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model.py
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model.py
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import numpy as np
from scipy import sparse
import random
from Stokeselvis import return_sparse_matrix_Stokes
from interpolate import interpolate, interpolate2m, interpolate_harmonic, fill_nans
from largetime import Time
import matplotlib.pyplot as plt
average = lambda x: (x[:-1,:-1] + x[1:,:-1] +x[1:,1:] +x[:-1,1:])/4.0
class Model(object):
def __init__(self, parameters):
defaults = {
'T' : Time(0),
'step' : 0,
'width' : None,
'height' : None,
'j_res' : None,
'i_res' : None,
'gx_0' : None,
'gy_0' : None,
'p0cell' : 0,
'right_bound' : None,
'left_bound' : None,
'top_bound' : None,
'bottom_bound' : None,
'stress_changes' : 'simple', # '2nd order', 'subgird'
'subgrid_relaxation' : .5,
'advect_scheme' : 'simple', # 'Runge-Kutta 2nd order'
'velocity_multiplier' : 10**-7,
}
self.markers = {'mxx' : None,
'myy' : None,
'm_cat' : None,
'm_rho' : None,
'm_eta' : None,
'm_C' : None,
'm_mu' : None,
'm_sinphi' : None,
'm_s_xx' : None,
'm_s_xy' : None,
'm_e_xx' : None,
'm_e_xy' : None,
'm_P' : None,
'markers_index_list' : None,
'moving_points_index_list' : None,
}
self.__dict__.update(defaults)
self.__dict__.update(self.markers)
for key in self.__dict__:
try:
self.__dict__[key] = parameters[key]
except KeyError:
pass
if self.__dict__[key] is None:
raise ValueError (f'{key} parameter must be set')
self.width = int(self.width)
self.height = int(self.height)
self.i_res = int(self.i_res)
self.j_res = int(self.j_res)
self.dx = self.width / (self.j_res-1)
self.dy = self.height /( self.i_res-1)
self.dx2, self.dy2 = self.dx**2, self.dy**2
self.kbond = 4*self.m_eta.min()/((self.dx+self.dy)**2)
self.kcont = 2*self.m_eta.min()/(self.dx+self.dy)
def make_step(self, maxT = 1):
dt_min=1e+10
mxx = self.mxx
myy = self.myy
m_cat = self.m_cat
m_rho = self.m_rho
m_eta = self.m_eta
m_mu = self.m_mu
m_C = self.m_C
m_sinphi = self.m_sinphi
m_s_xx = self.m_s_xx
m_s_xy = self.m_s_xy
m_e_xx = self.m_e_xx
m_e_xy = self.m_e_xy
m_P = self.m_P
m_s_ii_old = np.zeros(np.shape(mxx))
m_e_ii_old = np.zeros(np.shape(mxx))
i_res, j_res = self.i_res, self.j_res
dx, dy = self.dx, self.dy
gx_0, gy_0 = self.gx_0, self.gy_0
kbond, kcont = self.kbond, self.kcont
p0cell = self.p0cell
eta_min = 1e+10
eta_max = 1e+34
T = self.T
step = self.step
if not T : T = Time(0)
if not step: step = -1
dt = 0
plastic_iterations = 1
while T < maxT:
dt = max(dt, dt_min)
for i in range(plastic_iterations):
plastic_yield = False
m_xelvis = m_eta/(m_mu*dt + m_eta)
m_s_xx_new = m_s_xx*m_xelvis + 2*m_eta*m_e_xx*(1-m_xelvis)
m_s_xy_new = m_s_xy*m_xelvis + 2*m_eta*m_e_xy*(1-m_xelvis)
m_s_ii_new = (m_s_xx_new**2 + m_s_xy_new**2)**.5
m_s_ii_yield = m_C + m_sinphi*m_P
mask = m_s_ii_yield <0
m_s_ii_yield[mask] = 0
ym = m_s_ii_yield > m_s_ii_new # yielding mask
check_for_plastic = False
#print("step")
if check_for_plastic and np.all(~ym):
#ym = m_s_ii_yield < m_s_ii_new # yielding mask
#if not np.all(ym):
plastic_yield = True
print("plastic yield!")
m_e_ii_old[ym] = np.sqrt(m_e_xx[ym]**2 + m_e_xy[ym]**2)
m_eta[ym] = m_s_ii_yield[ym] /2/m_e_ii_old[ym]
m_s_ii_old[ym] = np.sqrt(m_s_xx[ym]**2 + m_s_xy[ym]**2)
m_s_xx[ym] = m_s_xx[ym]*m_s_ii_yield[ym]/m_s_ii_old[ym]
m_s_xy[ym] = m_s_xy[ym]*m_s_ii_yield[ym]/m_s_ii_old[ym]
# eta_min < eta < eta_max
# m_eta[m_eta<eta_min] = eta_min
# m_eta[m_eta>eta_max] = eta_max
eta_s, rho, so_xy = interpolate(mxx,myy,i_res,j_res, (m_eta, m_rho, m_s_xy))
eta_n, so_xx = interpolate(mxx+.5,myy+.5,i_res,j_res, (m_eta, m_s_xx))
mu_s = interpolate_harmonic(mxx,myy,i_res,j_res, m_mu )
mu_n = interpolate_harmonic(mxx+.5,myy+.5,i_res,j_res, m_mu )
eta_n = interpolate_harmonic(mxx+.5,myy+.5,i_res,j_res, m_eta )
eta_s = interpolate_harmonic(mxx,myy,i_res,j_res, m_eta )
# rho = interpolate_harmonic(mxx,myy,i_res,j_res, m_rho )
# so_xy = interpolate_harmonic(mxx,myy,i_res,j_res, m_s_xx )
# so_xx = interpolate_harmonic(mxx+.5,myy+.5,i_res,j_res, m_s_xx )
#Check if we have nans
if np.isnan(eta_s).any(): fill_nans(eta_s)
if np.isnan(eta_n).any(): fill_nans(eta_n)
if np.isnan(rho).any(): fill_nans(rho)
if np.isnan(mu_s).any(): fill_nans(mu_s)
if np.isnan(mu_n).any(): fill_nans(mu_n)
if np.isnan(so_xx).any(): fill_nans(so_xx)
if np.isnan(so_xy).any(): fill_nans(so_xy)
# compute viscoelastic (numerical) viscosity and stress
eta_s0 = eta_s
eta_n0 = eta_n
so_xy0 = so_xy
so_xx0 = so_xx
xelvis_s = eta_s/(eta_s+dt*mu_s)
xelvis_n = eta_n/(eta_n+dt*mu_n)
eta_s = eta_s*(1-xelvis_s)
eta_n = eta_n*(1-xelvis_n)
so_xy = so_xy*xelvis_s
so_xx = so_xx*xelvis_n
gx_0, gy_0 = self.gx_0, self.gy_0
Vbound = {}
for index, VxVy in self.moving_points_index_list:
x,y = mxx[index][0], myy[index][0]
# i,j = int(round(y)), int(round(x))
i,j = int(y), int(x)
# velocities defined as a function
if callable(VxVy):
Vx, Vy = VxVy(step=step, time=T)
else:
Vx, Vy = VxVy
Vx *= self.velocity_multiplier
Vy *= self.velocity_multiplier
Vbound[(i,j)] = [Vx,Vy]
print(Vbound)
eta_s_ = np.copy(eta_s)
eta_n_ = np.copy(eta_n)
rho_ = np.copy(rho)
so_xx_ = np.copy(so_xx)
so_xy_ = np.copy(so_xy)
Stokes_sparse, vector = return_sparse_matrix_Stokes(j_res, i_res, dx, dy,
eta_s, eta_n, rho, gx_0, gy_0, so_xx, so_xy, kbond, kcont, p0cell,
lower_boundary=self.bottom_bound, upper_boundary=self.top_bound,
right_boundary=self.right_bound, left_boundary=self.left_bound,
Vbound=Vbound)
Stokes_solve = sparse.linalg.spsolve(Stokes_sparse, vector)
P = Stokes_solve[::3].reshape((i_res),(j_res))
Vx = Stokes_solve[1::3].reshape((i_res),(j_res))
Vy = Stokes_solve[2::3].reshape((i_res),(j_res))
P *= kcont
Vx_max = np.abs(Vx).max()
Vy_max = np.abs(Vy).max()
dtx = 0.2 * dx / Vx_max
dty = 0.2 * dy / Vy_max
dt = min(dtx,dty)
#dVx, dVy = Vx[1:, :-1] - Vx[:-1, :-1], Vy[ :-1, 1:] - Vy[:-1, :-1]
#dVx_, dVy_ = Vx[ :, 1:-1] - Vx[:, :-2], Vy[1:-1, :] - Vy[:-2, :]
dVx_dx = (Vx[:-1,1:] - Vx[:-1,:-1])/dx
dVy_dy = (Vy[1:,:-1] - Vy[:-1,:-1])/dy
#dVx_dy = (Vx[:-1,1:] - Vx[:-1,:-1])/dy
#dVy_dx = (Vy[1:,:-1] - Vy[:-1,:-1])/dx
dVx_dy = (Vx[1:-1,:] - Vx[:-2,:])/dy
dVy_dx = (Vy[:,1:-1] - Vy[:,:-2])/dx
#concatenating array to add additional rows and columns. Just copy remaning columns
# abc ad aadd
# abc -> abc be -> bbee
# def def cf ccff
# def
dVx_dy = np.append(dVx_dy[0,:][None,:],dVx_dy,axis=0)
dVx_dy = np.append(dVx_dy,dVx_dy[-1,:][None,:],axis=0)
dVy_dx = np.append(dVy_dx[:,0][:,None],dVy_dx,axis=1)
dVy_dx = np.append(dVy_dx,dVy_dx[:,-1][:,None],axis=1)
e_xx = dVx_dx # strain rate
e_xy = .5 * (dVx_dy + dVy_dx)
s_xx = (1-xelvis_n[1:,1:])*2*eta_n0[1:,1:]*e_xx + xelvis_n[1:,1:]*so_xx0[1:,1:]
s_xy = (1-xelvis_s)*2*eta_s0*e_xy + xelvis_s*so_xy0
s_ii = (s_xx**2 + average(s_xy**2))**.5
e_ii = (e_xx**2 + average(e_xy**2))**.5
# ds_xx = s_xx - average(so_xx0)
ds_xx = s_xx - so_xx0[1:,1:]
ds_xy = s_xy - so_xy0
if not plastic_yield: break
m_Vx = interpolate2m(mxx , myy-.5, Vx[:-1,:])
m_Vy = interpolate2m(mxx-.5, myy , Vy[:,:-1])
m_P = interpolate2m(mxx-.5, myy-.5, P[1:,1:]) # tecnichaly, there must be +.5,+.5
# but since we slice P, indexing goes one item lower
w = 0.5*(dVy_dx - dVx_dy)
m_s_xx, m_s_xy = self.interpolate_stress_changes(mxx, myy,
m_s_xx, m_s_xy,
s_xx, s_xy,
ds_xx, ds_xy,
dt)
m_e_xx = interpolate2m(mxx-.5,myy-.5,e_xx)
m_e_xy = interpolate2m(mxx,myy,e_xy)
m_w = interpolate2m(mxx-.5 ,myy-.5 , w)
m_a = m_w * dt
# m_s_xx_ = m_s_xx - m_s_xy * 2 * m_a
# m_s_xy_ = m_s_xy + m_s_xx * 2 * m_a
# m_s_xx, m_s_xy = m_s_xx_, m_s_xy_
m_s_xx_ = m_s_xx*(np.cos(m_a)**2 - np.sin(m_a)**2 ) - m_s_xy*np.sin(2*m_a)
m_s_xy_ = m_s_xx*np.sin(2*m_a) + m_s_xy*np.cos(2*m_a)
self.advect(mxx, myy, m_Vx, m_Vy, Vx, Vy, dt)
T += dt
step +=1
parameters = {'T' : T,
'step' : step,
'eta_s' : eta_s,
'eta_n' : eta_n,
'mxx' : mxx,
'myy' : myy,
'm_cat' : m_cat,
'sii' : s_ii,
'eii' : e_ii,
'P' : P,
'Vx' : Vx,
'Vy' : Vy,
'e_xx' : e_xx,
'e_xy' : e_xy,
's_xx' : s_xx,
's_xy' : s_xy,
'xelvis_s' : xelvis_s,
'mu_n' : mu_n,
'mu_s' : mu_s,
'w' : w,
'markers_index_list' : self.markers_index_list,
'moving_points_index_list' : self.moving_points_index_list,
'eta_s_' : eta_s_,
'eta_n_' : eta_n_,
'rho_' : rho_,
'so_xx_' : so_xx_,
'so_xy_' : so_xy_,
}
yield parameters
def interpolate_stress_changes(self, mxx, myy, m_s_xx, m_s_xy, s_xx=None, s_xy=None, ds_xx=None, ds_xy=None, dt=None ):
if self.stress_changes == 'simple':
m_s_xx = interpolate2m(mxx-.5,myy-.5,s_xx)
m_s_xy = interpolate2m(mxx,myy,s_xy)
elif self.stress_changes == '2nd order':
print('2nd order')
m_ds_xx = interpolate2m(mxx-.5,myy-.5,ds_xx)
m_ds_xy = interpolate2m(mxx,myy,ds_xy)
m_s_xx = m_s_xx + m_ds_xx
m_s_xy = m_s_xy + m_ds_xy
elif self.stress_changes == 'subgrid':
print('subgrid')
d_ve = self.subgrid_relaxation
m_eta = self.m_eta
m_mu = self.m_mu
i_res, j_res = self.i_res, self.j_res
m_dt_maxwell = m_eta / m_mu
d_ = (-d_ve*dt/m_dt_maxwell).astype(np.float)
m_s_xx_nodes = interpolate2m(mxx-.5,myy-.5,s_xx)
m_s_xy_nodes = interpolate2m(mxx,myy,s_xy)
m_ds_xx_subgrid = (m_s_xx_nodes - m_s_xx)*(1-np.exp(d_))
m_ds_xy_subgrid = (m_s_xy_nodes - m_s_xy)*(1-np.exp(d_))
(ds_xx_subgrid,) = interpolate(mxx+.5,myy+.5,i_res,j_res, (m_ds_xx_subgrid, ))
(ds_xy_subgrid,) = interpolate(mxx,myy,i_res,j_res, (m_ds_xy_subgrid, ))
ds_xx_remaining = ds_xx - ds_xx_subgrid[1:,1:]
ds_xy_remaining = ds_xy - ds_xy_subgrid
m_ds_xx_remaining = interpolate2m(mxx-.5,myy-.5, ds_xx_remaining)
m_ds_xy_remaining = interpolate2m(mxx,myy, ds_xy_remaining)
m_s_xx += m_ds_xx_subgrid + m_ds_xx_remaining
m_s_xy += m_ds_xy_subgrid + m_ds_xy_remaining
return m_s_xx, m_s_xy
def advect(self, mxx, myy, m_Vx, m_Vy, Vx, Vy, dt ):
dx, dy = self.dx, self.dy
if self.advect_scheme=='simple':
mxx += m_Vx*dt/dx
myy += m_Vy*dt/dy
elif self.advect_scheme=='Runge-Kutta 2nd order':
mxx_b = mxx + 0.5*m_Vx*dt/dx
myy_b = myy + 0.5*m_Vy*dt/dy
m_Vx_eff = interpolate2m(mxx_b , myy_b-.5, Vx[:-1,:])
m_Vy_eff = interpolate2m(mxx_b-.5, myy_b , Vy[:,:-1])
mxx += m_Vx_eff*dt/dx
myy += m_Vy_eff*dt/dy
return mxx, myy