From 0854da74892c07442eb17f51311fb7ef3ca84d7c Mon Sep 17 00:00:00 2001
From: Dmitri Naumov <github@naumov.de>
Date: Tue, 31 Aug 2021 12:24:31 +0200
Subject: [PATCH] [PL/TH2M] Partially implement analytical Jacobian.
---
ProcessLib/TH2M/ConstitutiveVariables.h | 50 +
ProcessLib/TH2M/IntegrationPointData.h | 1 +
.../PhaseTransitionModel.h | 26 +
.../PhaseTransitionNone.cpp | 50 +
ProcessLib/TH2M/TH2MFEM-impl.h | 978 +++++++++++++++++-
5 files changed, 1095 insertions(+), 10 deletions(-)
diff --git a/ProcessLib/TH2M/ConstitutiveVariables.h b/ProcessLib/TH2M/ConstitutiveVariables.h
index b8d6276fc7d..c4c9496095e 100644
--- a/ProcessLib/TH2M/ConstitutiveVariables.h
+++ b/ProcessLib/TH2M/ConstitutiveVariables.h
@@ -20,9 +20,59 @@ struct ConstitutiveVariables
{
using KelvinMatrixType =
MathLib::KelvinVector::KelvinMatrixType<DisplacementDim>;
+ using DisplacementDimVector = Eigen::Matrix<double, DisplacementDim, 1>;
+ using DisplacementDimMatrix =
+ Eigen::Matrix<double, DisplacementDim, DisplacementDim>;
KelvinMatrixType C;
+ DisplacementDimMatrix dlambda_dp_GR;
+ DisplacementDimMatrix dlambda_dp_cap;
+ DisplacementDimMatrix dlambda_dT;
+ DisplacementDimVector drho_GR_h_w_eff_dp_GR_Npart;
+ DisplacementDimMatrix drho_GR_h_w_eff_dp_GR_gradNpart;
+ DisplacementDimVector drho_LR_h_w_eff_dp_cap_Npart;
+ DisplacementDimMatrix drho_LR_h_w_eff_dp_cap_gradNpart;
+ DisplacementDimVector drho_GR_h_w_eff_dT;
+ DisplacementDimMatrix dfW_4a_dp_GR;
+ DisplacementDimMatrix dfW_4a_dp_cap;
+ DisplacementDimMatrix dfW_4a_dT;
+ DisplacementDimMatrix dfW_4d_dp_GR;
+ DisplacementDimMatrix dfW_4d_dp_cap;
+ DisplacementDimMatrix dfW_4d_dT;
+ DisplacementDimMatrix dfC_4_LCpG_dT;
+ DisplacementDimMatrix dadvection_C_dp_GR;
+ double drho_LR_dT = std::numeric_limits<double>::quiet_NaN();
+ double drho_SR_dT = std::numeric_limits<double>::quiet_NaN();
+ double drho_u_eff_dT = std::numeric_limits<double>::quiet_NaN();
+ double drho_u_eff_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double drho_u_eff_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double drho_h_eff_dT = std::numeric_limits<double>::quiet_NaN();
+ double drho_h_eff_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double drho_h_eff_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dh_G_dT = std::numeric_limits<double>::quiet_NaN();
+ double dh_L_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfC_4_MCpG_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfC_4_MCpG_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfC_4_MCT_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfC_4_MCu_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfC_3a_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfC_3a_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dfC_3a_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfC_2a_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfC_2a_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dfC_2a_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2a_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2b_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2a_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2b_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2a_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfW_2b_dT = std::numeric_limits<double>::quiet_NaN();
+ double dfW_3a_dp_GR = std::numeric_limits<double>::quiet_NaN();
+ double dfW_3a_dp_cap = std::numeric_limits<double>::quiet_NaN();
+ double dfW_3a_dT = std::numeric_limits<double>::quiet_NaN();
+ double ds_L_dp_cap = std::numeric_limits<double>::quiet_NaN();
+
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
};
diff --git a/ProcessLib/TH2M/IntegrationPointData.h b/ProcessLib/TH2M/IntegrationPointData.h
index 67100620ddd..2e959a1da3a 100644
--- a/ProcessLib/TH2M/IntegrationPointData.h
+++ b/ProcessLib/TH2M/IntegrationPointData.h
@@ -122,6 +122,7 @@ struct IntegrationPointData final
// porosity
double phi = std::numeric_limits<double>::quiet_NaN();
+ double dphi_dT = std::numeric_limits<double>::quiet_NaN();
double muGR = std::numeric_limits<double>::quiet_NaN();
double muLR = std::numeric_limits<double>::quiet_NaN();
diff --git a/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionModel.h b/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionModel.h
index 54654ccbb04..b172d3f45d1 100644
--- a/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionModel.h
+++ b/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionModel.h
@@ -24,6 +24,23 @@ struct PhaseTransitionModelVariables
double rhoCGR = 0.;
double rhoWGR = 0.;
+ double drho_GR_dp_GR = 0.;
+ double drho_GR_dT = 0.;
+ double drho_C_GR_dp_GR = 0.;
+ double drho_C_GR_dT = 0.;
+ double drho_LR_dp_GR = 0.;
+ double drho_LR_dp_LR = 0.;
+ double drho_C_LR_dp_GR = 0.;
+ double drho_C_LR_dp_LR = 0.;
+ double drho_C_LR_dT = 0.;
+
+ double drho_W_LR_dp_LR = 0.;
+ double drho_W_LR_dp_GR = 0.;
+ double drho_W_GR_dT = 0.;
+ double drho_W_LR_dT = 0.;
+ double drho_W_GR_dp_GR = 0.;
+ double drho_W_GR_dp_cap = 0.;
+
// liquid phase density
double rhoLR = 0.;
double rhoWLR = 0.;
@@ -71,9 +88,18 @@ struct PhaseTransitionModelVariables
double hWG = 0;
double hL = 0;
+ double dh_G_dT = 0;
+ double dh_L_dT = 0;
+
// specific inner energies
double uG = 0;
double uL = 0;
+
+ double du_G_dT = 0;
+ double du_L_dT = 0;
+ double du_G_dp_GR = 0;
+ double du_L_dp_GR = 0;
+ double du_L_dp_cap = 0;
};
struct PhaseTransitionModel
diff --git a/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionNone.cpp b/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionNone.cpp
index def1a73daf3..9ce4254b4fe 100644
--- a/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionNone.cpp
+++ b/ProcessLib/TH2M/PhaseTransitionModels/PhaseTransitionNone.cpp
@@ -107,11 +107,61 @@ PhaseTransitionModelVariables PhaseTransitionNone::updateConstitutiveVariables(
// specific phase enthalpies
cv.hG = cpG * T;
cv.hL = cpL * T;
+ cv.dh_G_dT = cpG;
+ cv.dh_L_dT = cpL;
// specific inner energies
cv.uG = cv.hG - pGR / cv.rhoGR;
cv.uL = cv.hL;
+ auto const drho_GR_dT =
+ gas_phase[MaterialPropertyLib::PropertyType::density]
+ .template dValue<double>(variables,
+ MaterialPropertyLib::Variable::temperature,
+ pos, t, dt);
+ cv.du_G_dT = cpG + pGR * drho_GR_dT / cv.rhoGR / cv.rhoGR;
+
+ cv.du_L_dT = cpL;
+
+ cv.drho_GR_dp_GR =
+ gas_phase.property(MaterialPropertyLib::PropertyType::density)
+ .template dValue<double>(
+ variables, MaterialPropertyLib::Variable::phase_pressure, pos,
+ t, dt);
+ cv.drho_LR_dp_LR =
+ liquid_phase[MaterialPropertyLib::PropertyType::density]
+ .template dValue<double>(
+ variables, MaterialPropertyLib::Variable::liquid_phase_pressure,
+ pos, t, dt);
+ cv.drho_LR_dp_GR = cv.drho_LR_dp_LR;
+
+ cv.du_G_dp_GR =
+ -1 / cv.rhoGR + pGR * cv.drho_GR_dp_GR / cv.rhoGR / cv.rhoGR;
+
+ cv.drho_C_GR_dp_GR = cv.drho_GR_dp_GR;
+ cv.drho_C_LR_dp_LR = 0;
+ cv.drho_C_LR_dp_GR = 0;
+ cv.drho_C_GR_dT = drho_GR_dT;
+
+ auto const drho_LR_dT =
+ liquid_phase[MaterialPropertyLib::PropertyType::density]
+ .template dValue<double>(variables,
+ MaterialPropertyLib::Variable::temperature,
+ pos, t, dt);
+ cv.drho_C_LR_dT = 0;
+
+ cv.du_L_dp_GR = 0;
+ cv.du_L_dp_cap = 0;
+ /* TODO update to the following when uL has same structure as the uG:
+ +-1 / cv.rhoLR + pLR * cv.drho_LR_dp_cap / cv.rhoLR / cv.rhoLR;
+ */
+
+ cv.drho_W_LR_dp_LR = cv.drho_LR_dp_LR;
+ cv.drho_W_LR_dp_GR = cv.drho_LR_dp_GR;
+ cv.drho_W_LR_dT = drho_LR_dT;
+ cv.drho_W_GR_dT = 0;
+ cv.drho_W_GR_dp_GR = 0;
+ cv.drho_W_GR_dp_cap = 0;
return cv;
}
} // namespace TH2M
diff --git a/ProcessLib/TH2M/TH2MFEM-impl.h b/ProcessLib/TH2M/TH2MFEM-impl.h
index 9f4f9471951..d7763bb9713 100644
--- a/ProcessLib/TH2M/TH2MFEM-impl.h
+++ b/ProcessLib/TH2M/TH2MFEM-impl.h
@@ -125,6 +125,8 @@ TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
pos.setElementID(_element.getID());
auto const& medium = *_process_data.media_map->getMedium(_element.getID());
+ auto const& gas_phase = medium.phase("Gas");
+ auto const& liquid_phase = medium.phase("AqueousLiquid");
auto const& solid_phase = medium.phase("Solid");
unsigned const n_integration_points =
@@ -143,7 +145,7 @@ TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
auto const& NT = Np;
auto const& Nu = ip_data.N_u;
auto const& gradNu = ip_data.dNdx_u;
-
+ auto const& gradNp = ip_data.dNdx_p;
auto const x_coord =
NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
ShapeMatricesTypeDisplacement>(
@@ -153,6 +155,8 @@ TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
double const pGR = Np.dot(gas_pressure);
double const pCap = Np.dot(capillary_pressure);
double const pLR = pGR - pCap;
+ GlobalDimVectorType const gradpGR = gradNp * gas_pressure;
+ GlobalDimVectorType const gradpCap = gradNp * capillary_pressure;
MPL::VariableArray vars;
vars[static_cast<int>(MPL::Variable::temperature)] = T;
@@ -293,7 +297,7 @@ TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
auto const lambdaGR = MPL::formEigenTensor<DisplacementDim>(c.lambdaGR);
auto const lambdaLR = MPL::formEigenTensor<DisplacementDim>(c.lambdaLR);
- ip_data.lambda = phi_S * lambdaSR + phi_L * lambdaLR + phi_G * lambdaGR;
+ ip_data.lambda = phi_G * lambdaGR + phi_L * lambdaLR + phi_S * lambdaSR;
auto const cpS =
solid_phase.property(MPL::PropertyType::specific_heat_capacity)
@@ -340,6 +344,275 @@ TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
ip_data.h_G = c.hG;
ip_data.h_L = c.hL;
ip_data.pWGR = c.pWGR;
+
+ // ---------------------------------------------------------------------
+ // Derivatives for Jacobian
+ // ---------------------------------------------------------------------
+ ip_cv.drho_LR_dT =
+ liquid_phase.property(MPL::PropertyType::density)
+ .template dValue<double>(vars, MPL::Variable::temperature, pos,
+ t, dt);
+ ip_cv.drho_SR_dT =
+ solid_phase.property(MPL::PropertyType::density)
+ .template dValue<double>(vars, MPL::Variable::temperature,
+ pos, t, dt)
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ * (1. - ip_data.thermal_volume_strain +
+ (ip_data.alpha_B - 1.) * div_u) -
+ rho_ref_SR * ip_data.beta_T_SR
+#endif
+ ;
+
+ // porosity
+ auto const dphi_0_dT =
+ medium[MPL::PropertyType::porosity].template dValue<double>(
+ vars, MPL::Variable::temperature, pos, t, dt);
+
+ auto const dphi_S_0_dT = -dphi_0_dT;
+ const double dphi_S_dT = dphi_S_0_dT
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ * (1. + ip_data.thermal_volume_strain -
+ ip_data.alpha_B * div_u) +
+ phi_S_0 * ip_data.beta_T_SR
+#endif
+ ;
+
+ ip_cv.drho_u_eff_dT =
+ phi_G * c.drho_GR_dT * c.uG + phi_G * c.rhoGR * c.du_G_dT +
+ phi_L * ip_cv.drho_LR_dT * c.uL + phi_L * c.rhoLR * c.du_L_dT +
+ phi_S * ip_cv.drho_SR_dT * u_S + phi_S * rhoSR * cpS +
+ dphi_S_dT * rhoSR * u_S;
+
+ ip_cv.ds_L_dp_cap =
+ medium[MPL::PropertyType::saturation].template dValue<double>(
+ vars, MPL::Variable::capillary_pressure, pos, t, dt);
+ // TODO (naumov) Extend for partially saturated media.
+ constexpr double ds_L_dp_GR = 0;
+ double const ds_G_dp_GR = -ds_L_dp_GR;
+ double const ds_G_dp_cap = -ip_cv.ds_L_dp_cap;
+
+ double const dphi_G_dp_GR = -ds_L_dp_GR * ip_data.phi;
+ double const dphi_G_dp_cap = -ip_cv.ds_L_dp_cap * ip_data.phi;
+ double const dphi_L_dp_GR = ds_L_dp_GR * ip_data.phi;
+ double const dphi_L_dp_cap = ip_cv.ds_L_dp_cap * ip_data.phi;
+
+ auto const dlambda_GR_dT = MPL::formEigenTensor<DisplacementDim>(
+ gas_phase[MPL::PropertyType::thermal_conductivity].dValue(
+ vars, MPL::Variable::temperature, pos, t, dt));
+ auto const dlambda_LR_dT = MPL::formEigenTensor<DisplacementDim>(
+ liquid_phase[MPL::PropertyType::thermal_conductivity].dValue(
+ vars, MPL::Variable::temperature, pos, t, dt));
+ auto const dlambda_SR_dT = MPL::formEigenTensor<DisplacementDim>(
+ solid_phase[MPL::PropertyType::thermal_conductivity].dValue(
+ vars, MPL::Variable::temperature, pos, t, dt));
+
+ ip_cv.dlambda_dp_GR = dphi_G_dp_GR * lambdaGR + dphi_L_dp_GR * lambdaLR;
+
+ ip_cv.dlambda_dp_cap =
+ dphi_G_dp_cap * lambdaGR + dphi_L_dp_cap * lambdaLR;
+
+ ip_cv.dlambda_dT = phi_G * dlambda_GR_dT + phi_L * dlambda_LR_dT +
+ phi_S * dlambda_SR_dT + dphi_S_dT * lambdaSR;
+
+ // From p_LR = p_GR - p_cap it follows for
+ // drho_LR/dp_GR = drho_LR/dp_LR * dp_LR/dp_GR
+ // = drho_LR/dp_LR * (dp_GR/dp_GR - dp_cap/dp_GR)
+ // = drho_LR/dp_LR * (1 - 0)
+ double const drho_LR_dp_GR = c.drho_LR_dp_LR;
+ double const drho_LR_dp_cap = -c.drho_LR_dp_LR;
+ // And also for drho_GR/dp_LR = drho_GR/dp_GR * dp_GR/dp_LR:
+ double const drho_GR_dp_cap = 0;
+
+ ip_cv.drho_h_eff_dp_GR =
+ dphi_G_dp_GR * c.rhoGR * c.hG + phi_G * c.drho_GR_dp_GR * c.hG +
+ dphi_L_dp_GR * c.rhoLR * c.hL + phi_L * drho_LR_dp_GR * c.hL;
+ ip_cv.drho_h_eff_dp_cap =
+ dphi_G_dp_cap * c.rhoGR * c.hG + phi_G * drho_GR_dp_cap * c.hG +
+ dphi_L_dp_cap * c.rhoLR * c.hL + phi_L * drho_LR_dp_cap * c.hL;
+
+ // TODO (naumov) Extend for temperature dependent porosities.
+ constexpr double dphi_G_dT = 0;
+ constexpr double dphi_L_dT = 0;
+ ip_cv.drho_h_eff_dT =
+ dphi_G_dT * c.rhoGR * c.hG + phi_G * c.drho_GR_dT * c.hG +
+ phi_G * c.rhoGR * c.dh_G_dT + dphi_L_dT * c.rhoLR * c.hL +
+ phi_L * ip_cv.drho_LR_dT * c.hL + phi_L * c.rhoLR * c.dh_L_dT +
+ dphi_S_dT * rhoSR * ip_data.h_S +
+ phi_S * ip_cv.drho_SR_dT * ip_data.h_S + phi_S * rhoSR * cpS;
+
+ ip_cv.drho_u_eff_dp_GR =
+ dphi_G_dp_GR * c.rhoGR * c.uG + phi_G * c.drho_GR_dp_GR * c.uG +
+ phi_G * c.rhoGR * c.du_G_dp_GR + dphi_L_dp_GR * c.rhoLR * c.uL +
+ phi_L * drho_LR_dp_GR * c.uL + phi_L * c.rhoLR * c.du_L_dp_GR;
+
+ ip_cv.drho_u_eff_dp_cap =
+ dphi_G_dp_cap * c.rhoGR * c.uG + phi_G * drho_GR_dp_cap * c.uG +
+ dphi_L_dp_cap * c.rhoLR * c.uL + phi_L * drho_LR_dp_cap * c.uL +
+ phi_L * c.rhoLR * c.du_L_dp_cap;
+
+ auto const& b = _process_data.specific_body_force;
+ auto const k_over_mu_G =
+ (ip_data.k_S * ip_data.k_rel_G / ip_data.muGR).eval();
+ auto const k_over_mu_L =
+ (ip_data.k_S * ip_data.k_rel_L / ip_data.muLR).eval();
+ GlobalDimVectorType const w_GS =
+ k_over_mu_G * c.rhoGR * b - k_over_mu_G * gradpGR;
+ GlobalDimVectorType const w_LS = k_over_mu_L * gradpCap +
+ k_over_mu_L * c.rhoLR * b -
+ k_over_mu_L * gradpGR;
+
+ ip_cv.drho_GR_h_w_eff_dp_GR_Npart =
+ c.drho_GR_dp_GR * c.hG * w_GS +
+ c.rhoGR * c.hG * k_over_mu_G * c.drho_GR_dp_GR * b;
+ ip_cv.drho_GR_h_w_eff_dp_GR_gradNpart =
+ -c.rhoGR * c.hG * k_over_mu_G - c.rhoLR * c.hL * k_over_mu_L;
+
+ ip_cv.drho_LR_h_w_eff_dp_cap_Npart =
+ -drho_LR_dp_cap * c.hL * w_LS -
+ c.rhoLR * c.hL * k_over_mu_L * drho_LR_dp_cap * b;
+ ip_cv.drho_LR_h_w_eff_dp_cap_gradNpart =
+ // TODO (naumov) why the minus sign??????
+ -c.rhoLR * c.hL * k_over_mu_L;
+
+ ip_cv.drho_GR_h_w_eff_dT =
+ c.drho_GR_dT * c.hG * w_GS + c.rhoGR * c.dh_G_dT * w_GS +
+ ip_cv.drho_LR_dT * c.hL * w_LS + c.rhoLR * c.dh_L_dT * w_LS;
+ // TODO (naumov) + k_over_mu_G * drho_GR_dT * b + k_over_mu_L *
+ // drho_LR_dT * b
+
+ // Derivatives of s_G * rho_C_GR_dot + s_L * rho_C_LR_dot abbreviated
+ // here with S_rho_C_eff.
+ double const s_L = ip_data.s_L;
+ double const s_G = 1. - ip_data.s_L;
+ double const rho_C_GR_dot = (ip_data.rhoCGR - ip_data.rhoCGR_prev) / dt;
+ double const rho_C_LR_dot = (ip_data.rhoCLR - ip_data.rhoCLR_prev) / dt;
+ double const rho_C_FR = s_G * ip_data.rhoCGR + s_L * ip_data.rhoCLR;
+ double const rho_W_FR = s_G * ip_data.rhoWGR + s_L * ip_data.rhoWLR;
+ // TODO (naumov) Extend for partially saturated media.
+ constexpr double drho_C_GR_dp_cap = 0;
+ ip_cv.dfC_3a_dp_GR =
+ ds_G_dp_GR * rho_C_GR_dot + s_G * c.drho_C_GR_dp_GR / dt +
+ ds_L_dp_GR * rho_C_LR_dot + s_L * c.drho_C_LR_dp_GR / dt;
+ ip_cv.dfC_3a_dp_cap =
+ ds_G_dp_cap * rho_C_GR_dot + s_G * drho_C_GR_dp_cap / dt +
+ ip_cv.ds_L_dp_cap * rho_C_LR_dot - s_L * c.drho_C_LR_dp_LR / dt;
+ ip_cv.dfC_3a_dT = s_G * c.drho_C_GR_dT / dt + s_L * c.drho_C_LR_dT / dt;
+
+ double const drho_C_FR_dp_GR =
+ ds_G_dp_GR * ip_data.rhoCGR + s_G * c.drho_C_GR_dp_GR +
+ ds_L_dp_GR * ip_data.rhoCLR + s_L * c.drho_C_LR_dp_GR;
+ ip_cv.dfC_4_MCpG_dp_GR = drho_C_FR_dp_GR *
+ (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR;
+
+ double const drho_C_FR_dT = s_G * c.drho_C_GR_dT + s_L * c.drho_C_LR_dT;
+ ip_cv.dfC_4_MCpG_dT =
+ drho_C_FR_dT * (ip_data.alpha_B - ip_data.phi) * ip_data.beta_p_SR
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ - rho_C_FR * ip_data.dphi_dT * ip_data.beta_p_SR
+#endif
+ ;
+
+ ip_cv.dfC_4_MCT_dT =
+ drho_C_FR_dT * (ip_data.alpha_B - ip_data.phi) * ip_data.beta_T_SR
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ + rho_C_FR * (ip_data.alpha_B - ip_data.dphi_dT) * ip_data.beta_T_SR
+#endif
+ ;
+
+ ip_cv.dfC_4_MCu_dT = drho_C_FR_dT * ip_data.alpha_B;
+
+ ip_cv.dfC_2a_dp_GR = -ip_data.phi * c.drho_C_GR_dp_GR -
+ drho_C_FR_dp_GR * pCap *
+ (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR;
+
+ double const drho_C_FR_dp_cap =
+ ds_G_dp_cap * ip_data.rhoCGR + s_G * drho_C_GR_dp_cap +
+ ip_cv.ds_L_dp_cap * ip_data.rhoCLR - s_L * c.drho_C_LR_dp_LR;
+
+ ip_cv.dfC_2a_dp_cap =
+ ip_data.phi * (-c.drho_C_LR_dp_LR - drho_C_GR_dp_cap) -
+ drho_C_FR_dp_cap * pCap * (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR +
+ rho_C_FR * (ip_data.alpha_B - ip_data.phi) * ip_data.beta_p_SR;
+
+ ip_cv.dfC_2a_dT =
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ ip_data.dphi_dT * (ip_data.rhoCLR - ip_data.rhoCGR) +
+#endif
+ ip_data.phi * (c.drho_C_LR_dT - c.drho_C_GR_dT) -
+ drho_C_FR_dT * pCap * (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ + rho_C_FR * pCap * ip_data.dphi_dT * ip_data.beta_p_SR
+#endif
+ ;
+
+ ip_cv.dadvection_C_dp_GR =
+ c.drho_C_GR_dp_GR * k_over_mu_G + c.drho_C_LR_dp_GR * k_over_mu_L;
+
+ ip_cv.dfC_4_LCpG_dT =
+ c.drho_C_GR_dT * k_over_mu_G + c.drho_C_LR_dT * k_over_mu_L
+ // + ip_cv.ddiffusion_C_p_dT TODO (naumov)
+ ;
+
+ double const drho_W_FR_dp_GR =
+ ds_G_dp_GR * ip_data.rhoWGR + s_G * c.drho_W_GR_dp_GR +
+ ds_L_dp_GR * ip_data.rhoWLR + s_L * c.drho_W_LR_dp_GR;
+ double const drho_W_FR_dp_cap =
+ ds_G_dp_cap * ip_data.rhoWGR + s_G * c.drho_W_GR_dp_cap +
+ ip_cv.ds_L_dp_cap * ip_data.rhoWLR - s_L * c.drho_W_LR_dp_LR;
+ double const drho_W_FR_dT = s_G * c.drho_W_GR_dT + s_L * c.drho_W_LR_dT;
+
+ ip_cv.dfW_2a_dp_GR =
+ ip_data.phi * (c.drho_W_LR_dp_GR - c.drho_W_GR_dp_GR);
+ ip_cv.dfW_2b_dp_GR = drho_W_FR_dp_GR * pCap *
+ (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR;
+ ip_cv.dfW_2a_dp_cap =
+ ip_data.phi * (-c.drho_W_LR_dp_LR - c.drho_W_GR_dp_cap);
+ ip_cv.dfW_2b_dp_cap =
+ drho_W_FR_dp_cap * pCap * (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR +
+ rho_W_FR * (ip_data.alpha_B - ip_data.phi) * ip_data.beta_p_SR;
+
+ ip_cv.dfW_2a_dT =
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ ip_data.dphi_dT * (ip_data.rhoWLR - ip_data.rhoWGR) +
+#endif
+ ip_data.phi * (c.drho_W_LR_dT - c.drho_W_GR_dT);
+ ip_cv.dfW_2b_dT =
+ drho_W_FR_dT * pCap * (ip_data.alpha_B - ip_data.phi) *
+ ip_data.beta_p_SR
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ - rho_W_FR * pCap * ip_data.dphi_dT * ip_data.beta_p_SR
+#endif
+ ;
+
+ double const rho_W_GR_dot = (ip_data.rhoWGR - ip_data.rhoWGR_prev) / dt;
+ double const rho_W_LR_dot = (ip_data.rhoWLR - ip_data.rhoWLR_prev) / dt;
+
+ ip_cv.dfW_3a_dp_GR =
+ ds_G_dp_GR * rho_W_GR_dot + s_G * c.drho_W_GR_dp_GR / dt +
+ ds_L_dp_GR * rho_W_LR_dot + s_L * c.drho_W_LR_dp_GR / dt;
+ ip_cv.dfW_3a_dp_cap =
+ ds_G_dp_cap * rho_W_GR_dot + s_G * c.drho_W_GR_dp_cap / dt +
+ ip_cv.ds_L_dp_cap * rho_W_LR_dot - s_L * c.drho_W_LR_dp_LR / dt;
+ ip_cv.dfW_3a_dT = s_G * c.drho_W_GR_dT / dt + s_L * c.drho_W_LR_dT / dt;
+
+ ip_cv.dfW_4a_dp_GR = c.drho_W_GR_dp_GR * k_over_mu_G;
+ ip_cv.dfW_4a_dp_cap = -c.drho_W_LR_dp_LR * k_over_mu_L;
+ ip_cv.dfW_4a_dT =
+ c.drho_W_GR_dT * k_over_mu_G + c.drho_W_LR_dT * k_over_mu_L;
+
+ // TODO (naumov) for dxmW*/d* != 0
+ ip_cv.dfW_4d_dp_GR =
+ Eigen::Matrix<double, DisplacementDim, DisplacementDim>::Zero();
+ ip_cv.dfW_4d_dp_cap =
+ Eigen::Matrix<double, DisplacementDim, DisplacementDim>::Zero();
+ ip_cv.dfW_4d_dT =
+ Eigen::Matrix<double, DisplacementDim, DisplacementDim>::Zero();
}
return ip_constitutive_variables;
@@ -807,18 +1080,703 @@ template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
typename IntegrationMethod, int DisplacementDim>
void TH2MLocalAssembler<ShapeFunctionDisplacement, ShapeFunctionPressure,
IntegrationMethod, DisplacementDim>::
- assembleWithJacobian(double const /*t*/, double const /*dt*/,
- std::vector<double> const& /*local_x*/,
- std::vector<double> const& /*local_xdot*/,
+ assembleWithJacobian(double const t, double const dt,
+ std::vector<double> const& local_x,
+ std::vector<double> const& local_xdot,
const double /*dxdot_dx*/, const double /*dx_dx*/,
std::vector<double>& /*local_M_data*/,
std::vector<double>& /*local_K_data*/,
- std::vector<double>& /*local_rhs_data*/,
- std::vector<double>& /*local_Jac_data*/)
+ std::vector<double>& local_rhs_data,
+ std::vector<double>& local_Jac_data)
{
- OGS_FATAL(
- "TH2MLocalAssembler:assembleWithJacobian is currently not "
- "implemented.");
+ auto const matrix_size = gas_pressure_size + capillary_pressure_size +
+ temperature_size + displacement_size;
+ assert(local_x.size() == matrix_size);
+
+ auto const temperature = Eigen::Map<VectorType<temperature_size> const>(
+ local_x.data() + temperature_index, temperature_size);
+
+ auto const gas_pressure = Eigen::Map<VectorType<gas_pressure_size> const>(
+ local_x.data() + gas_pressure_index, gas_pressure_size);
+
+ auto const capillary_pressure =
+ Eigen::Map<VectorType<capillary_pressure_size> const>(
+ local_x.data() + capillary_pressure_index, capillary_pressure_size);
+
+ auto const gas_pressure_dot =
+ Eigen::Map<VectorType<gas_pressure_size> const>(
+ local_xdot.data() + gas_pressure_index, gas_pressure_size);
+
+ auto const capillary_pressure_dot =
+ Eigen::Map<VectorType<capillary_pressure_size> const>(
+ local_xdot.data() + capillary_pressure_index,
+ capillary_pressure_size);
+
+ auto const temperature_dot = Eigen::Map<VectorType<temperature_size> const>(
+ local_xdot.data() + temperature_index, temperature_size);
+
+ auto const displacement_dot =
+ Eigen::Map<VectorType<displacement_size> const>(
+ local_xdot.data() + displacement_index, displacement_size);
+
+ auto local_Jac =
+ MathLib::createZeroedMatrix<MatrixType<matrix_size, matrix_size>>(
+ local_Jac_data, matrix_size, matrix_size);
+
+ auto local_f = MathLib::createZeroedVector<VectorType<matrix_size>>(
+ local_rhs_data, matrix_size);
+
+ // component-formulation
+ // W - liquid phase main component
+ // C - gas phase main component
+
+ // C component equation matrices
+ MatrixType<C_size, gas_pressure_size> MCpG =
+ MatrixType<C_size, gas_pressure_size>::Zero(C_size, gas_pressure_size);
+ MatrixType<C_size, capillary_pressure_size> MCpC =
+ MatrixType<C_size, capillary_pressure_size>::Zero(
+ C_size, capillary_pressure_size);
+ MatrixType<C_size, temperature_size> MCT =
+ MatrixType<C_size, temperature_size>::Zero(C_size, temperature_size);
+ MatrixType<C_size, displacement_size> MCu =
+ MatrixType<C_size, displacement_size>::Zero(C_size, displacement_size);
+
+ MatrixType<C_size, gas_pressure_size> LCpG =
+ MatrixType<C_size, gas_pressure_size>::Zero(C_size, gas_pressure_size);
+ MatrixType<C_size, capillary_pressure_size> LCpC =
+ MatrixType<C_size, capillary_pressure_size>::Zero(
+ C_size, capillary_pressure_size);
+ MatrixType<C_size, temperature_size> LCT =
+ MatrixType<C_size, temperature_size>::Zero(C_size, temperature_size);
+
+ // mass matrix - W component equation
+ MatrixType<W_size, gas_pressure_size> MWpG =
+ MatrixType<W_size, gas_pressure_size>::Zero(W_size, gas_pressure_size);
+ MatrixType<W_size, capillary_pressure_size> MWpC =
+ MatrixType<W_size, capillary_pressure_size>::Zero(
+ W_size, capillary_pressure_size);
+ MatrixType<W_size, temperature_size> MWT =
+ MatrixType<W_size, temperature_size>::Zero(W_size, temperature_size);
+ MatrixType<W_size, displacement_size> MWu =
+ MatrixType<W_size, displacement_size>::Zero(W_size, displacement_size);
+
+ // stiffness matrix - W component equation
+ MatrixType<W_size, gas_pressure_size> LWpG =
+ MatrixType<W_size, gas_pressure_size>::Zero(W_size, gas_pressure_size);
+ MatrixType<W_size, capillary_pressure_size> LWpC =
+ MatrixType<W_size, capillary_pressure_size>::Zero(
+ W_size, capillary_pressure_size);
+ MatrixType<W_size, temperature_size> LWT =
+ MatrixType<W_size, temperature_size>::Zero(W_size, temperature_size);
+
+ // mass matrix - temperature equation
+ MatrixType<temperature_size, displacement_size> MTu =
+ MatrixType<temperature_size, displacement_size>::Zero(
+ temperature_size, displacement_size);
+
+ // stiffness matrix - temperature equation
+ MatrixType<temperature_size, temperature_size> KTT =
+ MatrixType<temperature_size, temperature_size>::Zero(temperature_size,
+ temperature_size);
+
+ // stiffness matrices - displacement equation coupling into pressures
+ MatrixType<displacement_size, gas_pressure_size> KUpG =
+ MatrixType<displacement_size, gas_pressure_size>::Zero(
+ displacement_size, gas_pressure_size);
+ MatrixType<displacement_size, capillary_pressure_size> KUpC =
+ MatrixType<displacement_size, capillary_pressure_size>::Zero(
+ displacement_size, capillary_pressure_size);
+
+ // pointer-vectors to the right hand side terms - C-component equation
+ auto fC = local_f.template segment<C_size>(C_index);
+ // pointer-vectors to the right hand side terms - W-component equation
+ auto fW = local_f.template segment<W_size>(W_index);
+ // pointer-vectors to the right hand side terms - temperature equation
+ auto fT = local_f.template segment<temperature_size>(temperature_index);
+ // pointer-vectors to the right hand side terms - displacement equation
+ auto fU = local_f.template segment<displacement_size>(displacement_index);
+
+ ParameterLib::SpatialPosition pos;
+ pos.setElementID(_element.getID());
+
+ unsigned const n_integration_points =
+ _integration_method.getNumberOfPoints();
+
+ auto const ip_constitutive_variables = updateConstitutiveVariables(
+ Eigen::Map<Eigen::VectorXd const>(local_x.data(), local_x.size()),
+ Eigen::Map<Eigen::VectorXd const>(local_xdot.data(), local_xdot.size()),
+ t, dt);
+
+ for (unsigned int_point = 0; int_point < n_integration_points; int_point++)
+ {
+ pos.setIntegrationPoint(int_point);
+ auto& ip = _ip_data[int_point];
+ auto& ip_cv = ip_constitutive_variables[int_point];
+
+ auto const& Np = ip.N_p;
+ auto const& NT = Np;
+ auto const& Nu = ip.N_u;
+
+ auto const& NpT = Np.transpose().eval();
+ auto const& NTT = NT.transpose().eval();
+
+ auto const& gradNp = ip.dNdx_p;
+ auto const& gradNT = gradNp;
+ auto const& gradNu = ip.dNdx_u;
+
+ auto const& gradNpT = gradNp.transpose().eval();
+ auto const& gradNTT = gradNT.transpose().eval();
+
+ auto const& Nu_op = ip.N_u_op;
+ auto const& w = ip.integration_weight;
+
+ auto const& m = Invariants::identity2;
+ auto const mT = m.transpose().eval();
+
+ auto const x_coord =
+ NumLib::interpolateXCoordinate<ShapeFunctionDisplacement,
+ ShapeMatricesTypeDisplacement>(
+ _element, Nu);
+
+ auto const Bu =
+ LinearBMatrix::computeBMatrix<DisplacementDim,
+ ShapeFunctionDisplacement::NPOINTS,
+ typename BMatricesType::BMatrixType>(
+ gradNu, Nu, x_coord, _is_axially_symmetric);
+
+ auto const BuT = Bu.transpose().eval();
+
+ double const div_u_dot = Invariants::trace(Bu * displacement_dot);
+
+ double const pCap = Np.dot(capillary_pressure);
+
+ GlobalDimVectorType const gradpGR = gradNp * gas_pressure;
+ GlobalDimVectorType const gradpCap = gradNp * capillary_pressure;
+ GlobalDimVectorType const gradT = gradNT * temperature;
+
+ double const pGR_dot = Np.dot(gas_pressure_dot);
+ double const pCap_dot = Np.dot(capillary_pressure_dot);
+ double const T_dot = NT.dot(temperature_dot);
+ auto& beta_T_SR = ip.beta_T_SR;
+
+ auto const I =
+ Eigen::Matrix<double, DisplacementDim, DisplacementDim>::Identity();
+
+ const double sD_G = ip.diffusion_coefficient_vapour;
+ const double sD_L = ip.diffusion_coefficient_solvate;
+
+ auto const D_C_G = (sD_G * I).eval();
+ auto const D_W_G = (sD_G * I).eval();
+ auto const D_C_L = (sD_L * I).eval();
+ auto const D_W_L = (sD_L * I).eval();
+
+ auto& k_S = ip.k_S;
+
+ auto& s_L = ip.s_L;
+ auto const s_G = 1. - s_L;
+ auto const s_L_dot = (s_L - ip.s_L_prev) / dt;
+
+ auto& alpha_B = ip.alpha_B;
+ auto& beta_p_SR = ip.beta_p_SR;
+
+ auto const& b = _process_data.specific_body_force;
+
+ // porosity
+ auto& phi = ip.phi;
+
+ // volume fraction
+ auto const phi_G = s_G * phi;
+ auto const phi_L = s_L * phi;
+ auto const phi_S = 1. - phi;
+
+ // solid phase density
+ auto& rho_SR = ip.rhoSR;
+ // effective density
+ auto const rho = phi_G * ip.rhoGR + phi_L * ip.rhoLR + phi_S * rho_SR;
+
+ // abbreviations
+ const double rho_C_FR = s_G * ip.rhoCGR + s_L * ip.rhoCLR;
+ const double rho_W_FR = s_G * ip.rhoWGR + s_L * ip.rhoWLR;
+
+ // phase specific enthalpies
+ auto& h_G = ip.h_G;
+ auto& h_L = ip.h_L;
+
+ auto const rho_C_GR_dot = (ip.rhoCGR - ip.rhoCGR_prev) / dt;
+ auto const rho_C_LR_dot = (ip.rhoCLR - ip.rhoCLR_prev) / dt;
+ auto const rho_W_GR_dot = (ip.rhoWGR - ip.rhoWGR_prev) / dt;
+ auto const rho_W_LR_dot = (ip.rhoWLR - ip.rhoWLR_prev) / dt;
+
+ auto const rho_h_eff = ip.rho_G_h_G + ip.rho_L_h_L + ip.rho_S_h_S;
+
+ auto const rho_u_eff_dot = (ip.rho_u_eff - ip.rho_u_eff_prev) / dt;
+
+ auto const k_over_mu_G = (k_S * ip.k_rel_G / ip.muGR).eval();
+ auto const k_over_mu_L = (k_S * ip.k_rel_L / ip.muLR).eval();
+
+ GlobalDimVectorType const w_GS =
+ k_over_mu_G * ip.rhoGR * b - k_over_mu_G * gradpGR;
+
+ GlobalDimVectorType const w_LS = k_over_mu_L * gradpCap +
+ k_over_mu_L * ip.rhoLR * b -
+ k_over_mu_L * gradpGR;
+
+ // ---------------------------------------------------------------------
+ // C-component equation
+ // ---------------------------------------------------------------------
+
+ MCpG.noalias() += NpT * rho_C_FR * (alpha_B - phi) * beta_p_SR * Np * w;
+ MCpC.noalias() -=
+ NpT * rho_C_FR * (alpha_B - phi) * beta_p_SR * s_L * Np * w;
+
+ if (_process_data.apply_mass_lumping)
+ {
+ if (pCap_dot != 0.) // avoid division by Zero
+ {
+ MCpC.noalias() +=
+ NpT *
+ (phi * (ip.rhoCLR - ip.rhoCGR) -
+ rho_C_FR * pCap * (alpha_B - phi) * beta_p_SR) *
+ s_L_dot / pCap_dot * Np * w;
+ }
+ }
+
+ MCT.noalias() -= NpT * rho_C_FR * (alpha_B - phi) * beta_T_SR * Np * w;
+ // d (fC_4_MCT * T_dot)/d T
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += NpT * ip_cv.dfC_4_MCT_dT * T_dot * NT * w;
+
+ MCu.noalias() += NpT * rho_C_FR * alpha_B * mT * Bu * w;
+ // d (fC_4_MCu * u_dot)/d T
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += NpT * ip_cv.dfC_4_MCu_dT * div_u_dot * NT * w;
+
+ auto const advection_C_G = (ip.rhoCGR * k_over_mu_G).eval();
+ auto const advection_C_L = (ip.rhoCLR * k_over_mu_L).eval();
+ auto const diffusion_C_G_p =
+ (phi_G * ip.rhoGR * D_C_G * ip.dxmCG_dpGR).eval();
+ auto const diffusion_C_L_p =
+ (phi_L * ip.rhoLR * D_C_L * ip.dxmCL_dpLR).eval();
+ auto const diffusion_C_G_T =
+ (phi_G * ip.rhoGR * D_C_G * ip.dxmCG_dT).eval();
+ auto const diffusion_C_L_T =
+ (phi_L * ip.rhoLR * D_C_L * ip.dxmCL_dT).eval();
+
+ auto const advection_C = (advection_C_G + advection_C_L).eval();
+ auto const diffusion_C_p = (diffusion_C_G_p + diffusion_C_L_p).eval();
+ auto const diffusion_C_T = (diffusion_C_G_T + diffusion_C_L_T).eval();
+
+ LCpG.noalias() += gradNpT * (advection_C + diffusion_C_p) * gradNp * w;
+
+ // d (fC_4_LCpG * grad p_GR)/d p_GR
+ local_Jac.template block<C_size, C_size>(C_index, C_index).noalias() +=
+ gradNpT *
+ (ip_cv.dadvection_C_dp_GR
+ // + ip_cv.ddiffusion_C_p_dp_GR TODO (naumov)
+ ) *
+ gradpGR * Np * w;
+
+ // d (fC_4_LCpG * grad p_GR)/d T
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += gradNpT * ip_cv.dfC_4_LCpG_dT * gradpGR * NT * w;
+
+ // d (fC_4_MCpG * p_GR_dot)/d p_GR
+ local_Jac.template block<C_size, C_size>(C_index, C_index).noalias() +=
+ NpT * ip_cv.dfC_4_MCpG_dp_GR * pGR_dot * Np * w;
+
+ // d (fC_4_MCpG * p_GR_dot)/d T
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += NpT * ip_cv.dfC_4_MCpG_dT * pGR_dot * NT * w;
+
+ LCpC.noalias() -=
+ gradNpT * (advection_C_L + diffusion_C_L_p) * gradNp * w;
+
+ LCT.noalias() += gradNpT * diffusion_C_T * gradNp * w;
+
+ // fC_1
+ fC.noalias() += gradNpT *
+ (advection_C_G * ip.rhoGR + advection_C_L * ip.rhoLR) *
+ b * w;
+
+ if (!_process_data.apply_mass_lumping)
+ {
+ // fC_2 = \int a * s_L_dot
+ auto const a = phi * (ip.rhoCLR - ip.rhoCGR) -
+ rho_C_FR * pCap * (alpha_B - phi) * beta_p_SR;
+ fC.noalias() -= NpT * a * s_L_dot * w;
+
+ // TODO (naumov) Extend for partially saturated media.
+ constexpr double ds_L_dp_GR = 0;
+ local_Jac.template block<C_size, C_size>(C_index, C_index)
+ .noalias() +=
+ NpT * (ip_cv.dfC_2a_dp_GR * s_L_dot - a * ds_L_dp_GR / dt) *
+ Np * w;
+
+ local_Jac.template block<C_size, W_size>(C_index, W_index)
+ .noalias() +=
+ NpT *
+ (ip_cv.dfC_2a_dp_cap * s_L_dot + a * ip_cv.ds_L_dp_cap / dt) *
+ Np * w;
+
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += NpT * ip_cv.dfC_2a_dT * s_L_dot * NT * w;
+ }
+ {
+ // fC_3 = \int phi * a
+ double const a = s_G * rho_C_GR_dot + s_L * rho_C_LR_dot;
+ fC.noalias() -= NpT * phi * a * w;
+
+ local_Jac.template block<C_size, C_size>(C_index, C_index)
+ .noalias() += NpT * phi * ip_cv.dfC_3a_dp_GR * Np * w;
+
+ local_Jac.template block<C_size, W_size>(C_index, W_index)
+ .noalias() += NpT * phi * ip_cv.dfC_3a_dp_cap * Np * w;
+
+ local_Jac
+ .template block<C_size, temperature_size>(C_index,
+ temperature_index)
+ .noalias() += NpT *
+ (
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ ip.dphi_dT * a +
+#endif // NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ phi * ip_cv.dfC_3a_dT) *
+ NT * w;
+ }
+ // ---------------------------------------------------------------------
+ // W-component equation
+ // ---------------------------------------------------------------------
+
+ MWpG.noalias() += NpT * rho_W_FR * (alpha_B - phi) * beta_p_SR * Np * w;
+ MWpC.noalias() -=
+ NpT * rho_W_FR * (alpha_B - phi) * beta_p_SR * s_L * Np * w;
+
+ if (_process_data.apply_mass_lumping)
+ {
+ if (pCap_dot != 0.) // avoid division by Zero
+ {
+ MWpC.noalias() +=
+ NpT *
+ (phi * (ip.rhoWLR - ip.rhoWGR) -
+ rho_W_FR * pCap * (alpha_B - phi) * beta_p_SR) *
+ s_L_dot / pCap_dot * Np * w;
+ }
+ }
+
+ MWT.noalias() -= NpT * rho_W_FR * (alpha_B - phi) * beta_T_SR * Np * w;
+
+ MWu.noalias() += NpT * rho_W_FR * alpha_B * mT * Bu * w;
+
+ auto const advection_W_G = (ip.rhoWGR * k_over_mu_G).eval();
+ auto const advection_W_L = (ip.rhoWLR * k_over_mu_L).eval();
+ auto const diffusion_W_G_p = phi_G * ip.rhoGR * D_W_G * ip.dxmWG_dpGR;
+ auto const diffusion_W_L_p = phi_L * ip.rhoLR * D_W_L * ip.dxmWL_dpLR;
+ auto const diffusion_W_G_T = phi_G * ip.rhoGR * D_W_G * ip.dxmWG_dT;
+ auto const diffusion_W_L_T = phi_L * ip.rhoLR * D_W_L * ip.dxmWL_dT;
+
+ auto const advection_W = advection_W_G + advection_W_L;
+ auto const diffusion_W_p = diffusion_W_G_p + diffusion_W_L_p;
+ auto const diffusion_W_T = diffusion_W_G_T + diffusion_W_L_T;
+
+ LWpG.noalias() += gradNpT * (advection_W + diffusion_W_p) * gradNp * w;
+
+ // fW_4 LWpG' parts; LWpG = \int grad (a + d) grad
+ local_Jac.template block<W_size, C_size>(W_index, C_index).noalias() -=
+ gradNpT * (ip_cv.dfW_4a_dp_GR + ip_cv.dfW_4d_dp_GR) * gradpGR * Np *
+ w;
+
+ local_Jac.template block<W_size, W_size>(W_index, W_index).noalias() -=
+ gradNpT * (ip_cv.dfW_4a_dp_cap + ip_cv.dfW_4d_dp_cap) * gradpGR *
+ Np * w;
+
+ local_Jac
+ .template block<W_size, temperature_size>(W_index,
+ temperature_index)
+ .noalias() -=
+ gradNpT * (ip_cv.dfW_4a_dT + ip_cv.dfW_4d_dT) * gradpGR * NT * w;
+
+ LWpC.noalias() -=
+ gradNpT * (advection_W_L + diffusion_W_L_p) * gradNp * w;
+
+ LWT.noalias() += gradNpT * (diffusion_W_T)*gradNp * w;
+
+ // fW_1
+ fW.noalias() += gradNpT *
+ (advection_W_G * ip.rhoGR + advection_W_L * ip.rhoLR) *
+ b * w;
+
+ // fW_2 = \int (f - g) * s_L_dot
+ if (!_process_data.apply_mass_lumping)
+ {
+ double const f = phi * (ip.rhoWLR - ip.rhoWGR);
+ double const g = rho_W_FR * pCap * (alpha_B - phi) * beta_p_SR;
+
+ fW.noalias() -= NpT * (f - g) * s_L_dot * w;
+
+ local_Jac.template block<W_size, C_size>(W_index, C_index)
+ .noalias() += NpT * (ip_cv.dfW_2a_dp_GR - ip_cv.dfW_2b_dp_GR) *
+ s_L_dot * Np * w;
+
+ // sign negated because of dp_cap = -dp_LR
+ // TODO (naumov) Had to change the sign to get equal Jacobian WW
+ // blocks in A2 Test. Where is the error?
+ local_Jac.template block<W_size, W_size>(W_index, W_index)
+ .noalias() +=
+ NpT *
+ ((ip_cv.dfW_2a_dp_cap - ip_cv.dfW_2b_dp_cap) * s_L_dot +
+ (f - g) * ip_cv.ds_L_dp_cap / dt) *
+ Np * w;
+
+ local_Jac
+ .template block<W_size, temperature_size>(W_index,
+ temperature_index)
+ .noalias() +=
+ NpT * (ip_cv.dfW_2a_dT - ip_cv.dfW_2b_dT) * s_L_dot * Np * w;
+ }
+
+ // fW_3 = \int phi * a
+ fW.noalias() -=
+ NpT * phi * (s_G * rho_W_GR_dot + s_L * rho_W_LR_dot) * w;
+
+ local_Jac.template block<W_size, C_size>(W_index, C_index).noalias() +=
+ NpT * phi * ip_cv.dfW_3a_dp_GR * Np * w;
+
+ local_Jac.template block<W_size, W_size>(W_index, W_index).noalias() +=
+ NpT * phi * ip_cv.dfW_3a_dp_cap * Np * w;
+
+ local_Jac
+ .template block<W_size, temperature_size>(W_index,
+ temperature_index)
+ .noalias() +=
+ NpT *
+ (
+#ifdef NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ ip.dphi_dT * (s_G * rho_W_GR_dot + s_L * rho_W_LR_dot) +
+#endif // NON_CONSTANT_SOLID_PHASE_VOLUME_FRACTION
+ phi * ip_cv.dfW_3a_dT) *
+ NT * w;
+
+ // ---------------------------------------------------------------------
+ // - temperature equation
+ // ---------------------------------------------------------------------
+
+ MTu.noalias() += NTT * rho_h_eff * mT * Bu * w;
+
+ // dfT_4/dp_GR
+ // d (MTu * u_dot)/dp_GR
+ local_Jac
+ .template block<temperature_size, C_size>(temperature_index,
+ C_index)
+ .noalias() += NTT * ip_cv.drho_h_eff_dp_GR * div_u_dot * NT * w;
+
+ // dfT_4/dp_cap
+ // d (MTu * u_dot)/dp_cap
+ local_Jac
+ .template block<temperature_size, W_size>(temperature_index,
+ W_index)
+ .noalias() -= NTT * ip_cv.drho_h_eff_dp_cap * div_u_dot * NT * w;
+
+ // dfT_4/dT
+ // d (MTu * u_dot)/dT
+ local_Jac
+ .template block<temperature_size, temperature_size>(
+ temperature_index, temperature_index)
+ .noalias() += NTT * ip_cv.drho_h_eff_dT * div_u_dot * NT * w;
+
+ KTT.noalias() += gradNTT * ip.lambda * gradNT * w;
+
+ // d KTT/dp_GR * T
+ local_Jac
+ .template block<temperature_size, C_size>(temperature_index,
+ C_index)
+ .noalias() += gradNTT * ip_cv.dlambda_dp_GR * gradT * Np * w;
+
+ // d KTT/dp_cap * T
+ local_Jac
+ .template block<temperature_size, W_size>(temperature_index,
+ W_index)
+ .noalias() += gradNTT * ip_cv.dlambda_dp_cap * gradT * Np * w;
+
+ // d KTT/dT * T
+ local_Jac
+ .template block<temperature_size, temperature_size>(
+ temperature_index, temperature_index)
+ .noalias() += gradNTT * ip_cv.dlambda_dT * gradT * NT * w;
+
+ // fT_1
+ fT.noalias() -= NTT * rho_u_eff_dot * w;
+
+ // dfT_1/dp_GR
+ local_Jac
+ .template block<temperature_size, C_size>(temperature_index,
+ C_index)
+ .noalias() += NpT / dt * ip_cv.drho_u_eff_dp_GR * Np * w;
+
+ // dfT_1/dp_cap
+ local_Jac
+ .template block<temperature_size, W_size>(temperature_index,
+ W_index)
+ .noalias() += NpT / dt * ip_cv.drho_u_eff_dp_cap * Np * w;
+
+ // dfT_1/dT
+ // MTT
+ local_Jac
+ .template block<temperature_size, temperature_size>(
+ temperature_index, temperature_index)
+ .noalias() += NTT * ip_cv.drho_u_eff_dT / dt * NT * w;
+
+ // fT_2
+ fT.noalias() +=
+ gradNTT * (ip.rhoGR * h_G * w_GS + ip.rhoLR * h_L * w_LS) * w;
+
+ // dfT_2/dp_GR
+ local_Jac
+ .template block<temperature_size, C_size>(temperature_index,
+ C_index)
+ .noalias() -=
+ // dfT_2/dp_GR first part
+ gradNTT * ip_cv.drho_GR_h_w_eff_dp_GR_Npart * Np * w +
+ // dfT_2/dp_GR second part
+ gradNTT * ip_cv.drho_GR_h_w_eff_dp_GR_gradNpart * gradNp * w;
+
+ // dfT_2/dp_cap
+ local_Jac
+ .template block<temperature_size, W_size>(temperature_index,
+ W_index)
+ .noalias() -=
+ // first part of dfT_2/dp_cap
+ gradNTT * (-ip_cv.drho_LR_h_w_eff_dp_cap_Npart) * Np * w +
+ // second part of dfT_2/dp_cap
+ gradNTT * (-ip_cv.drho_LR_h_w_eff_dp_cap_gradNpart) * gradNp * w;
+
+ // dfT_2/dT
+ local_Jac
+ .template block<temperature_size, temperature_size>(
+ temperature_index, temperature_index)
+ .noalias() -= gradNTT * ip_cv.drho_GR_h_w_eff_dT * NT * w;
+
+ // fT_3
+ fT.noalias() +=
+ NTT * (ip.rhoGR * w_GS.transpose() + ip.rhoLR * w_LS.transpose()) *
+ b * w;
+
+ // ---------------------------------------------------------------------
+ // - displacement equation
+ // ---------------------------------------------------------------------
+
+ KUpG.noalias() -= (BuT * alpha_B * m * Np) * w;
+
+ // dfU_2/dp_GR part i.e. part of the d(KUpG*p_GR)/dp_GR derivative is
+ // dKUpG/dp_GR + KUpG. The former is zero, the latter is handled below.
+
+ KUpC.noalias() += (BuT * alpha_B * s_L * m * Np) * w;
+
+ // dfU_2/dp_LR part i.e. part of the d(KUpC*p_cap)/dp_LR derivative is
+ // dKUpC/dp_LR + KUpC. The latter is handled below, the former here:
+ local_Jac
+ .template block<displacement_size, W_size>(displacement_index,
+ W_index)
+ .noalias() += BuT * alpha_B * ip_cv.ds_L_dp_cap * pCap * m * Np * w;
+
+ local_Jac
+ .template block<displacement_size, displacement_size>(
+ displacement_index, displacement_index)
+ .noalias() += BuT * ip_cv.C * Bu * w;
+
+ // fU_1
+ fU.noalias() -= (BuT * ip.sigma_eff - Nu_op.transpose() * rho * b) * w;
+
+ // KuT
+ local_Jac
+ .template block<displacement_size, temperature_size>(
+ displacement_index, temperature_index)
+ .noalias() -= BuT * (ip_cv.C * ip.alpha_T_SR) * NT * w;
+
+ /* TODO (naumov) Test with gravity needed to check this Jacobian part.
+ local_Jac
+ .template block<displacement_size, temperature_size>(
+ displacement_index, temperature_index)
+ .noalias() += Nu_op.transpose() * ip_cv.drho_dT * b * Nu_op * w;
+ */
+
+ if (_process_data.apply_mass_lumping)
+ {
+ MCpG = MCpG.colwise().sum().eval().asDiagonal();
+ MCpC = MCpC.colwise().sum().eval().asDiagonal();
+ MWpG = MWpG.colwise().sum().eval().asDiagonal();
+ MWpC = MWpC.colwise().sum().eval().asDiagonal();
+ }
+ } // int_point-loop
+
+ // --- Gas ---
+ // fC_4
+ fC.noalias() -= LCpG * gas_pressure + LCpC * capillary_pressure +
+ LCT * temperature + MCpG * gas_pressure_dot +
+ MCpC * capillary_pressure_dot + MCT * temperature_dot +
+ MCu * displacement_dot;
+
+ local_Jac.template block<C_size, C_size>(C_index, C_index).noalias() +=
+ LCpG + MCpG / dt;
+ local_Jac.template block<C_size, W_size>(C_index, W_index).noalias() +=
+ LCpC + MCpC / dt;
+ local_Jac
+ .template block<C_size, temperature_size>(C_index, temperature_index)
+ .noalias() += LCT + MCT / dt;
+ local_Jac
+ .template block<C_size, displacement_size>(C_index, displacement_index)
+ .noalias() += MCu / dt;
+
+ // --- Capillary pressure ---
+ // fW_4
+ fW.noalias() -= LWpG * gas_pressure + LWpC * capillary_pressure +
+ LWT * temperature + MWpG * gas_pressure_dot +
+ MWpC * capillary_pressure_dot + MWT * temperature_dot +
+ MWu * displacement_dot;
+
+ local_Jac.template block<W_size, W_size>(W_index, W_index).noalias() +=
+ LWpC + MWpC / dt;
+ local_Jac.template block<W_size, C_size>(W_index, C_index).noalias() +=
+ LWpG + MWpG / dt;
+ local_Jac
+ .template block<W_size, temperature_size>(W_index, temperature_index)
+ .noalias() += LWT + MWT / dt;
+ local_Jac
+ .template block<W_size, displacement_size>(W_index, displacement_index)
+ .noalias() += MWu / dt;
+
+ // --- Temperature ---
+ // fT_4
+ fT.noalias() -= KTT * temperature + MTu * displacement_dot;
+
+ local_Jac
+ .template block<temperature_size, temperature_size>(temperature_index,
+ temperature_index)
+ .noalias() += KTT;
+ local_Jac
+ .template block<temperature_size, displacement_size>(temperature_index,
+ displacement_index)
+ .noalias() += MTu / dt;
+
+ // --- Displacement ---
+ // fU_2
+ fU.noalias() -= KUpG * gas_pressure + KUpC * capillary_pressure;
+
+ local_Jac
+ .template block<displacement_size, C_size>(displacement_index, C_index)
+ .noalias() += KUpG;
+ local_Jac
+ .template block<displacement_size, W_size>(displacement_index, W_index)
+ .noalias() += KUpC;
}
template <typename ShapeFunctionDisplacement, typename ShapeFunctionPressure,
--
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