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fields.py
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fields.py
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import numpy as np
class Fields:
def __init__(self, rp):
self.rp = rp
self.input = rp.input
self.geo = rp.geo
self.mat = rp.mat
self.N = rp.geo.N
# Velocities (spatial cell edges)
self.u = self.initializeAtEdges(self.input.u)
self.u_p = np.copy(self.u)
self.u_old = np.copy(self.u)
self.u_IC = np.copy(self.u)
# Set left velocity BCs as necessary
if self.input.hydro_L == 'u':
if self.input.hydro_L_val == None:
self.u_L = self.input.u(0)
else:
self.u_L = self.input.hydro_bL_val
else:
self.u_L = None
# Set right velocity BCs as necessary
if self.input.hydro_R == 'u':
if self.input.hydro_R_val == None:
self.u_R = self.input.u(self.geo.r_half_old[-1])
else:
self.u_R = self.input.hydro_R_val
else:
self.u_R = None
# Temperature (spatial cell centers)
self.T = self.initializeAtCenters(self.input.T)
self.T_p = np.copy(self.T)
self.T_old = np.copy(self.T)
# Densities (spatial cell centers)
self.rho = self.initializeAtCenters(self.input.rho)
self.rho_p = np.copy(self.rho)
self.rho_old = np.copy(self.rho)
self.rho_IC = np.copy(self.rho)
# Pressures (spatial cell centers, IC: Eqs. 22 and 23)
self.P = (self.mat.gamma - 1) * self.mat.C_v * self.T * self.rho
self.P_p = np.copy(self.P)
self.P_old = np.copy(self.P)
# Set pressure BCs as necessary
if self.input.hydro_L == 'P':
self.P_L = self.input.hydro_L_val
else:
self.P_L = None
if self.input.hydro_R == 'P':
self.P_R = self.input.hydro_R_val
else:
self.P_R = None
# Internal energies (spatial cell centers)
self.e = self.mat.C_v * self.T_old
self.e_p = np.copy(self.e)
self.e_old = np.copy(self.e)
self.e_IC = np.copy(self.e)
# Radiation energies (spatial cell centers)
self.E = self.initializeAtCenters(self.input.E)
self.E_p = np.copy(self.E)
self.E_old = np.copy(self.E)
self.E_IC = np.copy(self.E)
# Set E boundary conditions
if self.input.rad_L == 'source':
self.E_bL = self.input.rad_L_val
else:
self.E_bL = None
if self.input.rad_R == 'source':
self.E_bR = self.input.rad_R_val
else:
self.E_bR = None
# Init the rest of the materials that depend on field variables
self.mat.initFromFields(self)
# Copy over all new fields to old positions
def stepFields(self):
np.copyto(self.u_old, self.u)
np.copyto(self.T_old, self.T)
np.copyto(self.rho_old, self.rho)
np.copyto(self.P_old, self.P)
np.copyto(self.e_old, self.e)
np.copyto(self.E_old, self.E)
# Initialize variable with function at the spatial cell centers
def initializeAtCenters(self, function):
values = np.zeros(self.N)
if function is not None:
for i in range(self.N):
values[i] = function(self.geo.r[i])
return values
# Initialize variable with function at the spatial cell edges
def initializeAtEdges(self, function):
values = np.zeros(self.N + 1)
if function is not None:
for i in range(self.N + 1):
values[i] = function(self.geo.r_half[i])
return values
# Recmpute density with updated cell volumes
def recomputeRho(self, predictor):
m = self.mat.m
if predictor:
rho_new = self.rho_p
V_new = self.geo.V_p
else:
rho_new = self.rho
V_new = self.geo.V
for i in range(self.N):
rho_new[i] = m[i] / V_new[i]
# Recompute radiation energy with updated internal energy
def recomputeInternalEnergy(self, dt, predictor):
# Constants
m = self.mat.m
a = self.input.a
c = self.input.c
C_v = self.mat.C_v
if predictor:
e = self.e_old
T_old = self.T_old
T_new = self.T_old # this is here for consistency below
E_k = (self.E_p + self.E_old) / 2
e_new = self.e_p
xi = self.rp.radPredictor.xi
else:
e = self.e_p
T_old = self.T_old
T_new = self.T_p
E_k = (self.E + self.E_old) / 2
e_new = self.e
xi = self.rp.radCorrector.xi
kappa_a = self.mat.kappa_a
# Compute factor to be added to k-1/2'th internal energy
T4 = (T_old**4 + T_new**4) / 2
increment = dt * C_v * (m * kappa_a * c * (E_k - a * T4) + xi)
increment /= m * C_v + dt * m * kappa_a * c * 2 * a * T_old**3
# Compute predictor internal energy
e_new = e + increment
# Recompute temperature with updated internal energy
def recomputeT(self, predictor):
C_v = self.mat.C_v
if predictor:
T_new = self.T_p
e_new = self.e_p
else:
T_new = self.T
e_new = self.e
for i in range(self.N):
T_new[i] = C_v * e_new[i]
# Recompute pressure with updated density and internal energy
def recomputeP(self, predictor):
gamma_minus = self.mat.gamma - 1
if predictor:
P_new = self.P_p
e_new = self.e_p
rho_new = self.rho_p
else:
P_new = self.P
e_new = self.e
rho_new = self.rho
for i in range(self.N):
P_new[i] = gamma_minus * rho_new[i] * e_new[i]
# Recompute radiation energy density
def recomputeE(self, dt, predictor):
if predictor:
self.radPredictor.computeAuxiliaryFields(dt)
self.radPredictor.assembleSystem(dt)
self.radPredictor.solveSystem(dt)
else:
self.radCorrector.computeAuxiliaryFields(dt)
self.radCorrector.assembleSystem(dt)
self.radCorrector.solveSystem(dt)
def conservationCheck(self, dt):
# Centered cell and median mesh cell masses
m = self.mat.m
m_half = self.mat.m_half
# Physical constants
a = self.input.a
c = self.input.c
N = self.geo.N
# Initial conditions
u_IC = self.u_IC
e_IC = self.e_IC
E_IC = self.E_IC
rho_IC = self.rho_IC
# k+1/2'th time-step quantities
u = self.u
e = self.e
E = self.E
rho = self.rho
# k'th time-step and predicted k'th time-step variables
A_k = (self.geo.A + self.geo.A_old) / 2
A_pk = (self.geo.A_p + self.geo.A_old) / 2
E_k = (self.E + self.E_old) / 2
E_pk = (self.E_p + self.E_old) / 2
rho_k = (self.rho + self.rho_old) / 2
rho_pk = (self.rho_p + self.rho_old) / 2
dr_k = (self.geo.dr + self.geo.dr_old) / 2
dr_pk = (self.geo.dr_p + self.geo.dr_old) / 2
P_pk = (self.P_p + self.P_old) / 2
u_k = (self.u + self.u_old) / 2
T_k = (self.T + self.T_old) / 2
self.mat.recomputeKappa_t(T_k)
kappa_t_k = self.mat.kappa_t
T_pk = (self.T_p + self.T_old) / 2
self.mat.recomputeKappa_a(T_pk)
kappa_t_pk = self.mat.kappa_a + self.mat.kappa_s
coeff_F_L = -2 * c / (3 * rho_k[0] * dr_k[0] * kappa_t_k[0] + 4)
coeff_F_R = -2 * c / (3 * rho_k[-1] * dr_k[-1] * kappa_t_k[-1] + 4)
coeff_E_L = 3 * rho_pk[0] * dr_pk[0] * kappa_t_pk[0]
coeff_E_R = 3 * rho_pk[-1] * dr_pk[-1] * kappa_t_pk[-1]
if self.input.rad_L is 'source':
E_bL_k = self.E_bL
E_bL_pk = self.E_bL
else:
E_bL_k = E_k[0]
E_bL_pk = E_pk[0]
if self.input.rad_R is 'source':
E_bR_k = self.E_bR
E_bR_pk = self.E_bR
else:
E_bR_k = E_k[-1]
E_bR_pk = E_pk[-1]
F_L = coeff_F_L * (E_k[0] - E_bL_k);
F_R = coeff_F_R * (E_k[-1] - E_bR_k);
E_L = (coeff_E_L * E_bL_pk + 4 * E_pk[0]) / (coeff_E_L + 4);
E_R = (coeff_E_R * E_bR_pk + 4 * E_pk[-1]) / (coeff_E_R + 4);
energy = 0
for i in range(N + 1):
energy += 1/2 * m_half[i] * (u[i]**2 - u_IC[i]**2)
if i < N:
energy += m[i] * (e[i] - e_IC[i])
energy += m[i] * (E[i] / rho[i] - E_IC[i] / rho_IC[i])
energy += (A_k[-1] * F_R - A_k[0] * F_L) * dt
energy += (A_pk[-1] * (1/3 * E_R + P_pk[-1]) * u_k[-1] - \
A_pk[0] * (1/3 * E_L + P_pk[0] ) * u_k[0] ) * dt
return energy