2.5ModelPython/helpers.py at main · ONeillLab/2.5ModelPython · GitHub

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import math
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from mpl_toolkits.axes_grid1 import make_axes_locatable
from parameters import dx


def pairshapeN2(locs, x, y, Br2, Wsh, N, dx):
    rad = math.ceil(np.sqrt(1 / Br2) / dx)
    xg, yg = np.meshgrid(np.arange(-rad, rad + 1), np.arange(-rad, rad + 1))
    gaus = Wsh * np.exp(-(Br2 * dx**2) / 0.3606 * ((xg + 0.5) ** 2 + (yg + 0.5) ** 2))

    wlayer = np.zeros(np.shape(x))

    buf = rad
    bufmat = np.zeros((N + 2 * rad, N + 2 * rad))
    nlocs = locs + rad

    jj = 1
    corners = nlocs - rad
    corners = corners.astype(np.int64)
    while jj <= np.shape(locs)[0]:
        bufmat[
            (corners[jj - 1, 0] - 1) : (corners[jj - 1, 0] + 2 * rad),
            (corners[jj - 1, 1] - 1) : (corners[jj - 1, 1] + 2 * rad),
        ] += gaus

        # bufmat[(corners[jj - 1, 0] - 1):(corners[jj - 1, 0] + 2*rad),(corners[jj - 1, 1] - 1):(corners[jj - 1, 1] + 2*rad)] + gaus

        jj += 1

    wlayer = bufmat[buf : N + buf, buf : N + buf]

    addlayer1 = np.zeros(np.shape(wlayer))
    addlayer2 = addlayer1
    addlayer3 = addlayer1
    addlayer4 = addlayer1

    addcorn1 = addlayer1
    addcorn2 = addcorn1
    addcorn3 = addcorn1
    addcorn4 = addcorn1

    addlayer1[0:buf, :] = bufmat[buf + N :, buf : N + buf]
    addlayer2[:, 0:buf] = bufmat[buf : N + buf, buf + N :]
    addlayer3[-buf:, :] = bufmat[0:buf, buf : N + buf]
    addlayer4[:, -buf:] = bufmat[buf : N + buf, 0:buf]

    addcorn1[0:buf, 0:buf] = bufmat[buf + N :, buf + N :]
    addcorn2[-buf:, -buf:] = bufmat[0:buf, 0:buf]
    addcorn3[0:buf, -buf:] = bufmat[buf + N :, 0:buf]
    addcorn4[-buf:, 0:buf] = bufmat[0:buf, buf + N :]

    wlayer = (
        wlayer
        + addlayer1
        + addlayer2
        + addlayer3
        + addlayer4
        + addcorn1
        + addcorn2
        + addcorn3
        + addcorn4
    )

    return wlayer


def pairfieldN2(L, dx, h1, wlayer):
    voldw = np.sum(wlayer) * dx**2
    area = L**2
    wcorrect = voldw / area
    Wmat = wlayer - wcorrect

    return Wmat


def paircountN2(num, N):
    locs = np.ceil(np.random.random((num, 2)) * N).astype(int)

    return locs


def yflux(f, v, dx, dt):
    fl = np.roll(f, 1, axis=0)
    fr = f
    fa = 0.5 * v * (fl + fr)

    return fa


def xflux(f, u, dx, dt):
    fl = np.roll(f, 1, axis=1)
    fr = f
    fa = 0.5 * u * (fl + fr)

    return fa


def viscN2(vel, Re, n):

    if n == 1:

        field = (
            -4 * vel
            + np.roll(vel, 1, axis=0)
            + np.roll(vel, -1, axis=0)
            + np.roll(vel, 1, axis=1)
            + np.roll(vel, -1, axis=1)
        )
        field = (
            n / dx**2
        ) * field  # in Morgan's code the n in this line is 'nu', but that's never defined; I think it's a typo

    if n == 2:

        field = (
            20 * vel
            + 2 * np.roll(np.roll(vel, 1, axis=0), 1, axis=1)
            + 2 * np.roll(np.roll(vel, 1, axis=0), -1, axis=1)
            + 2 * np.roll(np.roll(vel, -1, axis=0), 1, axis=1)
            + 2 * np.roll(np.roll(vel, -1, axis=0), -1, axis=1)
            - 8 * np.roll(vel, 1, axis=0)
            - 8 * np.roll(vel, -1, axis=0)
            - 8 * np.roll(vel, 1, axis=1)
            - 8 * np.roll(vel, -1, axis=1)
            + np.roll(vel, 2, axis=0)
            + np.roll(vel, -2, axis=0)
            + np.roll(vel, 2, axis=0)  # TYPO ?
            + np.roll(vel, -2, axis=1)
        )

        field = -1 / Re * (1 / dx**4) * field

    return field


def gauss(x, y, L):
    g = np.exp(-0.5 * (x**2) + (x**2) / L**2)

    return g


def BernN2(u1, v1, u2, v2, gm, c22h, c12h, h1, h2, ord):
    if ord == 1:
        B1 = "broke"
        B2 = "broke"
    else:
        B1 = (
            c12h * h1
            + c22h * h2
            + 0.25
            * (
                (u1**2)
                + (np.roll(u1, -1, axis=1) ** 2)
                + (v1**2)
                + (np.roll(v1, -1, axis=0) ** 2)
            )
        )

        B2 = (
            gm * c12h * h1
            + c22h * h2
            + 0.25
            * (
                (u1**2)
                + (np.roll(u1, -1, axis=1) ** 2)
                + (v1**2)
                + (np.roll(v1, -1, axis=0) ** 2)
            )
        )

    return B1, B2