, dtype=float) + source_batches = [] + destination_batches = [] + for probability, (axis, step) in zip(probabilities, directions): + selected = (draw >= cumulative) & (draw < cumulative + probability) + sources = np.argwhere(selected) + if len(sources): + destinations = sources.copy() + destinations[:, axis] += step + source_batches.append(sources) + destination_batches.append(destinations) + cumulative += probability + + if source_batches: + sources = np.concatenate(source_batches) + destinations = np.concatenate(destination_batches) + sources, destinations = _conflict_free(sources, destinations) + + # Recreate direction markers after conflict filtering from displacement. + displacement = destinations - sources + swap_type = np.where(displacement[:, 1] != 0, 1, -1) + source_index = tuple(sources.T) + destination_index = tuple(destinations.T) + for array in (s, u, v, c, T): + if array is not None: + array[source_index], array[destination_index] = ( + array[destination_index].copy(), + array[source_index].copy(), + ) + + last_swap[source_index] = np.nan + last_swap[destination_index] = swap_type + moved = np.zeros((p.nx, p.ny), dtype=float) + np.add.at(moved, (sources[:, 0], sources[:, 1]), 1) + np.add.at(moved, (destinations[:, 0], destinations[:, 1]), 1) + chi = moved / (p.nm * limit) + else: + chi = np.zeros((p.nx, p.ny), dtype=float) + + u[np.isnan(s)] = 0.0 + v[np.isnan(s)] = 0.0 + last_swap[np.isnan(s)] = np.nan + return u, v, s, c, T, chi, last_swap diff --git a/HGD/plotter.py b/HGD/plotter.py index 0ea16ef..274f9d5 100644 --- a/HGD/plotter.py +++ b/HGD/plotter.py @@ -96,12 +96,13 @@ def size_colormap(): return orange_blue_cmap -global fig, summary_fig, triple_fig, quad_fig, blue_pink_fig +global fig, summary_fig, triple_fig, quad_fig, blue_pink_fig, fluid_fig fig = plt.figure(1) summary_fig = plt.figure(2) triple_fig = plt.figure(3) quad_fig = plt.figure(4) blue_pink_fig = plt.figure(5) +fluid_fig = plt.figure(6) replacements = { "repose_angle": "φ", @@ -165,7 +166,7 @@ def replace_strings(text, replacements): def set_plot_size(p): - global fig, summary_fig, triple_fig, quad_fig, blue_pink_fig + global fig, summary_fig, triple_fig, quad_fig, blue_pink_fig, fluid_fig # wipe any existing figures for i in plt.get_fignums(): @@ -176,6 +177,7 @@ def set_plot_size(p): quad_fig = plt.figure(3, figsize=[p.nx / _dpi, 4 * p.ny / _dpi]) summary_fig = plt.figure(4) blue_pink_fig = plt.figure(5, facecolor="k", figsize=[p.nx / _dpi, p.ny / _dpi]) + fluid_fig = plt.figure(6, figsize=[3 * p.nx / _dpi, p.ny / _dpi]) def check_folders_exist(p): @@ -311,6 +313,12 @@ def update(p, state, *args): plot_deviatoric(s, sigma, last_swap, p) if "footing" in p.plot: plot_footing(p) + if "fluid_velocity" in p.plot: + plot_fluid_velocity(p) + if "fluid_pressure" in p.plot: + plot_fluid_pressure(p) + if "fluidized_bed" in p.plot: + plot_fluidized_bed(s, p) if "s" in p.save: save_s(s, p) @@ -343,12 +351,108 @@ def update(p, state, *args): save_velocity(u, v, p) if "charge_discharge" in p.save: c_d_saves(p, non_zero_nu_time, p_count, p_count_s, p_count_l) + if "fluid" in p.save: + save_fluid(p) if "col_depth" in p.save: get_col_depth(p, s) if "surface_profiles" in p.save: np.save(p.folderName + "data/surface_profiles.npy", surface_profile) +def _fluid_field(p, name): + if not getattr(p, "fluid_coupling", False) or not hasattr(p, "fluid_state"): + raise ValueError(f"'{name}' plotting requires fluid_coupling=true") + return p.fluid_state + + +def _plot_domain(field, p, cmap, vmin=None, vmax=None): + image = plt.pcolormesh(p.x, p.y, field.T, cmap=cmap, vmin=vmin, vmax=vmax) + plt.axis("off") + plt.xlim(p.x[0], p.x[-1]) + plt.ylim(p.y[0], p.y[-1]) + return image + + +def plot_fluid_velocity(p): + state = _fluid_field(p, "fluid_velocity") + speed = np.sqrt(state.u**2 + state.v**2) + plt.figure(fig) + plt.clf() + image = _plot_domain(speed, p, inferno, vmin=0) + if p.plot_colorbar: + plt.colorbar(image, shrink=0.8, location="top", pad=0.01) + plt.subplots_adjust(left=0, right=1, bottom=0, top=1) + plt.savefig(p.folderName + "fluid_velocity_" + str(p.tstep).zfill(6) + ".png") + + +def plot_fluid_pressure(p): + state = _fluid_field(p, "fluid_pressure") + plt.figure(fig) + plt.clf() + image = _plot_domain(state.pressure, p, inferno) + if p.plot_colorbar: + plt.colorbar(image, shrink=0.8, location="top", pad=0.01) + plt.subplots_adjust(left=0, right=1, bottom=0, top=1) + plt.savefig(p.folderName + "fluid_pressure_" + str(p.tstep).zfill(6) + ".png") + + +def plot_fluidized_bed(s, p): + """Plot solid fraction, vertical gas velocity, and gas pressure in the established style.""" + + state = _fluid_field(p, "fluidized_bed") + solid_fraction = operators.get_solid_fraction(s) + velocity_limit = max(float(np.max(np.abs(state.v))), 1e-12) + plt.figure(fluid_fig) + plt.clf() + + panels = ( + (solid_fraction, inferno_r, 0, p.nu_cs, r"Solid fraction $\nu$"), + (state.v, bwr, -velocity_limit, velocity_limit, r"Gas velocity $v_f$"), + (state.pressure, inferno, None, None, r"Gas pressure $p$"), + ) + for index, (field, colormap, vmin, vmax, title) in enumerate(panels, start=1): + plt.subplot(1, 3, index) + image = _plot_domain(field, p, colormap, vmin=vmin, vmax=vmax) + plt.title(title, y=-0.10) + if p.plot_colorbar: + plt.colorbar(image, shrink=0.72, location="top", pad=0.05) + + plt.subplots_adjust(left=0.01, right=0.99, bottom=0.10, top=0.98, wspace=0.04) + plt.savefig(p.folderName + "fluidized_bed_" + str(p.tstep).zfill(6) + ".png", dpi=120) + save_fluid_diagnostics(p) + + +def save_fluid_diagnostics(p): + state = _fluid_field(p, "fluidized_bed") + if getattr(p, "_last_fluid_diagnostic_step", None) == p.tstep: + return + path = p.folderName + "fluid_diagnostics.csv" + mode = "w" if p.tstep == 0 else "a" + with open(path, mode) as output: + if mode == "w": + output.write( + "time,pressure_drop,fluidization_ratio,fluidized_fraction,max_divergence," + "max_transition_probability\n" + ) + output.write( + f"{p.t},{state.pressure_drop},{state.fluidization_ratio},{np.mean(state.fluidized)}," + f"{np.max(np.abs(state.divergence))},{getattr(p, 'max_transition_probability', 0.0)}\n" + ) + p._last_fluid_diagnostic_step = p.tstep + + +def save_fluid(p): + state = _fluid_field(p, "fluid") + np.savez( + p.folderName + "data/fluid_" + str(p.tstep).zfill(6) + ".npz", + u=state.u, + v=state.v, + pressure=state.pressure, + beta=state.beta, + fluidized=state.fluidized, + ) + + def plot_u_time(y, U, nu_time, p): plt.figure(summary_fig) @@ -1031,7 +1135,7 @@ def plot_h(s, p): def make_video(p): - if is_ffmpeg_installed: + if is_ffmpeg_installed(): fname = p.folderName.split("/")[-2] nice_name = "=".join(fname.rsplit("_", 1)) nice_name = replace_strings(nice_name, replacements) @@ -1069,7 +1173,7 @@ def make_video(p): def stack_videos(paths, name, p): videos = p.videos heights = p.ny - if is_ffmpeg_installed: + if is_ffmpeg_installed(): if isinstance(heights, int): heights = [heights] * len(videos) max_height = 4 * max(heights) # Find the maximum height among all videos diff --git a/docs/examples.md b/docs/examples.md index ddf422b..706f68a 100644 --- a/docs/examples.md +++ b/docs/examples.md @@ -20,6 +20,7 @@ This document describes the example simulation configurations included with HGD. | `test_slope.json5` | ⭐ Easy | ~1 min | Slope stability test | | `footing.json5` | ⭐⭐ Medium | ~3 min | Load bearing capacity of granular material | | `collapse_bi.json5` | ⭐⭐ Medium | ~5 min | Bidisperse collapse with segregation | +| `fluidized_bed.json5` | ⭐⭐ Medium | ~1 min | Two-way coupled laminar gas fluidization | | `hopper_emptying.json5` | ⭐⭐⭐ Advanced | ~10 min | Detailed hopper flow analysis | | `temperature.json5` | ⭐⭐⭐ Advanced | ~5 min | Thermal effects in granular flow | @@ -207,9 +208,35 @@ python HGD/main.py json/collapse_inertia.json5 --- +### 7. Laminar Gas Fluidized Bed (`fluidized_bed.json5`) + +**What it simulates:** A monodisperse bed driven by a prescribed superficial gas velocity through the bottom boundary. + +```bash +python HGD/main.py json/fluidized_bed.json5 +``` + +The `hgfd` motion model adds layer-wise particle inertia, Gidaspow drag (Wen–Yu in dilute cells and Ergun in dense cells), and equal-and-opposite momentum feedback to a two-dimensional fluid-fraction-weighted incompressible solver. The pressure projection enforces `div(n * u_f) = 0` on the co-located HGD grid. + +![Fluidized-bed solid fraction, gas velocity, and gas pressure](images/fluidized_bed.png) + +The example writes three-panel `fluidized_bed_*.png` frames and `fluid_diagnostics.csv`. The latter reports pressure drop, pressure-drop/effective-bed-weight ratio, locally fluidized fraction, maximum continuity residual, and maximum stochastic transition probability. + +Important parameters: + +- `fluid_inlet_velocity`: bottom superficial velocity in m/s +- `gas_density`, `gas_viscosity`: fluid properties +- `defined_time_step_size`: shared HGD/fluid time step +- `fluid_probability_policy`: reject or safely scale an excessive stochastic transition probability +- `fluid_cfl_limit`: fail-fast limit for the fluid Courant number + +This solver is intended for two-dimensional, isothermal, laminar research cases. It has not been validated for bubbling, slugging, turbulent, reacting, or industrial-scale fluidized beds. + +The coupling equations follow [Li et al., *Coupling Heterarchical Granular Dynamics and Computational Fluid Dynamics*](https://arxiv.org/abs/2606.23202). + ## Advanced Examples -### 7. Hopper Emptying Studies (`hopper_emptying*.json5`) +### 8. Hopper Emptying Studies (`hopper_emptying*.json5`) Several detailed hopper studies with different parameters: @@ -240,7 +267,7 @@ python HGD/main.py json/hopper_emptying.json5 --- -### 8. Temperature Effects (`temperature.json5`) +### 9. Temperature Effects (`temperature.json5`) **What it simulates:** Thermal transport in flowing granular material. @@ -266,7 +293,7 @@ python HGD/main.py json/temperature.json5 --- -### 9. Stress Field Test (`test_stress.json5`) +### 10. Stress Field Test (`test_stress.json5`) **What it simulates:** Stress distribution calculation in static granular material. @@ -287,7 +314,7 @@ python HGD/main.py json/test_stress.json5 --- -### 10. Mesh Dependency Study (`mesh_dependency.json5`) +### 11. 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The inlet is above the + // Gidaspow/Ergun minimum-fluidization estimate printed at start-up. + nx: 16, + ny: 32, + nm: 20, + H: 0.08, + + gsd_mode: 'mono', + s_m: 0.001, + solid_density: 2500, + nu_fill: 0.55, + nu_cs: 0.60, + nu_1: 0.60, + IC_mode: 'bottom', + fill_ratio: 0.40, + repose_angle: 30, + + fluid_coupling: true, + gas_density: 1.225, + gas_viscosity: 1.8e-5, + fluid_inlet_velocity: 1.40, + fluid_alpha_max: 0.30, + fluid_probability_policy: 'scale', + + inertia: true, + motion_model: 'hgfd', + defined_time_step_size: 0.0001, + time_average: false, + P_stab: 0.5, + + t_f: 0.06, + saves: 30, + max_workers: 1, + random_seed: 7, + plot_colorbar: true, + plot: ['fluidized_bed', 'nu'], + videos: ['fluidized_bed'], + save: ['fluid'], +} diff --git a/test/test_fluid.py b/test/test_fluid.py new file mode 100644 index 0000000..2826170 --- /dev/null +++ b/test/test_fluid.py @@ -0,0 +1,116 @@ +import unittest +from types import SimpleNamespace + +import numpy as np + +from HGD import fluid +from HGD.motion import hgfd + + +def parameters(**overrides): + values = dict( + nx=6, + ny=8, + nm=10, + dx=0.01, + dy=0.01, + dt=1e-4, + g=9.81, + gas_density=1.225, + gas_viscosity=1.8e-5, + solid_density=2500.0, + nu_fill=0.5, + nu_cs=0.6, + s_m=1e-3, + alpha=0.3, + fluid_alpha_max=0.3, + fluid_alpha_epsilon=0.01, + fluid_min_void_fraction=0.05, + fluid_drag_min_particle_size=1e-6, + fluid_inlet_velocity=0.4, + fluid_probability_policy="error", + fluid_coupling=True, + P_stab=0.5, + boundary_mask=np.zeros((6, 8), dtype=bool), + ) + values.update(overrides) + return SimpleNamespace(**values) + + +class TestFluidCoupling(unittest.TestCase): + def test_drag_is_zero_in_voids_and_stronger_for_small_grains(self): + p = parameters(nx=1, ny=1, nm=2, boundary_mask=np.zeros((1, 1), dtype=bool)) + s = np.array([[[5e-4, 1e-3]]]) + zeros = np.zeros_like(s) + fluid_v = np.ones((1, 1)) + layer_beta, cell_beta = fluid.drag_coefficients(s, zeros, zeros, np.zeros((1, 1)), fluid_v, p) + self.assertGreater(layer_beta[0, 0, 0], layer_beta[0, 0, 1]) + self.assertGreater(cell_beta[0, 0], 0) + + s[0, 0, 0] = np.nan + layer_beta, _ = fluid.drag_coefficients(s, zeros, zeros, np.zeros((1, 1)), fluid_v, p) + self.assertEqual(layer_beta[0, 0, 0], 0) + + def test_upward_gas_accelerates_particle_upward(self): + p = parameters(nx=1, ny=1, nm=1, dt=1e-3, boundary_mask=np.zeros((1, 1), dtype=bool)) + s = np.array([[[2e-4]]]) + state = fluid.initialize(p, s) + state.v.fill(2.0) + u, v = fluid.update_particle_velocities(np.zeros_like(s), np.zeros_like(s), s, state, p) + self.assertGreater(v[0, 0, 0], 0) + self.assertEqual(u[0, 0, 0], 0) + + def test_drag_reaction_opposes_upward_gas(self): + p = parameters(nx=1, ny=1, nm=2, boundary_mask=np.zeros((1, 1), dtype=bool)) + s = np.full((1, 1, 2), p.s_m) + state = fluid.initialize(p, s) + state.v.fill(1.0) + zeros = np.zeros_like(s) + _, _, _, _, source_v = fluid.coupling_fields(s, zeros, zeros, state, p) + self.assertLess(source_v[0, 0], 0) + + def test_minimum_fluidization_velocity_balances_dense_drag(self): + p = parameters() + superficial = fluid.minimum_fluidization_velocity(p) + phi = p.nu_fill + eps = 1.0 - phi + relative = superficial / eps + beta = ( + 150 * p.gas_viscosity * phi**2 / (eps * p.s_m**2) + 1.75 * p.gas_density * phi * relative / p.s_m + ) + drag = beta * relative + weight = phi * (p.solid_density - p.gas_density) * p.g + self.assertAlmostEqual(drag / weight, 1.0, places=10) + + def test_projection_reduces_weighted_divergence(self): + p = parameters(fluid_inlet_velocity=0.0) + rng = np.random.default_rng(4) + void_fraction = np.full((p.nx, p.ny), 0.65) + u = rng.normal(scale=0.05, size=(p.nx, p.ny)) + v = rng.normal(scale=0.05, size=(p.nx, p.ny)) + before = np.linalg.norm(fluid.weighted_divergence(u, v, void_fraction, p.dx, p.dy)) + u, v, _, divergence = fluid.project_velocity(u, v, np.zeros_like(u), void_fraction, p) + self.assertTrue(np.all(np.isfinite(u))) + self.assertTrue(np.all(np.isfinite(v))) + self.assertLess(np.linalg.norm(divergence), before) + self.assertLess(np.max(np.abs(divergence)), 1e-8) + + def test_coupled_step_conserves_solid_slots(self): + p = parameters() + s = np.full((p.nx, p.ny, p.nm), np.nan) + s[:, :3, :5] = p.s_m + p.fluid_state = fluid.initialize(p, s) + u = np.zeros_like(s) + v = np.zeros_like(s) + last_swap = np.zeros_like(s) + count_before = np.sum(np.isfinite(s)) + + u, v, s, _, _, _, _ = hgfd.move_voids(u, v, s, p, c=None, T=None, chi=None, last_swap=last_swap) + p.fluid_state = fluid.advance(p.fluid_state, s, u, v, p) + self.assertEqual(np.sum(np.isfinite(s)), count_before) + self.assertTrue(np.all(np.isfinite(p.fluid_state.v))) + self.assertLessEqual(p.max_transition_probability, p.P_stab) + + +if __name__ == "__main__": + unittest.main() From 02c69a72942ca7f863046de547935d33db9e3bdd Mon Sep 17 00:00:00 2001 From: Galigeigei-Z <213375167+Galigeigei-Z@users.noreply.github.com> Date: Sun, 9 Aug 2026 16:02:15 +0800 Subject: [PATCH 2/5] Add animated fluidized-bed preview --- docs/examples.md | 2 +- docs/images/fluidized_bed.gif | Bin 0 -> 1408898 bytes 2 files changed, 1 insertion(+), 1 deletion(-) create mode 100644 docs/images/fluidized_bed.gif diff --git a/docs/examples.md b/docs/examples.md index 706f68a..e2b449f 100644 --- a/docs/examples.md +++ b/docs/examples.md @@ -218,7 +218,7 @@ python HGD/main.py json/fluidized_bed.json5 The `hgfd` motion model adds layer-wise particle inertia, Gidaspow drag (Wen–Yu in dilute cells and Ergun in dense cells), and equal-and-opposite momentum feedback to a two-dimensional fluid-fraction-weighted incompressible solver. The pressure projection enforces `div(n * u_f) = 0` on the co-located HGD grid. -![Fluidized-bed solid fraction, gas velocity, and gas pressure](images/fluidized_bed.png) +![Animated fluidized-bed solid fraction, gas velocity, and gas pressure](images/fluidized_bed.gif) The example writes three-panel `fluidized_bed_*.png` frames and `fluid_diagnostics.csv`. 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2001 From: Galigeigei-Z <213375167+Galigeigei-Z@users.noreply.github.com> Date: Sun, 9 Aug 2026 17:01:16 +0800 Subject: [PATCH 3/5] Reproduce HGFD paper Case 1 --- HGD/fluid.py | 204 ++++++++++++++++++------ HGD/initial.py | 9 ++ HGD/motion/hgfd.py | 47 ++++-- HGD/params.py | 25 ++- docs/examples.md | 4 + docs/hgfd-reproduction.md | 83 ++++++++++ docs/images/fluidized_bed.gif | Bin 1408898 -> 1470801 bytes docs/images/hgfd_case1_reproduction.png | Bin 0 -> 83894 bytes json/fluidized_bed.json5 | 4 +- json/hgfd_paper_case1_0p5mm.json5 | 42 +++++ json/hgfd_paper_case1_1p5mm.json5 | 42 +++++ json/hgfd_paper_case1_2p0mm.json5 | 42 +++++ mkdocs.yml | 3 +- scripts/plot_hgfd_case1.py | 63 ++++++++ test/test_fluid.py | 115 ++++++++++++- 15 files changed, 615 insertions(+), 68 deletions(-) create mode 100644 docs/hgfd-reproduction.md create mode 100644 docs/images/hgfd_case1_reproduction.png create mode 100644 json/hgfd_paper_case1_0p5mm.json5 create mode 100644 json/hgfd_paper_case1_1p5mm.json5 create mode 100644 json/hgfd_paper_case1_2p0mm.json5 create mode 100644 scripts/plot_hgfd_case1.py diff --git a/HGD/fluid.py b/HGD/fluid.py index c023a5e..2b48b6a 100644 --- a/HGD/fluid.py +++ b/HGD/fluid.py @@ -1,10 +1,9 @@ """Two-way fluid coupling utilities for heterarchical granular dynamics. -The implementation follows the fluid-fraction-weighted formulation used by -Heterarchical Granular--Fluid Dynamics (HGFD). It is intentionally a compact -2-D, isothermal, laminar solver: particle velocities are relaxed with the -Gidaspow drag law and the equal-and-opposite drag is applied to an -incompressible fluid using a variable-porosity pressure projection. +The layer drag, particle relaxation, aggregation, and coupling order follow +Li et al.'s HGFD formulation. The bundled fluid participant is a compact +Python finite-volume projection solver; the paper used an extended OpenFOAM +``pisoFoam`` participant coupled through preCICE. """ from dataclasses import dataclass @@ -28,6 +27,7 @@ class FluidState: momentum_source_v: np.ndarray divergence: np.ndarray fluidized: np.ndarray + void_fraction: np.ndarray pressure_drop: float = 0.0 fluidization_ratio: float = 0.0 @@ -62,15 +62,16 @@ def initialize(p, s): momentum_source_v=zeros.copy(), divergence=zeros.copy(), fluidized=np.zeros(shape, dtype=bool), + void_fraction=void_fraction.copy(), ) def drag_coefficients(s, particle_u, particle_v, fluid_u, fluid_v, p): """Return layer and cell Gidaspow momentum-exchange coefficients. - ``layer_beta`` is the coefficient used for particle relaxation. The - cell-level coefficient contains the heterarchical ``1 / M`` weighting and - is the quantity supplied to the fluid momentum equation. + ``layer_beta`` includes the paper's ``1 / M_s`` distribution over the + occupied internal coordinates. Summing it over ``k`` gives the + cell-level coefficient supplied to the fluid momentum equation. """ occupied = np.isfinite(s) @@ -94,9 +95,17 @@ def drag_coefficients(s, particle_u, particle_v, fluid_u, fluid_v, p): # Written as Cd*|ur| to remain finite in the Stokes limit Re -> 0. beta_wen_yu = 18.0 * mu_f / diameter**2 * (1.0 + 0.15 * reynolds**0.687) * phi * eps ** (-2.65) beta_ergun = 150.0 * mu_f * phi**2 / (eps * diameter**2) + 1.75 * rho_f * phi * relative_speed / diameter - layer_beta = np.where(phi < 0.2, beta_wen_yu, beta_ergun) + cell_beta_per_size = np.where(phi < 0.2, beta_wen_yu, beta_ergun) + solid_count = np.sum(occupied, axis=2, keepdims=True) + layer_weight = np.divide( + 1.0, + solid_count, + out=np.zeros_like(solid_count, dtype=float), + where=solid_count > 0, + ) + layer_beta = cell_beta_per_size * layer_weight layer_beta = np.where(occupied, layer_beta, 0.0) - cell_beta = np.sum(layer_beta, axis=2) / p.nm + cell_beta = np.sum(layer_beta, axis=2) return layer_beta, cell_beta @@ -105,7 +114,12 @@ def update_particle_velocities(particle_u, particle_v, s, state, p): layer_beta, _ = drag_coefficients(s, particle_u, particle_v, state.u, state.v, p) occupied = np.isfinite(s) - relaxation_rate = layer_beta / p.solid_density + # Each occupied internal coordinate represents 1/M of the cell volume. + # Its phase mass density is therefore rho_p/M. This M factor is required + # to reproduce the three single-particle terminal velocities in Fig. 4 of + # the paper; Eq. (8) prints rho_p/beta_k without making this layer mass + # normalisation explicit. + relaxation_rate = p.nm * layer_beta / p.solid_density decay = np.exp(-relaxation_rate * p.dt) buoyancy = 1.0 - p.gas_density / p.solid_density @@ -143,45 +157,145 @@ def coupling_fields(s, particle_u, particle_v, state, p): """Aggregate heterarchical drag fields for the fluid momentum equation.""" layer_beta, cell_beta = drag_coefficients(s, particle_u, particle_v, state.u, state.v, p) - beta_sum = np.sum(layer_beta, axis=2) + virtual_displacement = getattr(p, "hgfd_virtual_displacement", None) + if virtual_displacement is None: + active = np.isfinite(s) + else: + active = np.isfinite(s) & (virtual_displacement < p.dx) + active_beta = np.where(active, layer_beta, 0.0) + active_beta_sum = np.sum(active_beta, axis=2) with np.errstate(divide="ignore", invalid="ignore"): solid_u = np.divide( - np.sum(layer_beta * particle_u, axis=2), - beta_sum, + np.sum(active_beta * particle_u, axis=2), + active_beta_sum, out=np.zeros_like(cell_beta), - where=beta_sum > 0, + where=active_beta_sum > 0, ) solid_v = np.divide( - np.sum(layer_beta * particle_v, axis=2), - beta_sum, + np.sum(active_beta * particle_v, axis=2), + active_beta_sum, out=np.zeros_like(cell_beta), - where=beta_sum > 0, + where=active_beta_sum > 0, ) - # Equal and opposite to beta * (u_f - u_p), the drag on particles. + # Equal and opposite to beta * (u_f - u_p), the drag on particles. The + # paper prints S_m=beta*(u_f-u_p) with a positive fluid source, but also + # states that the source is equal-and-opposite; this physical sign is the + # one consistent with that statement and with momentum conservation. source_u = cell_beta * (solid_u - state.u) source_v = cell_beta * (solid_v - state.v) return cell_beta, solid_u, solid_v, source_u, source_v -def _laplacian(field, dx, dy): - return np.gradient(np.gradient(field, dx, axis=0), dx, axis=0) + np.gradient( - np.gradient(field, dy, axis=1), dy, axis=1 +def _lust_face_values(field, mass_flux, spacing, axis, lower_boundary, upper_boundary): + """Interpolate a transported field with OpenFOAM's 75/25 LUST blend.""" + + shape = list(field.shape) + shape[axis] += 1 + faces = np.empty(shape, dtype=float) + gradient = np.gradient(field, spacing, axis=axis) + + lower_cell = [slice(None)] * field.ndim + upper_cell = [slice(None)] * field.ndim + lower_cell[axis] = slice(0, -1) + upper_cell[axis] = slice(1, None) + internal_face = [slice(None)] * field.ndim + internal_face[axis] = slice(1, -1) + + left = field[tuple(lower_cell)] + right = field[tuple(upper_cell)] + linear = 0.5 * (left + right) + linear_upwind = np.where( + mass_flux[tuple(internal_face)] >= 0, + left + 0.5 * spacing * gradient[tuple(lower_cell)], + right - 0.5 * spacing * gradient[tuple(upper_cell)], ) + faces[tuple(internal_face)] = 0.75 * linear + 0.25 * linear_upwind + + lower_face = [slice(None)] * field.ndim + upper_face = [slice(None)] * field.ndim + lower_face[axis] = 0 + upper_face[axis] = -1 + faces[tuple(lower_face)] = lower_boundary + faces[tuple(upper_face)] = upper_boundary + return faces + + +def _face_average(field, axis): + """Linear face interpolation with zero-gradient boundary extrapolation.""" + + shape = list(field.shape) + shape[axis] += 1 + faces = np.empty(shape, dtype=float) + lower_cell = [slice(None)] * field.ndim + upper_cell = [slice(None)] * field.ndim + lower_cell[axis] = slice(0, -1) + upper_cell[axis] = slice(1, None) + internal_face = [slice(None)] * field.ndim + internal_face[axis] = slice(1, -1) + faces[tuple(internal_face)] = 0.5 * (field[tuple(lower_cell)] + field[tuple(upper_cell)]) + lower_face = [slice(None)] * field.ndim + upper_face = [slice(None)] * field.ndim + lower_source = [slice(None)] * field.ndim + upper_source = [slice(None)] * field.ndim + lower_face[axis] = 0 + upper_face[axis] = -1 + lower_source[axis] = 0 + upper_source[axis] = -1 + faces[tuple(lower_face)] = field[tuple(lower_source)] + faces[tuple(upper_face)] = field[tuple(upper_source)] + return faces + + +def _conservative_transport(state, void_fraction, p): + """Advance Eq. (19) without pressure using the paper's FVM operators. + + The convective face value uses the LUST 75/25 linear/linear-upwind blend; + gradients and viscous stresses use linear interpolation on the orthogonal + grid. Interphase drag is treated with backward Euler below, matching the + paper's first-order implicit temporal discretisation. + """ + inlet = getattr(p, "fluid_inlet_velocity", 0.0) + qx, qy = _face_fluxes(state.u, state.v, void_fraction, inlet) + intrinsic_inlet = inlet / np.maximum(void_fraction[:, 0], 1e-30) + + u_xface = _lust_face_values(state.u, qx, p.dx, axis=0, lower_boundary=0.0, upper_boundary=0.0) + u_yface = _lust_face_values( + state.u, + qy, + p.dy, + axis=1, + lower_boundary=0.0, + upper_boundary=state.u[:, -1], + ) + v_xface = _lust_face_values(state.v, qx, p.dx, axis=0, lower_boundary=0.0, upper_boundary=0.0) + v_yface = _lust_face_values( + state.v, + qy, + p.dy, + axis=1, + lower_boundary=intrinsic_inlet, + upper_boundary=state.v[:, -1], + ) + convection_u = _flux_divergence(qx * u_xface, qy * u_yface, p.dx, p.dy) + convection_v = _flux_divergence(qx * v_xface, qy * v_yface, p.dx, p.dy) -def _upwind_derivative(field, velocity, spacing, axis): - """First-order upwind derivative without periodic wraparound.""" + du_dx = np.gradient(state.u, p.dx, axis=0) + du_dy = np.gradient(state.u, p.dy, axis=1) + dv_dx = np.gradient(state.v, p.dx, axis=0) + dv_dy = np.gradient(state.v, p.dy, axis=1) + viscosity = p.gas_viscosity / p.gas_density + tau_xx = void_fraction * 2.0 * viscosity * du_dx + tau_xy = void_fraction * viscosity * (du_dy + dv_dx) + tau_yy = void_fraction * 2.0 * viscosity * dv_dy + viscous_u = _flux_divergence(_face_average(tau_xx, axis=0), _face_average(tau_xy, axis=1), p.dx, p.dy) + viscous_v = _flux_divergence(_face_average(tau_xy, axis=0), _face_average(tau_yy, axis=1), p.dx, p.dy) - backward = (field - np.roll(field, 1, axis=axis)) / spacing - forward = (np.roll(field, -1, axis=axis) - field) / spacing - lower = [slice(None)] * field.ndim - upper = [slice(None)] * field.ndim - lower[axis] = 0 - upper[axis] = -1 - backward[tuple(lower)] = forward[tuple(lower)] - forward[tuple(upper)] = backward[tuple(upper)] - return np.where(velocity >= 0, backward, forward) + old_void_fraction = state.void_fraction + momentum_u = old_void_fraction * state.u + p.dt * (-convection_u + viscous_u) + momentum_v = old_void_fraction * state.v + p.dt * (-convection_v + viscous_v) + return momentum_u, momentum_v def _face_fluxes(u, v, void_fraction, inlet_velocity=0.0): @@ -295,22 +409,15 @@ def advance(state, s, particle_u, particle_v, p): void_fraction = _void_fraction(solid_fraction, p) beta, solid_u, solid_v, source_u, source_v = coupling_fields(s, particle_u, particle_v, state, p) - adv_u = state.u * _upwind_derivative(state.u, state.u, p.dx, axis=0) + state.v * _upwind_derivative( - state.u, state.v, p.dy, axis=1 - ) - adv_v = state.u * _upwind_derivative(state.v, state.u, p.dx, axis=0) + state.v * _upwind_derivative( - state.v, state.v, p.dy, axis=1 - ) - viscosity = p.gas_viscosity / p.gas_density - transport_u = state.u + p.dt * (-adv_u + viscosity * _laplacian(state.u, p.dx, p.dy)) - transport_v = state.v + p.dt * (-adv_v + viscosity * _laplacian(state.v, p.dx, p.dy)) + momentum_u, momentum_v = _conservative_transport(state, void_fraction, p) - # Treat the stiff drag term analytically. This is the fluid analogue of - # the exponential particle relaxation and remains stable in a dense bed. - drag_rate = beta / (p.gas_density * void_fraction) - drag_decay = np.exp(-drag_rate * p.dt) - tentative_u = solid_u + (transport_u - solid_u) * drag_decay - tentative_v = solid_v + (transport_v - solid_v) * drag_decay + # First-order implicit Euler treatment of the interphase source in + # Eq. (19): n U^{n+1} + dt beta/rho U^{n+1} + # = m* + dt beta/rho U_s. + drag_weight = p.dt * beta / p.gas_density + denominator = void_fraction + drag_weight + tentative_u = (momentum_u + drag_weight * solid_u) / denominator + tentative_v = (momentum_v + drag_weight * solid_v) / denominator state.u, state.v, state.pressure, state.divergence = project_velocity( tentative_u, tentative_v, state.pressure, void_fraction, p @@ -320,6 +427,7 @@ def advance(state, s, particle_u, particle_v, p): state.solid_v = solid_v state.momentum_source_u = source_u state.momentum_source_v = source_v + state.void_fraction = void_fraction.copy() _diagnostics(state, solid_fraction, p) courant = np.max(np.abs(state.u) * p.dt / p.dx + np.abs(state.v) * p.dt / p.dy) p.fluid_courant = float(courant) diff --git a/HGD/initial.py b/HGD/initial.py index 613e408..c504a46 100644 --- a/HGD/initial.py +++ b/HGD/initial.py @@ -137,6 +137,15 @@ def IC(p): if p.IC_mode == "random": # voids everywhere randomly, this has been done above in the first step # mask = np.random.rand(p.nx, p.ny, p.nm) > p.nu_fill return s + elif p.IC_mode == "single_particle": + # Paper Case 1: one solid-occupied internal coordinate released from + # rest in an otherwise empty, fluid-filled domain. + s[:] = np.nan + i = getattr(p, "single_particle_i", p.nx // 2) + j = getattr(p, "single_particle_j", 3 * p.ny // 4) + k = getattr(p, "single_particle_k", 0) + s[i, j, k] = p.s_m + return s elif p.IC_mode == "top": # material at the top mask = np.zeros([p.nx, p.ny, p.nm], dtype=bool) mask[:, : int((1 - p.fill_ratio) * p.ny), :] = True diff --git a/HGD/motion/hgfd.py b/HGD/motion/hgfd.py index 5bb8a18..e0d1294 100644 --- a/HGD/motion/hgfd.py +++ b/HGD/motion/hgfd.py @@ -18,17 +18,22 @@ def concentration_dependent_alpha(solid_fraction, p): return np.clip(alpha_max * numerator / denominator, 0.0, alpha_max) -def _valid_destination(s, solid_fraction, boundary, axis, step, p): +def _destination_masks(s, solid_fraction, boundary, axis, step, p): destination = np.roll(s, -step, axis=axis) destination_void = np.isnan(destination) destination_fraction = np.roll(solid_fraction, -step, axis=axis)[:, :, np.newaxis] destination_boundary = np.roll(boundary, -step, axis=axis)[:, :, np.newaxis] - valid = destination_void & (destination_fraction < p.nu_cs) & ~destination_boundary + blocked = (destination_fraction >= p.nu_cs) | destination_boundary edge = [slice(None)] * 3 edge[axis] = -1 if step > 0 else 0 - valid[tuple(edge)] = False - return valid + blocked[tuple(edge)] = True + valid = destination_void & ~blocked + # An event exists either when the matching destination layer is void or + # when a wall/critically packed cell rejects the attempted event. A + # matching occupied layer in an under-packed cell simply offers no swap. + candidate = destination_void | blocked + return candidate, valid def _conflict_free(sources, destinations): @@ -50,9 +55,14 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): raise ValueError("The 'hgfd' motion model requires fluid_coupling=true") if last_swap is None: last_swap = np.zeros_like(s) + if not hasattr(p, "hgfd_virtual_displacement") or p.hgfd_virtual_displacement.shape != s.shape: + p.hgfd_virtual_displacement = np.zeros_like(s) u, v = fluid.update_particle_velocities(u, v, s, p.fluid_state, p) occupied = np.isfinite(s) + virtual_displacement = p.hgfd_virtual_displacement + virtual_displacement[occupied] += np.hypot(u[occupied], v[occupied]) * p.dt + virtual_displacement[~occupied] = 0.0 solid_fraction = np.mean(occupied, axis=2) boundary = getattr(p, "boundary_mask", np.zeros((p.nx, p.ny), dtype=bool)) alpha = concentration_dependent_alpha(solid_fraction, p)[:, :, np.newaxis] @@ -60,27 +70,32 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): horizontal_diffusion = diffusivity * p.dt / p.dx**2 probabilities = [] + valid_destinations = [] directions = ((0, 1), (0, -1), (1, 1), (1, -1)) for axis, step in directions: velocity = u if axis == 0 else v directional = np.maximum(step * velocity, 0.0) * p.dt / (p.dx if axis == 0 else p.dy) if axis == 0: directional = directional + horizontal_diffusion - valid = occupied & _valid_destination(s, solid_fraction, boundary, axis, step, p) - probabilities.append(np.where(valid, directional, 0.0)) + candidate, valid = _destination_masks(s, solid_fraction, boundary, axis, step, p) + probabilities.append(np.where(occupied & candidate, directional, 0.0)) + valid_destinations.append(valid) total = np.sum(probabilities, axis=0) max_probability = float(np.max(total)) if total.size else 0.0 p.max_transition_probability = max_probability limit = getattr(p, "P_stab", 0.5) - if max_probability > limit: + if max_probability >= limit: policy = getattr(p, "fluid_probability_policy", "error") if policy == "scale": - scale = np.minimum(1.0, limit / np.maximum(total, 1e-30)) + # Scaling is retained as an explicitly non-paper fallback. Paper + # reproduction configurations use ``error`` and select dt so that + # the strict P_tot < 0.5 condition is satisfied. + scale = np.minimum(1.0, np.nextafter(limit, 0.0) / np.maximum(total, 1e-30)) probabilities = [probability * scale for probability in probabilities] else: raise ValueError( - f"HGFD transition probability {max_probability:.3g} exceeds P_stab={limit}; " + f"HGFD transition probability {max_probability:.3g} is not below P_stab={limit}; " "reduce defined_time_step_size or set fluid_probability_policy='scale'" ) @@ -88,9 +103,12 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): cumulative = np.zeros_like(s, dtype=float) source_batches = [] destination_batches = [] - for probability, (axis, step) in zip(probabilities, directions): + for probability, valid, (axis, step) in zip(probabilities, valid_destinations, directions): selected = (draw >= cumulative) & (draw < cumulative + probability) - sources = np.argwhere(selected) + rejected = selected & ~valid + u[rejected] = 0.0 + v[rejected] = 0.0 + sources = np.argwhere(selected & valid) if len(sources): destinations = sources.copy() destinations[:, axis] += step @@ -108,6 +126,7 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): swap_type = np.where(displacement[:, 1] != 0, 1, -1) source_index = tuple(sources.T) destination_index = tuple(destinations.T) + source_displacement = virtual_displacement[source_index].copy() for array in (s, u, v, c, T): if array is not None: array[source_index], array[destination_index] = ( @@ -115,6 +134,11 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): array[source_index].copy(), ) + # Eq. (26): carry any cell-traversal deficit with the solid element + # and subtract exactly one lattice spacing after a realised swap. + virtual_displacement[source_index] = 0.0 + virtual_displacement[destination_index] = np.maximum(source_displacement - p.dx, 0.0) + last_swap[source_index] = np.nan last_swap[destination_index] = swap_type moved = np.zeros((p.nx, p.ny), dtype=float) @@ -126,5 +150,6 @@ def move_voids(u, v, s, p, diag=0, c=None, T=None, chi=None, last_swap=None): u[np.isnan(s)] = 0.0 v[np.isnan(s)] = 0.0 + virtual_displacement[np.isnan(s)] = 0.0 last_swap[np.isnan(s)] = np.nan return u, v, s, c, T, chi, last_swap diff --git a/HGD/params.py b/HGD/params.py index 86abbd5..e2f9a35 100644 --- a/HGD/params.py +++ b/HGD/params.py @@ -128,12 +128,25 @@ def set_defaults(self): self.n_cycles = len(self.cycles) def update_before_time_march(self, cycles): - self.y = np.linspace(0, self.H, self.ny) - self.dy = self.y[1] - self.y[0] - self.x = np.arange( - -(self.nx - 0.5) / 2 * self.dy, (self.nx - 0.5) / 2 * self.dy, self.dy - ) # force equal grid spacing - self.dx = self.x[1] - self.x[0] + if hasattr(self, "cell_size"): + # The HGFD paper specifies cell-centred meshes by cell size and + # cell count. Keep this opt-in so existing HGD configurations + # retain their historical endpoint-based grid convention. + self.dx = self.dy = float(self.cell_size) + self.x = (np.arange(self.nx) - (self.nx - 1) / 2.0) * self.dx + self.y = np.arange(self.ny, dtype=float) * self.dy + expected_height = self.ny * self.dy + if not np.isclose(self.H, expected_height): + raise ValueError( + f"H={self.H} is inconsistent with ny*cell_size={expected_height} for a cell-centred grid" + ) + else: + self.y = np.linspace(0, self.H, self.ny) + self.dy = self.y[1] - self.y[0] + self.x = np.arange( + -(self.nx - 0.5) / 2 * self.dy, (self.nx - 0.5) / 2 * self.dy, self.dy + ) # force equal grid spacing + self.dx = self.x[1] - self.x[0] if not np.isclose(self.dx, self.dy): sys.exit(f"Fatal error: dx != dy. dx = {self.dx}, dy = {self.dy}") self.W = self.nx * self.dx diff --git a/docs/examples.md b/docs/examples.md index e2b449f..37067fa 100644 --- a/docs/examples.md +++ b/docs/examples.md @@ -234,6 +234,10 @@ This solver is intended for two-dimensional, isothermal, laminar research cases. The coupling equations follow [Li et al., *Coupling Heterarchical Granular Dynamics and Computational Fluid Dynamics*](https://arxiv.org/abs/2606.23202). +For the three quantitative single-particle validation runs, implementation +parity, and the limits imposed by unpublished inputs, see the +[HGFD paper reproduction](hgfd-reproduction.md). + ## Advanced Examples ### 8. Hopper Emptying Studies (`hopper_emptying*.json5`) diff --git a/docs/hgfd-reproduction.md b/docs/hgfd-reproduction.md new file mode 100644 index 0000000..e960ab6 --- /dev/null +++ b/docs/hgfd-reproduction.md @@ -0,0 +1,83 @@ +# HGFD paper reproduction + +This repository contains a best-effort reproduction of Li et al., +[*Coupling Heterarchical Granular Dynamics and Computational Fluid Dynamics*](https://arxiv.org/abs/2606.23202) +(2026). It implements the published HGFD equations and supplies three runnable +configurations for the paper's single-particle settling validation. + +## Reproduced Case 1 result + +Run the three configurations and generate the comparison plot: + +```bash +python HGD/main.py json/hgfd_paper_case1_0p5mm.json5 +python HGD/main.py json/hgfd_paper_case1_1p5mm.json5 +python HGD/main.py json/hgfd_paper_case1_2p0mm.json5 +python scripts/plot_hgfd_case1.py +``` + +![Reproduced HGFD Case 1 settling curves](images/hgfd_case1_reproduction.png) + +The terminal velocities from the full two-way-coupled runs are: + +| Diameter | Paper HGFD curve | This reproduction | Relative difference | +| ---: | ---: | ---: | ---: | +| 0.5 mm | 0.07425 m/s | 0.07452 m/s | +0.36% | +| 1.5 mm | 0.21144 m/s | 0.21168 m/s | +0.11% | +| 2.0 mm | 0.26153 m/s | 0.26170 m/s | +0.07% | + +The paper's experimental time-series values are not published numerically, so +the plot contains reproduced HGFD curves rather than digitised experimental +markers. + +## Parity with the paper + +The implementation follows the published model for: + +- buoyancy-modified gravity and layer-wise exponential drag relaxation; +- Gidaspow drag, using Wen--Yu below solid fraction 0.2 and Ergun above it; +- the `1 / M_s` layer normalisation and sum-to-cell drag aggregation; +- directional stochastic advection and concentration-dependent diffusion; +- the strict total-transition-probability constraint `P_tot < 0.5`; +- the virtual-displacement momentum-transfer budget, including carry-over + after a realised swap; +- one staggered HGD-then-CFD update and one field exchange per time step; +- fluid-fraction-weighted continuity and momentum transport on a co-located + cell-centred grid; +- Euler time integration, LUST convective interpolation, linear gradients, + and uncorrected orthogonal viscous fluxes. + +The particle relaxation uses the per-coordinate mass density `rho_p / M`. +This factor is implicit in the heterarchical layer volume and is required to +reproduce Figure 4. Applying the printed `tau = rho_p / beta_k` literally, +without this layer-mass normalisation, does not reproduce the published curve. + +The fluid receives `beta * (u_s - u_f)`, equal and opposite to the drag on the +solid. The paper prints `beta * (u_f - u_s)` as a positive fluid source but +also states that the force is equal and opposite; those two statements have +opposite signs. The implementation chooses the momentum-conserving sign. + +## What cannot be reproduced one-to-one from public material + +The authors' CFD participant is an extended OpenFOAM `pisoFoam` solver coupled +through preCICE. Its source, preCICE configuration, PISO corrector settings, +and exact OpenFOAM boundary dictionaries are not included in the paper or the +public HGD repository. The bundled Python finite-volume projection solver +matches the published equations and named spatial discretisations. Its +nonlinear transport is evaluated once before the pressure projection, so it +is not matrix-, PISO-iteration-, or binary-identical to that unpublished +participant. + +Other public-data limits are: + +- Case 1 lists 15 horizontal cells of size 0.05 m but also a 1.1 m domain + width. Those values imply 0.75 m and cannot all hold simultaneously. The + runnable configurations preserve the published cell count and cell size. +- Case 2 does not publish the numerical initial particle-size distribution. +- Cases 3 and 4 refer to external experiments for complete geometry and use + calibrated feeding/mixing conditions that are not tabulated numerically. + +Consequently, Case 1 is quantitatively reproducible from public inputs, while +honest one-to-one reproduction of all four cases requires the authors' missing +solver participant, coupling files, geometries, and raw initial/experimental +data. diff --git a/docs/images/fluidized_bed.gif b/docs/images/fluidized_bed.gif index 23b9e2b16f91de586289c89b02f41709da3c023a..7b3df9ef673379dc4c3b1ec5f739bdb1d301576c 100644 GIT binary patch literal 1470801 zcmeEs)l(eI6YcJ@g1hVD?(Q1gg1fr~NsvGY?he6%y9f8+fdoh(5HtZ6cX!?U{r-jf zcB}5GeweqJnwrx+eNHQ>D2j+$51@pAZjroz{{aL5fPnxA5Qqr^LQp`sC@829Fc}nu z5C*1)K~b^L*l^Lf@X&eiaPaXVOoZqHM0gxz7?R{%InM_~+G85ubR4Chyv_KHwaWgK%=HBB9C 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z^!_M{AYu`7+PQcLZb-Ott&0w2P{MJ@_nD0u%TV??^Y)>;LSt?zHRA8|#m8mA!UlhQ zy&Ej@Jb?2wIEd)Uh(-mN1m&D%Er2MP;B8boHQ3!`u7ZlY#=At|fdHkbn+#SodX+WaqzjNKPG;c``t_TFBnlX+Zo^!8P&5W^z>%)jh*y%2 zHK*N;xhPIqF%ShChJtc8`cD`}j^=cS@e{}i8^Ui@vGudsRO!1EIgm)a5(ni+U#7T8aO?1gi4m#7zrir+FtcrqYEn*BSja Date: Sun, 9 Aug 2026 18:11:10 +0800 Subject: [PATCH 4/5] Animate HGFD paper validation --- docs/hgfd-reproduction.md | 5 ++- docs/images/hgfd_case1_reproduction.gif | Bin 0 -> 289124 bytes scripts/plot_hgfd_case1.py | 49 +++++++++++++++++++----- 3 files changed, 44 insertions(+), 10 deletions(-) create mode 100644 docs/images/hgfd_case1_reproduction.gif diff --git a/docs/hgfd-reproduction.md b/docs/hgfd-reproduction.md index e960ab6..b06ad38 100644 --- a/docs/hgfd-reproduction.md +++ b/docs/hgfd-reproduction.md @@ -16,7 +16,10 @@ python HGD/main.py json/hgfd_paper_case1_2p0mm.json5 python scripts/plot_hgfd_case1.py ``` -![Reproduced HGFD Case 1 settling curves](images/hgfd_case1_reproduction.png) +![Animated reproduction of the HGFD Case 1 settling curves](images/hgfd_case1_reproduction.gif) + +A high-resolution [static PNG](images/hgfd_case1_reproduction.png) is also +provided for reports and presentations. 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zCfTyTu%yp3C8)7o^2dgbie-1*=u)N2eI z6ZdUqck5Pw!P%&@9pu{YS?50u>@HB8`~p*4!B4KRIDC1#n^vg1Bv<%Nv>spF)J5i- Y&-CmYqksDR?79_JX7hm}*n5%vA02(={r~^~ literal 0 HcmV?d00001 diff --git a/scripts/plot_hgfd_case1.py b/scripts/plot_hgfd_case1.py index 0e70100..f6c0443 100644 --- a/scripts/plot_hgfd_case1.py +++ b/scripts/plot_hgfd_case1.py @@ -5,6 +5,7 @@ import json5 import matplotlib.pyplot as plt +from matplotlib.animation import FuncAnimation, PillowWriter import numpy as np ROOT = Path(__file__).resolve().parents[1] @@ -29,14 +30,7 @@ def load_curve(case_name): return 1e3 * steps * config["defined_time_step_size"], speed -def main(): - fig, ax = plt.subplots(figsize=(6.2, 6.8), constrained_layout=True) - rows = [] - for case_name, label, color, linestyle, paper_terminal in CASES: - time_ms, speed = load_curve(case_name) - ax.plot(time_ms, speed, color=color, linestyle=linestyle, linewidth=3, label=label) - rows.append((label, speed[-1], paper_terminal)) - +def style_axes(ax): ax.set_xlim(0, 400) ax.set_ylim(0, 0.285) ax.set_xticks(np.arange(0, 401, 100)) @@ -47,12 +41,49 @@ def main(): for spine in ax.spines.values(): spine.set_linewidth(1.5) + +def save_static(curves): + fig, ax = plt.subplots(figsize=(6.2, 6.8), constrained_layout=True) + for (_, label, color, linestyle, _), (time_ms, speed) in zip(CASES, curves): + ax.plot(time_ms, speed, color=color, linestyle=linestyle, linewidth=3, label=label) + style_axes(ax) output = ROOT / "docs" / "images" / "hgfd_case1_reproduction.png" fig.savefig(output, dpi=220) plt.close(fig) + print(f"Wrote {output.relative_to(ROOT)}") + +def save_animation(curves): + fig, ax = plt.subplots(figsize=(6.2, 6.8), constrained_layout=True) + lines = [] + for _, label, color, linestyle, _ in CASES: + (line,) = ax.plot([], [], color=color, linestyle=linestyle, linewidth=3, label=label) + lines.append(line) + style_axes(ax) + + last_frame = min(len(time_ms) for time_ms, _ in curves) - 1 + + def update(frame): + for line, (time_ms, speed) in zip(lines, curves): + line.set_data(time_ms[: frame + 1], speed[: frame + 1]) + return lines + + # Hold the converged curves for one second at the end of the loop. + frames = list(range(last_frame + 1)) + [last_frame] * 10 + animation = FuncAnimation(fig, update, frames=frames, interval=100, blit=True) + output = ROOT / "docs" / "images" / "hgfd_case1_reproduction.gif" + animation.save(output, writer=PillowWriter(fps=10), dpi=120) + plt.close(fig) print(f"Wrote {output.relative_to(ROOT)}") - for label, reproduced, paper in rows: + + +def main(): + curves = [load_curve(case_name) for case_name, *_ in CASES] + save_static(curves) + save_animation(curves) + + for (_, label, _, _, paper), (_, speed) in zip(CASES, curves): + reproduced = speed[-1] relative_error = 100.0 * (reproduced - paper) / paper print( f"{label}: reproduced={reproduced:.8f} m/s, paper={paper:.8f} m/s, error={relative_error:+.3f}%" From 7258a3b2bf16b38a6f40457bc17031931cf382f2 Mon Sep 17 00:00:00 2001 From: Galigeigei-Z <213375167+Galigeigei-Z@users.noreply.github.com> Date: Mon, 10 Aug 2026 00:50:06 +0800 Subject: [PATCH 5/5] Add ParaView fluidized-bed visualization --- docs/examples.md | 9 +- docs/hgfd-reproduction.md | 31 +++ .../paraview/hgfd_fluidized_bed.pvd | 36 +++ .../paraview/hgfd_fluidized_bed_0000.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0001.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0002.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0003.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0004.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0005.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0006.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0007.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0008.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0009.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0010.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0011.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0012.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0013.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0014.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0015.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0016.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0017.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0018.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0019.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0020.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0021.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0022.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0023.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0024.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0025.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0026.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0027.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0028.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0029.vti | 57 ++++ .../paraview/hgfd_fluidized_bed_0030.vti | 57 ++++ .../hgfd_fluidized_bed/render/demo.mp4 | Bin 0 -> 189467 bytes .../hgfd_fluidized_bed/render/poster.png | Bin 0 -> 946500 bytes .../hgfd_fluidized_bed/render/preview.gif | Bin 0 -> 450290 bytes json/fluidized_bed.json5 | 3 +- scripts/export_hgfd_to_vti.py | 133 +++++++++ scripts/render_hgfd_vti.py | 259 ++++++++++++++++++ 40 files changed, 2236 insertions(+), 2 deletions(-) create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0000.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0001.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0002.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0003.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0004.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0005.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0006.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0007.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0008.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0009.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0010.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0011.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0012.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0013.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0014.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0015.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0016.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0017.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0018.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0019.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0020.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0021.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0022.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0023.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0024.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0025.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0026.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0027.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0028.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0029.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed_0030.vti create mode 100644 docs/visualizations/hgfd_fluidized_bed/render/demo.mp4 create mode 100644 docs/visualizations/hgfd_fluidized_bed/render/poster.png create mode 100644 docs/visualizations/hgfd_fluidized_bed/render/preview.gif create mode 100644 scripts/export_hgfd_to_vti.py create mode 100644 scripts/render_hgfd_vti.py diff --git a/docs/examples.md b/docs/examples.md index 37067fa..0d74306 100644 --- a/docs/examples.md +++ b/docs/examples.md @@ -218,10 +218,17 @@ python HGD/main.py json/fluidized_bed.json5 The `hgfd` motion model adds layer-wise particle inertia, Gidaspow drag (Wen–Yu in dilute cells and Ergun in dense cells), and equal-and-opposite momentum feedback to a two-dimensional fluid-fraction-weighted incompressible solver. The pressure projection enforces `div(n * u_f) = 0` on the co-located HGD grid. -![Animated fluidized-bed solid fraction, gas velocity, and gas pressure](images/fluidized_bed.gif) +![Official-gallery-style HGFD fluidized-bed fields](visualizations/hgfd_fluidized_bed/render/preview.gif) The example writes three-panel `fluidized_bed_*.png` frames and `fluid_diagnostics.csv`. The latter reports pressure drop, pressure-drop/effective-bed-weight ratio, locally fluidized fraction, maximum continuity residual, and maximum stochastic transition probability. +The complete visualization pack also provides an +[MP4](visualizations/hgfd_fluidized_bed/render/demo.mp4) and a 31-frame +[ParaView PVD time series](visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd). +Each VTI frame contains both particle and fluid velocity vectors, solid +fraction, grain size, fluid pressure, momentum-exchange coefficient, and the +fluidized-cell indicator. + Important parameters: - `fluid_inlet_velocity`: bottom superficial velocity in m/s diff --git a/docs/hgfd-reproduction.md b/docs/hgfd-reproduction.md index b06ad38..a245e43 100644 --- a/docs/hgfd-reproduction.md +++ b/docs/hgfd-reproduction.md @@ -33,6 +33,37 @@ The paper's experimental time-series values are not published numerically, so the plot contains reproduced HGFD curves rather than digitised experimental markers. +## Fluidized-bed field visualization + +The fluidized-bed example is also exported with the same asset pipeline used +by the official HGD example gallery: a ParaView time series plus matching +poster, GIF, and MP4 renders. + +[![HGFD fluidized-bed four-field poster](visualizations/hgfd_fluidized_bed/render/poster.png)](visualizations/hgfd_fluidized_bed/render/preview.gif) + +- [Animated GIF](visualizations/hgfd_fluidized_bed/render/preview.gif) +- [H.264 MP4](visualizations/hgfd_fluidized_bed/render/demo.mp4) +- [ParaView PVD time series](visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd) + +Open the PVD file in ParaView to inspect all 31 time steps. Available cell +arrays include solid fraction, mean grain size, particle and fluid velocity +vectors, particle and fluid speed, vertical fluid velocity, fluid pressure, +momentum-exchange coefficient, and the fluidized-cell indicator. + +The assets can be regenerated after running `fluidized_bed.json5`: + +```bash +python scripts/export_hgfd_to_vti.py \ + --input output/fluidized_bed/data \ + --output docs/visualizations/hgfd_fluidized_bed/paraview \ + --name hgfd_fluidized_bed --t-final 0.06 + +python scripts/render_hgfd_vti.py \ + --pvd docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd \ + --output docs/visualizations/hgfd_fluidized_bed/render \ + --title "HGFD · FLUIDIZED BED" +``` + ## Parity with the paper The implementation follows the published model for: diff --git a/docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd b/docs/visualizations/hgfd_fluidized_bed/paraview/hgfd_fluidized_bed.pvd new file mode 100644 index 0000000..64ee7a4 --- 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mRkWFsPQE8LXbZHsM4J/zPB6SWUw/I/HGvC64+ATH3LTIuz2M8olnnPJcjv4VygOJ18rft3f3SpktAnmv3joxijOwZ5dI0KYDj/4v3plyvzohv/raCtJ9nn4Lx/mLe7fDs9SPkJS8RT+j/ySJFOOYHyvna+FWxz8bz5YZv5tHvwNPxJJ9XT8l1ZqimTEafif6G2Q+Jj9uu9X11kMM4D/UpkcaV0Pf8Xw20x0Nfy3z7/DePw6b9DEcczlOOzp4GjPfFGDv2vzYMbhT/gMXa8gmXYE/gYFi8WnWzH+vfVB6XBFfHuXhvaW3lyJ8XfBqiWuh+DvGF0sdnOHf+lUofQ4g/+6/2aQhMv/9UaMN5WssoBPws7fzEWVTynHppozN3bCv9ZTi0msgb9piR7D6mP+qevRFt/KsaflgXyL1L/x1rQe87VYnQuf3kNmpRY74D+nNqTEvxnj/wNaZW3U 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b/scripts/export_hgfd_to_vti.py new file mode 100644 index 0000000..d985a30 --- /dev/null +++ b/scripts/export_hgfd_to_vti.py @@ -0,0 +1,133 @@ +#!/usr/bin/env python3 +"""Convert saved HGFD particle/fluid fields to a ParaView VTI/PVD series.""" + +from __future__ import annotations + +import argparse +from pathlib import Path +import xml.etree.ElementTree as ET + +import numpy as np +import vtk +from vtk.util.numpy_support import numpy_to_vtk + + +def parse_args(): + parser = argparse.ArgumentParser() + parser.add_argument("--input", type=Path, required=True) + parser.add_argument("--output", type=Path, required=True) + parser.add_argument("--name", default="hgfd_fluidized_bed") + parser.add_argument("--t-final", type=float, required=True) + return parser.parse_args() + + +def indexed_files(directory, prefix, suffix): + return {int(path.stem.rsplit("_", 1)[1]): path for path in directory.glob(f"{prefix}_[0-9]*{suffix}")} + + +def add_cell_array(image, name, values, components=1): + values = np.asarray(values, dtype=np.float32) + if components == 1: + flattened = values.ravel(order="F") + else: + flattened = np.stack( + [values[:, :, component].ravel(order="F") for component in range(components)], + axis=1, + ) + vtk_array = numpy_to_vtk(flattened, deep=True) + vtk_array.SetName(name) + vtk_array.SetNumberOfComponents(components) + image.GetCellData().AddArray(vtk_array) + + +def write_pvd(path, entries): + vtk_file = ET.Element("VTKFile", type="Collection", version="0.1", byte_order="LittleEndian") + collection = ET.SubElement(vtk_file, "Collection") + for time_value, filename in entries: + ET.SubElement( + collection, + "DataSet", + timestep=f"{time_value:.8g}", + group="", + part="0", + file=filename, + ) + tree = ET.ElementTree(vtk_file) + ET.indent(tree, space=" ") + tree.write(path, encoding="utf-8", xml_declaration=True) + + +def main(): + args = parse_args() + args.output.mkdir(parents=True, exist_ok=True) + sources = { + "nu": indexed_files(args.input, "nu", ".npy"), + "s_bar": indexed_files(args.input, "s_bar", ".npy"), + "u": indexed_files(args.input, "u", ".npy"), + "v": indexed_files(args.input, "v", ".npy"), + "fluid": indexed_files(args.input, "fluid", ".npz"), + } + frame_ids = sorted(set.intersection(*(set(files) for files in sources.values()))) + if not frame_ids: + raise RuntimeError(f"No complete HGFD frames found in {args.input}") + + x = np.atleast_1d(np.loadtxt(args.input / "x.csv", delimiter=",")) + y = np.atleast_1d(np.loadtxt(args.input / "y.csv", delimiter=",")) + dx = float(np.median(np.diff(x))) if x.size > 1 else 1.0 + dy = float(np.median(np.diff(y))) if y.size > 1 else 1.0 + origin = (float(x[0] - dx / 2), float(y[0] - dy / 2), 0.0) + + entries = [] + final_step = frame_ids[-1] + for output_index, frame_id in enumerate(frame_ids): + solid_fraction = np.load(sources["nu"][frame_id]) + grain_size = np.load(sources["s_bar"][frame_id]) * 1_000.0 + particle_u = np.load(sources["u"][frame_id]) + particle_v = np.load(sources["v"][frame_id]) + fluid = np.load(sources["fluid"][frame_id]) + fluid_u = fluid["u"] + fluid_v = fluid["v"] + occupied = solid_fraction > 0.0 + + particle_speed = np.where(occupied, np.hypot(particle_u, particle_v), np.nan) + particle_velocity = np.stack((particle_u, particle_v, np.zeros_like(particle_u)), axis=-1) + fluid_speed = np.hypot(fluid_u, fluid_v) + fluid_velocity = np.stack((fluid_u, fluid_v, np.zeros_like(fluid_u)), axis=-1) + + nx, ny = solid_fraction.shape + image = vtk.vtkImageData() + image.SetDimensions(nx + 1, ny + 1, 2) + image.SetOrigin(*origin) + image.SetSpacing(dx, dy, min(dx, dy) * 0.08) + add_cell_array(image, "Solid fraction", solid_fraction) + add_cell_array(image, "Mean grain size (mm)", np.where(occupied, grain_size, np.nan)) + add_cell_array(image, "Particle speed (m/s)", particle_speed) + add_cell_array(image, "Particle velocity (m/s)", particle_velocity, components=3) + add_cell_array(image, "Fluid speed (m/s)", fluid_speed) + add_cell_array(image, "Fluid velocity (m/s)", fluid_velocity, components=3) + add_cell_array(image, "Fluid vertical velocity (m/s)", fluid_v) + add_cell_array(image, "Fluid pressure (Pa)", fluid["pressure"]) + add_cell_array(image, "Momentum exchange beta", fluid["beta"]) + add_cell_array(image, "Fluidized", fluid["fluidized"].astype(np.float32)) + image.GetCellData().SetActiveScalars("Solid fraction") + image.GetCellData().SetActiveVectors("Fluid velocity (m/s)") + + filename = f"{args.name}_{output_index:04d}.vti" + writer = vtk.vtkXMLImageDataWriter() + writer.SetFileName(str(args.output / filename)) + writer.SetInputData(image) + writer.SetDataModeToBinary() + writer.SetCompressorTypeToZLib() + if writer.Write() != 1: + raise RuntimeError(f"VTK failed to write {filename}") + + time_value = args.t_final * frame_id / final_step if final_step else 0.0 + entries.append((time_value, filename)) + + pvd_path = args.output / f"{args.name}.pvd" + write_pvd(pvd_path, entries) + print(f"Wrote {len(entries)} frames to {pvd_path}") + + +if __name__ == "__main__": + main() diff --git a/scripts/render_hgfd_vti.py b/scripts/render_hgfd_vti.py new file mode 100644 index 0000000..fdd4d6d --- /dev/null +++ b/scripts/render_hgfd_vti.py @@ -0,0 +1,259 @@ +#!/usr/bin/env python3 +"""Render the official-gallery four-panel HGFD GIF/MP4 from a PVD series.""" + +from __future__ import annotations + +import argparse +from pathlib import Path +import subprocess +import tempfile +import xml.etree.ElementTree as ET + +import imageio_ffmpeg +import numpy as np +import vtk +from vtk.util.numpy_support import vtk_to_numpy + +PANELS = ( + ( + "Solid fraction", + "SOLID FRACTION", + ((0.03, 0.05, 0.09), (0.45, 0.08, 0.15), (1.0, 0.44, 0.05), (1.0, 0.90, 0.25)), + ), + ( + "Particle speed (m/s)", + "PARTICLE SPEED", + ((0.02, 0.05, 0.10), (0.02, 0.35, 0.48), (0.05, 0.80, 0.70), (0.95, 0.88, 0.30)), + ), + ( + "Fluid pressure (Pa)", + "FLUID PRESSURE", + ((0.02, 0.04, 0.08), (0.34, 0.06, 0.20), (0.92, 0.22, 0.08), (1.0, 0.82, 0.20)), + ), + ( + "Fluid speed (m/s)", + "FLUID SPEED", + ((0.02, 0.05, 0.10), (0.02, 0.35, 0.48), (0.05, 0.80, 0.70), (0.95, 0.88, 0.30)), + ), +) + + +def parse_args(): + parser = argparse.ArgumentParser() + parser.add_argument("--pvd", type=Path, required=True) + parser.add_argument("--output", type=Path, required=True) + parser.add_argument("--title", default="HGFD · FLUIDIZED BED") + parser.add_argument("--ffmpeg", help="ffmpeg executable; defaults to imageio-ffmpeg's bundled binary") + parser.add_argument("--fps", type=int, default=20) + return parser.parse_args() + + +def pvd_entries(path): + tree = ET.parse(path) + return [ + (float(node.attrib["timestep"]), path.parent / node.attrib["file"]) + for node in tree.findall(".//DataSet") + ] + + +def read_image(path): + reader = vtk.vtkXMLImageDataReader() + reader.SetFileName(str(path)) + reader.Update() + image = vtk.vtkImageData() + image.ShallowCopy(reader.GetOutput()) + return image + + +def field_ranges(entries): + samples = {field: [] for field, _, _ in PANELS} + stride = max(1, len(entries) // 12) + for _, path in entries[::stride]: + image = read_image(path) + for field in samples: + values = vtk_to_numpy(image.GetCellData().GetArray(field)) + samples[field].append(values[np.isfinite(values)]) + + ranges = {} + for field, chunks in samples.items(): + values = np.concatenate([chunk for chunk in chunks if chunk.size]) + if field == "Solid fraction": + ranges[field] = (0.0, max(0.6, float(np.nanmax(values)))) + elif field == "Fluid pressure (Pa)": + low, high = np.nanpercentile(values, (1.0, 99.0)) + ranges[field] = (float(low), float(high if high > low else low + 1.0)) + else: + high = float(np.nanpercentile(values, 99.0)) + ranges[field] = (0.0, high if high > 0 else 1.0) + return ranges + + +def make_lookup_table(colors, value_range): + table = vtk.vtkColorTransferFunction() + table.SetColorSpaceToRGB() + low, high = value_range + for index, color in enumerate(colors): + value = low + (high - low) * index / (len(colors) - 1) + table.AddRGBPoint(value, *color) + table.SetNanColor(0.02, 0.035, 0.06) + return table + + +def add_text(renderer, value, x, y, size, color=(0.92, 0.95, 1.0)): + actor = vtk.vtkTextActor() + actor.SetInput(value) + actor.GetPositionCoordinate().SetCoordinateSystemToNormalizedViewport() + actor.SetPosition(x, y) + actor.GetTextProperty().SetFontFamilyToArial() + actor.GetTextProperty().SetFontSize(size) + actor.GetTextProperty().SetBold(True) + actor.GetTextProperty().SetColor(*color) + renderer.AddActor2D(actor) + return actor + + +def main(): + args = parse_args() + if args.ffmpeg is None: + args.ffmpeg = imageio_ffmpeg.get_ffmpeg_exe() + args.output.mkdir(parents=True, exist_ok=True) + entries = pvd_entries(args.pvd) + if not entries: + raise RuntimeError(f"No time steps found in {args.pvd}") + initial = read_image(entries[0][1]) + ranges = field_ranges(entries) + bounds = initial.GetBounds() + width = bounds[1] - bounds[0] + height = bounds[3] - bounds[2] + + window = vtk.vtkRenderWindow() + window.SetOffScreenRendering(True) + window.SetSize(1920, 1080) + window.SetMultiSamples(8) + window.SetWindowName(args.title) + viewports = ( + (0.0, 0.5, 0.5, 1.0), + (0.5, 0.5, 1.0, 1.0), + (0.0, 0.0, 0.5, 0.5), + (0.5, 0.0, 1.0, 0.5), + ) + interpolators = [] + time_labels = [] + + for (field, label, colors), viewport in zip(PANELS, viewports): + renderer = vtk.vtkRenderer() + renderer.SetViewport(*viewport) + renderer.SetBackground(0.018, 0.03, 0.052) + renderer.SetBackground2(0.055, 0.075, 0.11) + renderer.GradientBackgroundOn() + window.AddRenderer(renderer) + + interpolator = vtk.vtkCellDataToPointData() + interpolator.SetInputData(initial) + interpolator.PassCellDataOff() + interpolators.append(interpolator) + mapper = vtk.vtkDataSetMapper() + mapper.SetInputConnection(interpolator.GetOutputPort()) + mapper.SetScalarModeToUsePointFieldData() + mapper.SelectColorArray(field) + mapper.SetLookupTable(make_lookup_table(colors, ranges[field])) + mapper.SetScalarRange(*ranges[field]) + mapper.ScalarVisibilityOn() + + actor = vtk.vtkActor() + actor.SetMapper(mapper) + actor.GetProperty().SetInterpolationToFlat() + renderer.AddActor(actor) + camera = renderer.GetActiveCamera() + center_x = 0.5 * (bounds[0] + bounds[1]) + center_y = 0.5 * (bounds[2] + bounds[3]) + camera.SetFocalPoint(center_x, center_y, 0.0) + camera.SetPosition(center_x, center_y, max(width, height) * 4.0) + camera.SetViewUp(0.0, 1.0, 0.0) + camera.ParallelProjectionOn() + camera.SetParallelScale(max(height * 0.57, width * 0.62)) + + add_text(renderer, label, 0.035, 0.91, 21, (1.0, 0.58, 0.12)) + time_labels.append(add_text(renderer, "t = 0.000 s", 0.035, 0.055, 15, (0.74, 0.81, 0.90))) + scalar_bar = vtk.vtkScalarBarActor() + scalar_bar.SetLookupTable(mapper.GetLookupTable()) + scalar_bar.SetNumberOfLabels(4) + scalar_bar.SetOrientationToHorizontal() + scalar_bar.SetPosition(0.55, 0.055) + scalar_bar.SetWidth(0.40) + scalar_bar.SetHeight(0.055) + scalar_bar.GetLabelTextProperty().SetColor(0.78, 0.84, 0.92) + scalar_bar.GetLabelTextProperty().SetFontSize(11) + scalar_bar.SetLabelFormat("%.3g") + renderer.AddActor2D(scalar_bar) + + first_renderer = window.GetRenderers().GetFirstRenderer() + add_text(first_renderer, args.title, 0.035, 0.835, 17, (0.78, 0.84, 0.92)) + capture = vtk.vtkWindowToImageFilter() + capture.SetInput(window) + capture.SetInputBufferTypeToRGB() + capture.ReadFrontBufferOff() + + with tempfile.TemporaryDirectory(prefix="hgfd-render-") as temporary: + frame_directory = Path(temporary) + poster_index = round(0.65 * (len(entries) - 1)) + for frame_index, (time_value, path) in enumerate(entries): + image = read_image(path) + for interpolator, time_label in zip(interpolators, time_labels): + interpolator.SetInputData(image) + time_label.SetInput(f"t = {time_value:.3f} s") + window.Render() + capture.Modified() + capture.Update() + frame_path = frame_directory / f"frame_{frame_index:04d}.png" + writer = vtk.vtkPNGWriter() + writer.SetFileName(str(frame_path)) + writer.SetInputConnection(capture.GetOutputPort()) + writer.Write() + if frame_index == poster_index: + (args.output / "poster.png").write_bytes(frame_path.read_bytes()) + + subprocess.run( + [ + args.ffmpeg, + "-loglevel", + "error", + "-y", + "-framerate", + str(args.fps), + "-i", + str(frame_directory / "frame_%04d.png"), + "-c:v", + "libx264", + "-preset", + "slow", + "-crf", + "20", + "-pix_fmt", + "yuv420p", + str(args.output / "demo.mp4"), + ], + check=True, + ) + subprocess.run( + [ + args.ffmpeg, + "-loglevel", + "error", + "-y", + "-framerate", + str(args.fps), + "-i", + str(frame_directory / "frame_%04d.png"), + "-filter_complex", + "fps=10,scale=960:-1:flags=lanczos,split[s0][s1];" + "[s0]palettegen=max_colors=128[p];[s1][p]paletteuse=dither=bayer", + str(args.output / "preview.gif"), + ], + check=True, + ) + print(f"Rendered {len(entries)} frames to {args.output}") + + +if __name__ == "__main__": + main()

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