def applyStrongBCLinearSystemRHSVector(self, U_old, b):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U_old, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase,
self.model_type)
arhoA = vf * self.rho
b[self.i_arhoA] = arhoA
def applyStrongBCNonlinearSystem(self, U, r, J):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase, self.model_type)
arhoA = U[self.i_arhoA]
arhouA = U[self.i_arhouA]
arhoEA_solution = U[self.i_arhoEA]
u, du_darhoA, du_darhouA = computeVelocity(arhoA, arhouA)
rho, drho_dvf, drho_darhoA, _ = computeDensity(vf, arhoA, A)
drho_daA1 = drho_dvf * dvf_daA1
v, dv_drho = computeSpecificVolume(rho)
dv_daA1 = dv_drho * drho_daA1
dv_darhoA = dv_drho * drho_darhoA
e, de_dv, de_dp = self.eos.e(v, self.p)
de_daA1 = de_dv * dv_daA1
de_darhoA = de_dv * dv_darhoA
arhoEA = arhoA * (e + 0.5 * u * u)
darhoEA_daA1 = arhoA * de_dv * dv_daA1
darhoEA_darhoA = (e + 0.5 * u * u) + arhoA * (de_dv * dv_darhoA + u * du_darhoA)
darhoEA_darhouA = arhoA * u * du_darhouA
# energy
r[self.i_arhoEA] = arhoEA_solution - arhoEA
J[self.i_arhoEA,:] = 0
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhoEA,self.i_aA1] = - darhoEA_daA1
J[self.i_arhoEA,self.i_arhoA] = - darhoEA_darhoA
J[self.i_arhoEA,self.i_arhouA] = - darhoEA_darhouA
J[self.i_arhoEA,self.i_arhoEA] = 1
def getPhaseSolution(self, U, phase):
aA1 = np.array([self.aA1(U, k) for k in xrange(self.n_node)])
vf, _ = computeVolumeFraction(aA1, self.A, phase, self.model_type)
arhoA = self.getSolution(U, VariableName.ARhoA, phase)
arhouA = self.getSolution(U, VariableName.ARhoUA, phase)
arhoEA = self.getSolution(U, VariableName.ARhoEA, phase)
return (vf, arhoA, arhouA, arhoEA)
def applyWeakBC(self, U, r, J):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U, self.k)
arhoA = U[self.i_arhoA]
arhouA = U[self.i_arhouA]
arhoEA = U[self.i_arhoEA]
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase,
self.model_type)
u, du_darhoA, du_darhouA = computeVelocity(arhoA, arhouA)
rho, drho_dvf, drho_darhoA, _ = computeDensity(vf, arhoA, A)
drho_daA1 = drho_dvf * dvf_daA1
v, dv_drho = computeSpecificVolume(rho)
dv_daA1 = dv_drho * drho_daA1
dv_darhoA = dv_drho * drho_darhoA
E, dE_darhoA, dE_darhoEA = computeSpecificTotalEnergy(arhoA, arhoEA)
e, de_du, de_dE = computeSpecificInternalEnergy(u, E)
de_darhoA = de_du * du_darhoA + de_dE * dE_darhoA
de_darhouA = de_du * du_darhouA
de_darhoEA = de_dE * dE_darhoEA
p, dp_dv, dp_de = self.eos.p(v, e)
dp_daA1 = dp_dv * dv_daA1
dp_darhoA = dp_dv * dv_darhoA + dp_de * de_darhoA
dp_darhouA = dp_de * de_darhouA
dp_darhoEA = dp_de * de_darhoEA
# mass
r[self.i_arhoA] += arhouA * self.nx
J[self.i_arhoA, self.i_arhouA] += self.nx
# momentum
r[self.i_arhouA] += (arhouA * u + vf * p) * self.nx
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhouA,
self.i_aA1] += (dvf_daA1 * p + vf * dp_daA1) * self.nx
J[self.i_arhouA,
self.i_arhoA] += (arhouA * du_darhoA + vf * dp_darhoA) * self.nx
J[self.i_arhouA, self.i_arhouA] += (arhouA * du_darhouA + u +
vf * dp_darhouA) * self.nx
J[self.i_arhouA, self.i_arhoEA] += vf * dp_darhoEA * self.nx
# energy
r[self.i_arhoEA] += (arhoEA + vf * p) * u * self.nx
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhoEA,
self.i_aA1] += (dvf_daA1 * p + vf * dp_daA1) * u * self.nx
J[self.i_arhoEA, self.i_arhoA] += (
(arhoEA + vf * p) * du_darhoA + vf * dp_darhoA * u) * self.nx
J[self.i_arhoEA, self.i_arhouA] += (
(arhoEA + vf * p) * du_darhouA + vf * dp_darhouA * u) * self.nx
J[self.i_arhoEA, self.i_arhoEA] += (1 + vf * dp_darhoEA) * u * self.nx
def applyStrongBCLinearSystemRHSVector(self, U_old, b):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U_old, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase, self.model_type)
arhoA = U_old[self.i_arhoA]
arhouA = U_old[self.i_arhouA]
u, du_darhoA, du_darhouA = computeVelocity(arhoA, arhouA)
rho, drho_dvf, drho_darhoA = computeDensity(vf, arhoA)
v, dv_drho = computeSpecificVolume(rho)
e, de_dv, de_dp = self.eos.e(v, self.p)
arhoEA = arhoA * (e + 0.5 * u * u)
b[self.i_arhoEA] = arhoEA
def applyStrongBCNonlinearSystem(self, U, r, J):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase,
self.model_type)
arhoA = U[self.i_arhoA]
arhoBC = vf * self.rho
darhoBC_daA1 = self.rho * dvf_daA1
# mass
r[self.i_arhoA] = arhoA - arhoBC
J[self.i_arhoA, :] = 0
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhoA, self.i_aA1] = -darhoBC_daA1
J[self.i_arhoA, self.i_arhoA] = 1
def applyWeakBC(self, U, r, J):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase, self.model_type)
arhoA = U[self.i_arhoA]
arhouA = U[self.i_arhouA]
u, du_darhoA, du_darhouA = computeVelocity(arhoA, arhouA)
# mass
r[self.i_arhoA] += arhouA * self.nx
J[self.i_arhoA,self.i_arhouA] += self.nx
# momentum
r[self.i_arhouA] += (arhouA * u + vf * self.p) * self.nx
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhouA,self.i_aA1] += dvf_daA1 * self.p * self.nx
J[self.i_arhouA,self.i_arhoA] += arhouA * du_darhoA * self.nx
J[self.i_arhouA,self.i_arhouA] += (arhouA * du_darhouA + u) * self.nx
def applyWeakBC(self, U, r, J):
A = self.dof_handler.A[self.k]
aA1 = self.dof_handler.aA1(U, self.k)
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase,
self.model_type)
arhoEA = U[self.i_arhoEA]
arhoBC = vf * self.rho
darhoBC_daA1 = self.rho * dvf_daA1
arhouABC = vf * self.rho * self.u
darhouABC_daA1 = self.rho * self.u * dvf_daA1
v, _ = computeSpecificVolume(self.rho)
E, dE_darhoBC, dE_darhoEA = computeSpecificTotalEnergy(arhoBC, arhoEA)
dE_daA1 = dE_darhoBC * darhoBC_daA1
e, _, de_dE = computeSpecificInternalEnergy(self.u, E)
de_daA1 = de_dE * dE_daA1
de_darhoEA = de_dE * dE_darhoEA
p, _, dp_de = self.eos.p(v, e)
dp_daA1 = dp_de * de_daA1
dp_darhoEA = dp_de * de_darhoEA
# momentum
r[self.i_arhouA] += (arhouABC * self.u + vf * p) * self.nx
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhouA,
self.i_aA1] += (self.u * darhouABC_daA1 + dvf_daA1 * p +
vf * dp_daA1) * self.nx
J[self.i_arhouA, self.i_arhoEA] += vf * dp_darhoEA * self.nx
# energy
r[self.i_arhoEA] += self.u * (arhoEA + vf * p) * self.nx
if (self.model_type == ModelType.TwoPhase):
J[self.i_arhoEA,
self.i_aA1] += self.u * (dvf_daA1 * p + vf * dp_daA1) * self.nx
J[self.i_arhoEA,
self.i_arhoEA] += self.u * (1 + vf * dp_darhoEA) * self.nx
def applyStronglyToNonlinearSystem(self, U_new, U_old, r, J):
n_values = 6
L = 0
R = 1
L_old = 2
R_old = 3
LL_old = 4
RR_old = 5
k = [0] * n_values
k[L] = self.k_left
k[R] = self.k_right
k[L_old] = self.k_left
k[R_old] = self.k_right
k[LL_old] = self.k_left_adjacent
k[RR_old] = self.k_right_adjacent
i_arhoA = [0] * n_values
i_arhoA[L] = self.i_arhoL
i_arhoA[R] = self.i_arhoR
i_arhoA[L_old] = self.i_arhoL
i_arhoA[R_old] = self.i_arhoR
i_arhoA[LL_old] = self.i_arhoLL
i_arhoA[RR_old] = self.i_arhoRR
i_arhouA = [0] * n_values
i_arhouA[L] = self.i_arhouAL
i_arhouA[R] = self.i_arhouAR
i_arhouA[L_old] = self.i_arhouAL
i_arhouA[R_old] = self.i_arhouAR
i_arhouA[LL_old] = self.i_arhouALL
i_arhouA[RR_old] = self.i_arhouARR
i_arhoEA = [0] * n_values
i_arhoEA[L] = self.i_arhoEAL
i_arhoEA[R] = self.i_arhoEAR
i_arhoEA[L_old] = self.i_arhoEAL
i_arhoEA[R_old] = self.i_arhoEAR
i_arhoEA[LL_old] = self.i_arhoEALL
i_arhoEA[RR_old] = self.i_arhoEARR
U = [0] * n_values
U[L] = U_new
U[R] = U_new
U[L_old] = U_old
U[R_old] = U_old
U[LL_old] = U_old
U[RR_old] = U_old
# initialize lists
rho = [0] * n_values
drho_daA1 = [0] * n_values
drho_darhoA = [0] * n_values
u = [0] * n_values
du_darhoA = [0] * n_values
du_darhouA = [0] * n_values
e = [0] * n_values
de_darhoA = [0] * n_values
de_darhouA = [0] * n_values
de_darhoEA = [0] * n_values
p = [0] * n_values
dp_daA1 = [0] * n_values
dp_darhoA = [0] * n_values
dp_darhouA = [0] * n_values
dp_darhoEA = [0] * n_values
c = [0] * n_values
dc_daA1 = [0] * n_values
dc_darhoA = [0] * n_values
dc_darhouA = [0] * n_values
dc_darhoEA = [0] * n_values
if not self.use_momentum_flux_balance:
p0 = [0] * n_values
dp0_daA1 = [0] * n_values
dp0_darhoA = [0] * n_values
dp0_darhouA = [0] * n_values
dp0_darhoEA = [0] * n_values
# loop over subscript/superscript combinations
for i in xrange(n_values):
A = self.dof_handler.A[k[i]]
aA1 = self.dof_handler.aA1(U[i], k[i])
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase, self.model_type)
arhoA = U[i][i_arhoA[i]]
arhouA = U[i][i_arhouA[i]]
arhoEA = U[i][i_arhoEA[i]]
rho[i], drho_dvf, drho_darhoA[i], _ = computeDensity(vf, arhoA, A)
drho_daA1[i] = drho_dvf * dvf_daA1
u[i], du_darhoA[i], du_darhouA[i] = computeVelocity(arhoA, arhouA)
v, dv_drho = computeSpecificVolume(rho[i])
dv_daA1 = dv_drho * drho_daA1[i]
dv_darhoA = dv_drho * drho_darhoA[i]
E, dE_darhoA, dE_darhoEA = computeSpecificTotalEnergy(arhoA, arhoEA)
e[i], de_du, de_dE = computeSpecificInternalEnergy(u[i], E)
de_darhoA[i] = de_du * du_darhoA[i] + de_dE * dE_darhoA
de_darhouA[i] = de_du * du_darhouA[i]
de_darhoEA[i] = de_dE * dE_darhoEA
p[i], dp_dv, dp_de = self.eos.p(v, e[i])
dp_daA1[i] = dp_dv * dv_daA1
dp_darhoA[i] = dp_dv * dv_darhoA + dp_de * de_darhoA[i]
dp_darhouA[i] = dp_de * de_darhouA[i]
dp_darhoEA[i] = dp_de * de_darhoEA[i]
c[i], dc_dv, dc_de = self.eos.c(v, e[i])
dc_daA1[i] = dc_dv * dv_daA1
dc_darhoA[i] = dc_dv * dv_darhoA + dc_de * de_darhoA[i]
dc_darhouA[i] = dc_de * de_darhouA[i]
dc_darhoEA[i] = dc_de * de_darhoEA[i]
if not self.use_momentum_flux_balance:
s, ds_dv, ds_de = self.eos.s(v, e[i])
ds_daA1 = ds_dv * dv_daA1
ds_darhoA = ds_dv * dv_darhoA + ds_de * de_darhoA[i]
ds_darhouA = ds_de * de_darhouA[i]
ds_darhoEA = ds_de * de_darhoEA[i]
h, dh_de, dh_dp, dh_drho = computeSpecificEnthalpy(e[i], p[i], rho[i])
dh_daA1 = dh_dp * dp_daA1[i]
dh_darhoA = dh_de * de_darhoA[i] + dh_dp * dp_darhoA[i] + dh_drho * drho_darhoA[i]
dh_darhouA = dh_de * de_darhouA[i] + dh_dp * dp_darhouA[i]
dh_darhoEA = dh_de * de_darhoEA[i] + dh_dp * dp_darhoEA[i]
h0 = h + 0.5 * u[i]**2
dh0_daA1 = dh_daA1
dh0_darhoA = dh_darhoA + u[i] * du_darhoA[i]
dh0_darhouA = dh_darhouA + u[i] * du_darhouA[i]
dh0_darhoEA = dh_darhoEA
p0[i], dp0_dh0, dp0_ds = self.eos.p_from_h_s(h0, s)
dp0_daA1[i] = dp0_dh0 * dh0_daA1 + dp0_ds * ds_daA1
dp0_darhoA[i] = dp0_dh0 * dh0_darhoA + dp0_ds * ds_darhoA
dp0_darhouA[i] = dp0_dh0 * dh0_darhouA + dp0_ds * ds_darhouA
dp0_darhoEA[i] = dp0_dh0 * dh0_darhoEA + dp0_ds * ds_darhoEA
# compute old average quantities
rhoL = 0.5 * (rho[L_old] + rho[LL_old])
rhoR = 0.5 * (rho[R_old] + rho[RR_old])
uL = 0.5 * (u[L_old] + u[LL_old])
uR = 0.5 * (u[R_old] + u[RR_old])
pL = 0.5 * (p[L_old] + p[LL_old])
pR = 0.5 * (p[R_old] + p[RR_old])
cL = 0.5 * (c[L_old] + c[LL_old])
cR = 0.5 * (c[R_old] + c[RR_old])
# residual indices
i1 = self.i_arhoL
i2 = self.i_arhouAL
i3 = self.i_arhoEAL
i4 = self.i_arhoR
i5 = self.i_arhouAR
i6 = self.i_arhoEAR
# reset Jacobian rows
J[i1,:] = 0
J[i2,:] = 0
J[i3,:] = 0
J[i4,:] = 0
J[i5,:] = 0
J[i6,:] = 0
# compute residuals and Jacobians
r[i1] = p[L] - pL + rhoL * (cL - uL) * (u[L] - uL)
J_i1_vf1L = dp_daA1[L]
J[i1,self.i_arhoL] = dp_darhoA[L] + rhoL * (cL - uL) * du_darhoA[L]
J[i1,self.i_arhouAL] = dp_darhouA[L] + rhoL * (cL - uL) * du_darhouA[L]
J[i1,self.i_arhoEAL] = dp_darhoEA[L]
r[i2] = p[R] - pR - rhoR * (cR - uR) * (u[R] - uR)
J_i2_vf1R = dp_daA1[R]
J[i2,self.i_arhoR] = dp_darhoA[R] - rhoR * (cR - uR) * du_darhoA[R]
J[i2,self.i_arhouAR] = dp_darhouA[R] - rhoR * (cR - uR) * du_darhouA[R]
J[i2,self.i_arhoEAR] = dp_darhoEA[R]
if u[L] >= 0:
if u[R] < 0:
error("Assumption violated: Both velocity conditions were true.")
r[i3] = rho[L] - rhoL - (p[L] - pL) / cL**2
J_i3_vf1L = drho_daA1[L] - dp_daA1[L] / cL**2
J_i3_vf1R = 0
J[i3,self.i_arhoL] = drho_darhoA[L] - dp_darhoA[L] / cL**2
J[i3,self.i_arhouAL] = - dp_darhouA[L] / cL**2
J[i3,self.i_arhoEAL] = - dp_darhoEA[L] / cL**2
elif u[R] < 0:
r[i3] = rho[R] - rhoR - (p[R] - pR) / cR**2
J_i3_vf1R = drho_daA1[R] - dp_daA1[R] / cR**2
J_i3_vf1L = 0
J[i3,self.i_arhoR] = drho_darhoA[R] - dp_darhoA[R] / cR**2
J[i3,self.i_arhouAR] = - dp_darhouA[R] / cR**2
J[i3,self.i_arhoEAR] = - dp_darhoEA[R] / cR**2
else:
error("Assumption violated: Neither velocity condition was true.")
r[i4] = rho[L] * u[L] - rho[R] * u[R]
J_i4_vf1L = drho_daA1[L] * u[L]
J[i4,self.i_arhoL] = drho_darhoA[L] * u[L] + rho[L] * du_darhoA[L]
J[i4,self.i_arhouAL] = rho[L] * du_darhouA[L]
J_i4_vf1R = -drho_daA1[R] * u[R]
J[i4,self.i_arhoR] = -(drho_darhoA[R] * u[R] + rho[R] * du_darhoA[R])
J[i4,self.i_arhouAR] = -rho[R] * du_darhouA[R]
r[i5] = e[L] + p[L] / rho[L] + 0.5 * u[L]**2 - (e[R] + p[R] / rho[R] + 0.5 * u[R]**2)
J_i5_vf1L = dp_daA1[L] / rho[L] - p[L] / rho[L]**2 * drho_daA1[L]
J[i5,self.i_arhoL] = de_darhoA[L] + dp_darhoA[L] / rho[L] - p[L] / rho[L]**2 * drho_darhoA[L] + u[L] * du_darhoA[L]
J[i5,self.i_arhouAL] = de_darhouA[L] + dp_darhouA[L] / rho[L] + u[L] * du_darhouA[L]
J[i5,self.i_arhoEAL] = de_darhoEA[L] + dp_darhoEA[L] / rho[L]
J_i5_vf1R = -(dp_daA1[R] / rho[R] - p[R] / rho[R]**2 * drho_daA1[R])
J[i5,self.i_arhoR] = -(de_darhoA[R] + dp_darhoA[R] / rho[R] - p[R] / rho[R]**2 * drho_darhoA[R] + u[R] * du_darhoA[R])
J[i5,self.i_arhouAR] = -(de_darhouA[R] + dp_darhouA[R] / rho[R] + u[R] * du_darhouA[R])
J[i5,self.i_arhoEAR] = -(de_darhoEA[R] + dp_darhoEA[R] / rho[R])
if self.use_momentum_flux_balance:
r[i6] = rho[L] * u[L]**2 + p[L] - (rho[R] * u[R]**2 + p[R])
J_i6_vf1L = drho_daA1[L] * u[L]**2 + dp_daA1[L]
J[i6,self.i_arhoL] = drho_darhoA[L] * u[L]**2 + rho[L] * 2.0 * u[L] * du_darhoA[L] + dp_darhoA[L]
J[i6,self.i_arhouAL] = rho[L] * 2.0 * u[L] * du_darhouA[L] + dp_darhouA[L]
J[i6,self.i_arhoEAL] = dp_darhoEA[L]
J_i6_vf1R = -(drho_daA1[R] * u[R]**2 + dp_daA1[R])
J[i6,self.i_arhoR] = -(drho_darhoA[R] * u[R]**2 + rho[R] * 2.0 * u[R] * du_darhoA[R] + dp_darhoA[R])
J[i6,self.i_arhouAR] = -(rho[R] * 2.0 * u[R] * du_darhouA[R] + dp_darhouA[R])
J[i6,self.i_arhoEAR] = -dp_darhoEA[R]
else:
r[i6] = p0[L] - p0[R]
J_i6_vf1L = dp0_daA1[L]
J[i6,self.i_arhoL] = dp0_darhoA[L]
J[i6,self.i_arhouAL] = dp0_darhouA[L]
J[i6,self.i_arhoEAL] = dp0_darhoEA[L]
J_i6_vf1R = -dp0_daA1[R]
J[i6,self.i_arhoR] = -dp0_darhoA[R]
J[i6,self.i_arhouAR] = -dp0_darhouA[R]
J[i6,self.i_arhoEAR] = -dp0_darhoEA[R]
if self.model_type == ModelType.TwoPhase:
J[i1,self.i_aA1L] = J_i1_vf1L
J[i2,self.i_aA1R] = J_i2_vf1R
J[i3,self.i_aA1L] = J_i3_vf1L
J[i3,self.i_aA1R] = J_i3_vf1R
J[i4,self.i_aA1L] = J_i4_vf1L
J[i4,self.i_aA1R] = J_i4_vf1R
J[i5,self.i_aA1L] = J_i5_vf1L
J[i5,self.i_aA1R] = J_i5_vf1R
J[i6,self.i_aA1L] = J_i6_vf1L
J[i6,self.i_aA1R] = J_i6_vf1R
def computeFluxes(self, U):
self.f_mass = [0] * self.n_meshes
self.df_mass_darhouA = [0] * self.n_meshes
self.f_momentum = [0] * self.n_meshes
self.df_momentum_daA1 = [0] * self.n_meshes
self.df_momentum_darhoA = [0] * self.n_meshes
self.df_momentum_darhouA = [0] * self.n_meshes
self.df_momentum_darhoEA = [0] * self.n_meshes
self.f_energy = [0] * self.n_meshes
self.df_energy_daA1 = [0] * self.n_meshes
self.df_energy_darhoA = [0] * self.n_meshes
self.df_energy_darhouA = [0] * self.n_meshes
self.df_energy_darhoEA = [0] * self.n_meshes
for i in xrange(self.n_meshes):
nx = self.nx[i]
A = self.dof_handler.A[self.node_indices[i]]
aA1 = self.dof_handler.aA1(U, self.node_indices[i])
vf, dvf_daA1 = computeVolumeFraction(aA1, A, self.phase,
self.model_type)
arhoA = U[self.i_arhoA[i]]
arhouA = U[self.i_arhouA[i]]
arhoEA = U[self.i_arhoEA[i]]
u, du_darhoA, du_darhouA = computeVelocity(arhoA, arhouA)
rho, drho_dvf, drho_darhoA, _ = computeDensity(vf, arhoA, A)
drho_daA1 = drho_dvf * dvf_daA1
v, dv_drho = computeSpecificVolume(rho)
dv_daA1 = dv_drho * drho_daA1
dv_darhoA = dv_drho * drho_darhoA
E, dE_darhoA, dE_darhoEA = computeSpecificTotalEnergy(
arhoA, arhoEA)
e, de_du, de_dE = computeSpecificInternalEnergy(u, E)
de_darhoA = de_du * du_darhoA + de_dE * dE_darhoA
de_darhouA = de_du * du_darhouA
de_darhoEA = de_dE * dE_darhoEA
p, dp_dv, dp_de = self.eos.p(v, e)
dp_daA1 = dp_dv * dv_daA1
dp_darhoA = dp_dv * dv_darhoA + dp_de * de_darhoA
dp_darhouA = dp_de * de_darhouA
dp_darhoEA = dp_de * de_darhoEA
self.f_mass[i] = arhouA * nx
self.df_mass_darhouA[i] = nx
self.f_momentum[i] = (arhouA * u + vf * p) * nx
self.df_momentum_daA1[i] = (dvf_daA1 * p + vf * dp_daA1) * nx
self.df_momentum_darhoA[i] = (arhouA * du_darhoA +
vf * dp_darhoA) * nx
self.df_momentum_darhouA[i] = (arhouA * du_darhouA + u +
vf * dp_darhouA) * nx
self.df_momentum_darhoEA[i] = vf * dp_darhoEA * nx
self.f_energy[i] = (arhoEA + vf * p) * u * nx
self.df_energy_daA1[i] = (dvf_daA1 * p + vf * dp_daA1) * u * nx
self.df_energy_darhoA[i] = (
(arhoEA + vf * p) * du_darhoA + vf * dp_darhoA * u) * nx
self.df_energy_darhouA[i] = (
(arhoEA + vf * p) * du_darhouA + vf * dp_darhouA * u) * nx
self.df_energy_darhoEA[i] = (1 + vf * dp_darhoEA) * u * nx
