2.5LayerPython/Helper_functions.py at main · ONeillLab/2.5LayerPython · GitHub

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import numpy as np
import math


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


def paircountN2(num, N):
    """
    Generates a list of coordinate pairs.
    """

    locs = np.ceil(np.random.rand(num, 2) * N).astype(int)
    return locs


def pairfieldN2(L, dx, h1, wlayer):
    """
    Creates the weather matrix for the storms, S_st in paper.
    """
    voldw = np.sum(np.sum(wlayer)) * dx**2
    area = L**2
    wcorrect = voldw / area
    Wmat = wlayer - wcorrect
    return Wmat


def Axl(f, l, r):
    """
    Redundant?
    """
    fa = 0.5 * (f + f[:, l-1])
    return fa

def Ayl(f, l, r):
    """
    Redundant?
    """
    fa = 0.5 * (f + f[l-1, :])
    return fa


def viscND(vel, Re, n, dx):
    """
        n is exponent of Laplacian operator
        Where visc term is nu*(-1)^(n+1) (\/^2)^n
        so for regular viscosity n = 1, for hyperviscosity n=2

        TODO: for n=1 nu is not defined...
    """

    if n == 1:

        field = vel[0,:] + vel[r-1,:] + vel[:,r-1]-4*vel;
        field = (nu/dx**2) * field

        return field

    if n == 2:

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

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

        return field


def pairshapeN2(locs, x, y, Br2, Wsh, N, dx):
    """
    Create Gaussians on smaller scales and then convolve them with the weather layer.
    """
    rad = int(np.ceil(np.sqrt(1/Br2) / dx))
    xg, yg = np.meshgrid(range(-rad, rad+1), range(-rad, rad+1))
    gaus = Wsh * np.exp(-(Br2 * dx**2) / 0.3606 * ((xg + 0.5)**2 + (yg + 0.5)**2))

    wlayer = np.zeros(x.shape)

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

    corners = nlocs - rad

    for jj in range(locs.shape[0]):
        bufmat[corners[jj, 0]:corners[jj, 0] + gaus.shape[0],
               corners[jj, 1]:corners[jj, 1] + gaus.shape[1]] += gaus


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

    addlayer1 = np.zeros_like(wlayer)
    addlayer2 = np.zeros_like(wlayer)
    addlayer3 = np.zeros_like(wlayer)
    addlayer4 = np.zeros_like(wlayer)
    addcorn1 = np.zeros_like(wlayer)
    addcorn2 = np.zeros_like(wlayer)
    addcorn3 = np.zeros_like(wlayer)
    addcorn4 = np.zeros_like(wlayer)

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

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

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

    layersum = np.sum(wlayer)
    return wlayer


def BernN2(u1,v1,u2,v2,gm,c22h,c12h,h1,h2,ord,r):
    """
    Generates Bernstein polynomial
    """
    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


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

    fa = 0.5 * u * (fl+fr)

    return fa

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

    fa = 0.5 * v * (fl+fr)

    return fa