[PL/RM] Add microporosity computation.

Used in double porosity structure models.

ProcessLib/RichardsMechanics/ComputeMicroPorosity.h

+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2021, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ */
+
+#pragma once
+
+#include <cassert>
+#include <ostream>
+
+#include "MaterialLib/MPL/Medium.h"
+#include "MaterialLib/MPL/Utils/FormEigenTensor.h"
+#include "MathLib/KelvinVector.h"
+#include "NumLib/NewtonRaphson.h"
+
+namespace ProcessLib::RichardsMechanics
+{
+template <int DisplacementDim>
+struct MicroPorosityStateSpace
+{
+    double phi_m;
+    double e_sw;
+    double p_L_m;
+    MathLib::KelvinVector::KelvinVectorType<DisplacementDim> sigma_sw;
+
+    MicroPorosityStateSpace& operator += (MicroPorosityStateSpace const& state)
+    {
+        phi_m += state.phi_m;
+        e_sw += state.e_sw;
+        p_L_m += state.p_L_m;
+        sigma_sw += state.sigma_sw;
+        return *this;
+    }
+
+    EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
+};
+
+template <int DisplacementDim>
+std::ostream& operator<<(std::ostream& os,
+                         MicroPorosityStateSpace<DisplacementDim> const& state)
+{
+    return os << "phi_m: " << state.phi_m << ", "
+              << "e_sw: " << state.e_sw << ", "
+              << "p_L_m: " << state.p_L_m << ", "
+              << "sigma_sw: " << state.sigma_sw.transpose();
+}
+
+template <int DisplacementDim>
+MicroPorosityStateSpace<DisplacementDim> computeMicroPorosity(
+    MathLib::KelvinVector::KelvinVectorType<DisplacementDim> const&
+        I_2_C_el_inverse,
+    double const rho_LR_m,  // for simplification equal to rho_LR_M
+    double const mu_LR, double const alpha_bar, double const alpha_B,
+    double const phi_M, double const p_L, double const p_L_m_prev,
+    MaterialPropertyLib::VariableArray const& /*variables_prev*/,
+    double const S_L_m_prev, double const phi_m_prev,
+    ParameterLib::SpatialPosition const pos, double const t, double const dt,
+    MaterialPropertyLib::Property const& saturation_micro,
+    MaterialPropertyLib::Property const& swelling_stress_rate)
+{
+    namespace MPL = MaterialPropertyLib;
+    static constexpr int kelvin_vector_size =
+        MathLib::KelvinVector::KelvinVectorDimensions<DisplacementDim>::value;
+    // phi_m, e_sw, p_L_m, sigma_sw
+    static constexpr int nls_size = 1 + 1 + 1 + kelvin_vector_size;
+
+    static constexpr int i_phi_m = 0;
+    static constexpr int i_e_sw = 1;
+    static constexpr int i_p_L_m = 2;
+    static constexpr int i_sigma_sw = 3;
+
+    using ResidualVectorType = Eigen::Matrix<double, nls_size, 1>;
+    using JacobianMatrix =
+        Eigen::Matrix<double, nls_size, nls_size, Eigen::RowMajor>;
+
+    Eigen::FullPivLU<Eigen::Matrix<double, nls_size, nls_size, Eigen::RowMajor>>
+        linear_solver;
+
+    JacobianMatrix jacobian;
+
+    // Agglomerated solution vector construction.
+    ResidualVectorType solution = ResidualVectorType::Zero();
+
+    if (p_L >= 0 && p_L_m_prev >= 0)
+    {
+        return {solution[i_phi_m], solution[i_e_sw], solution[i_p_L_m],
+                solution.template segment<kelvin_vector_size>(i_sigma_sw)};
+    }
+
+    auto const update_residual = [&](ResidualVectorType& residual) {
+        double const delta_phi_m = solution[i_phi_m];
+        double const delta_e_sw = solution[i_e_sw];
+        auto const& delta_sigma_sw =
+            solution.template segment<kelvin_vector_size>(i_sigma_sw);
+        double const delta_p_L_m = solution[i_p_L_m];
+
+        double const phi_m = phi_m_prev + delta_phi_m;
+        double const p_L_m = p_L_m_prev + delta_p_L_m;
+        MPL::VariableArray variables_prev;
+        variables_prev[static_cast<int>(MPL::Variable::capillary_pressure)] =
+            -p_L_m_prev;
+        variables_prev[static_cast<int>(MPL::Variable::liquid_saturation)] =
+            S_L_m_prev;
+
+        MPL::VariableArray variables;
+        variables[static_cast<int>(MPL::Variable::capillary_pressure)] = -p_L_m;
+
+        double const S_L_m =
+            saturation_micro.template value<double>(variables, pos, t, dt);
+        variables[static_cast<int>(MPL::Variable::liquid_saturation)] = S_L_m;
+        double const delta_S_L_m = S_L_m - S_L_m_prev;
+
+
+        auto const sigma_sw_dot =
+            MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
+                swelling_stress_rate.template value<Eigen::Matrix3d>(
+                    variables, variables_prev, pos, t, dt));
+
+        residual[i_phi_m] = delta_phi_m - (alpha_B - phi_M) * delta_e_sw;
+        residual[i_e_sw] = delta_e_sw + I_2_C_el_inverse.dot(delta_sigma_sw);
+        residual.template segment<kelvin_vector_size>(i_sigma_sw).noalias() =
+            delta_sigma_sw - sigma_sw_dot * dt;
+
+        residual[i_p_L_m] =
+            rho_LR_m *
+                (phi_m * delta_S_L_m - (alpha_B - phi_M) * S_L_m * delta_e_sw) +
+            phi_m * S_L_m * rho_LR_m * delta_e_sw -
+            alpha_bar / mu_LR * (p_L - p_L_m) * dt;
+    };
+
+    auto const update_jacobian = [&](JacobianMatrix& jacobian) {
+        jacobian = JacobianMatrix::Identity();
+
+        double const delta_phi_m = solution[i_phi_m];
+        double const delta_e_sw = solution[i_e_sw];
+        double const delta_p_L_m = solution[i_p_L_m];
+
+        double const phi_m = phi_m_prev + delta_phi_m;
+        double const p_L_m = p_L_m_prev + delta_p_L_m;
+        MPL::VariableArray variables_prev;
+        variables_prev[static_cast<int>(MPL::Variable::capillary_pressure)] =
+            -p_L_m_prev;
+        MPL::VariableArray variables;
+        variables[static_cast<int>(MPL::Variable::capillary_pressure)] = -p_L_m;
+
+        double const S_L_m =
+            saturation_micro.template value<double>(variables, pos, t, dt);
+        variables_prev[static_cast<int>(MPL::Variable::liquid_saturation)] =
+            S_L_m_prev;
+        variables[static_cast<int>(MPL::Variable::liquid_saturation)] = S_L_m;
+        double const delta_S_L_m = S_L_m - S_L_m_prev;
+
+        double const dS_L_m_dp_cap_m = saturation_micro.template dValue<double>(
+            variables, MPL::Variable::capillary_pressure, pos, t, dt);
+        auto const dsigma_sw_dS_L_m =
+            MathLib::KelvinVector::tensorToKelvin<DisplacementDim>(
+                swelling_stress_rate.template dValue<Eigen::Matrix3d>(
+                    variables, variables_prev, MPL::Variable::liquid_saturation,
+                    pos, t, dt));
+
+        jacobian(i_phi_m, i_e_sw) = -(alpha_B - phi_M);
+
+        jacobian.template block<1, kelvin_vector_size>(i_e_sw, i_sigma_sw) =
+            I_2_C_el_inverse.transpose();
+
+        jacobian.template block<kelvin_vector_size, 1>(
+            i_sigma_sw, i_p_L_m) = -dsigma_sw_dS_L_m * dS_L_m_dp_cap_m;
+
+
+        jacobian(i_p_L_m, i_phi_m) =
+            rho_LR_m * (delta_S_L_m + phi_m * delta_e_sw);
+
+        jacobian(i_p_L_m, i_e_sw) = -rho_LR_m * S_L_m * (alpha_B - phi_M - phi_m);
+
+        jacobian(i_p_L_m, i_p_L_m) =
+            alpha_bar / mu_LR * dt -
+            rho_LR_m * (phi_m - (alpha_B - phi_M - phi_m) * delta_e_sw) *
+                dS_L_m_dp_cap_m;
+    };
+
+    auto const update_solution = [&](ResidualVectorType const& increment) {
+        solution += increment;
+    };
+
+    static const NumLib::NewtonRaphsonSolverParameters
+        nonlinear_solver_parameters{1000, 1e-8, 1e-15};
+
+    auto newton_solver =
+        NumLib::NewtonRaphson<decltype(linear_solver), JacobianMatrix,
+                              decltype(update_jacobian), ResidualVectorType,
+                              decltype(update_residual),
+                              decltype(update_solution)>(
+            linear_solver, update_jacobian, update_residual, update_solution,
+            nonlinear_solver_parameters);
+
+    auto const success_iterations = newton_solver.solve(jacobian);
+
+    if (!success_iterations)
+    {
+        OGS_FATAL(
+            "Could not find solution for local double structure nonlinear "
+            "problem.");
+    }
+
+    return {solution[i_phi_m], solution[i_e_sw], solution[i_p_L_m],
+            solution.template segment<kelvin_vector_size>(i_sigma_sw)};
+}
+}  // namespace ProcessLib::RichardsMechanics