From e6cd01102ee1f128f7f08b1915853cd7cc56570d Mon Sep 17 00:00:00 2001 From: umairhussaincmm Date: Wed, 3 Jul 2024 12:14:22 +0530 Subject: [PATCH] Add the 'Crystal_Growth_Phase_Field_Model' code gallery program. --- .../.cmake/api/v1/query/cache-v2 | 0 .../.cmake/api/v1/query/cmakeFiles-v1 | 0 .../.cmake/api/v1/query/codemodel-v2 | 0 .../.cmake/api/v1/query/toolchains-v1 | 0 .../reply/cache-v2-7d83443b2a5f6aabcad4.json | 1199 + .../cmakeFiles-v1-456e948a93672ae952f4.json | 752 + .../codemodel-v2-d170913d9a2a93130cd2.json | 122 + .../reply/index-2024-07-02T10-37-33-0866.json | 92 + ...i_Parallel-Debug-44a3edf76a0b1d6ce63e.json | 909 + ...rget-debug-Debug-437935d3bee2b5247a4b.json | 74 + ...-distclean-Debug-c7bb04d03470732a1bf6.json | 74 + ...arget-info-Debug-674f5ad97c283606d33a.json | 74 + ...et-release-Debug-369c002c3664eeb6fab0.json | 74 + ...target-run-Debug-4e9e7476fde444444aa7.json | 80 + ...t-runclean-Debug-00d511f9b7de392a16ba.json | 74 + 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a/Crystal_Growth_Phase_Field_Model/.idea/Crystal_Growth_Phase_Field_Model.iml b/Crystal_Growth_Phase_Field_Model/.idea/Crystal_Growth_Phase_Field_Model.iml new file mode 100644 index 0000000..f08604b --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/.idea/Crystal_Growth_Phase_Field_Model.iml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/Crystal_Growth_Phase_Field_Model/.idea/misc.xml b/Crystal_Growth_Phase_Field_Model/.idea/misc.xml new file mode 100644 index 0000000..0b76fe5 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/.idea/misc.xml @@ -0,0 +1,7 @@ + + + + + + \ No newline at end of file diff --git a/Crystal_Growth_Phase_Field_Model/.idea/modules.xml b/Crystal_Growth_Phase_Field_Model/.idea/modules.xml new file mode 100644 index 0000000..8183506 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/.idea/modules.xml @@ -0,0 +1,8 @@ + + + + + + + + \ No newline at end of file diff --git a/Crystal_Growth_Phase_Field_Model/.idea/vcs.xml 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recent) version of deal.II. ***\n\n" + "You may want to either pass a flag -DDEAL_II_DIR=/path/to/deal.II to cmake\n" + "or set an environment variable \"DEAL_II_DIR\" that contains this path." + ) +ENDIF() + +DEAL_II_INITIALIZE_CACHED_VARIABLES() +PROJECT(${TARGET}) +DEAL_II_INVOKE_AUTOPILOT() diff --git a/Crystal_Growth_Phase_Field_Model/InitialValues.cpp b/Crystal_Growth_Phase_Field_Model/InitialValues.cpp new file mode 100644 index 0000000..64a3948 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/InitialValues.cpp @@ -0,0 +1,8 @@ +#include "PhaseFieldSolver.h" + +void InitialValues::vector_value(const Point<2> &p, + Vector & values) const +{ + values(0)= 0.0; //Initial p value of domain + values(1)= 0.2; //Initial temperature of domain +} diff --git a/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.cpp b/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.cpp new file mode 100644 index 0000000..3e59527 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.cpp @@ -0,0 +1,21 @@ +#include "PhaseFieldSolver.h" + +PhaseFieldSolver::PhaseFieldSolver() +: mpi_communicator(MPI_COMM_WORLD) +, n_mpi_processes(Utilities::MPI::n_mpi_processes(mpi_communicator)) +, this_mpi_process(Utilities::MPI::this_mpi_process(mpi_communicator)) +, pcout(std::cout, (this_mpi_process == 0)) +, fe(FE_Q<2>(1), 2) +, dof_handler(triangulation) +, time(0.0) +, final_time(1.) +, time_step(.0002) +, theta(0.5) +, epsilon(0.01) +, tau(0.0003) +, gamma(10.) +, latent_heat(1.4) +, alpha(0.9) +, t_eq(1.) +, a(0.01) +{} diff --git a/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.h b/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.h new file mode 100644 index 0000000..e6a4dd5 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/PhaseFieldSolver.h @@ -0,0 +1,94 @@ +#ifndef KOBAYASHI_PARALLEL_PHASEFIELDSOLVER_H +#define KOBAYASHI_PARALLEL_PHASEFIELDSOLVER_H + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + +//For Parallel Computation +#include +#include +#include +#include +#include +#include +#include +#include + +#include + +#include +#include + +using namespace dealii; + +class PhaseFieldSolver { +public: + PhaseFieldSolver(); + void run(); + +private: + void make_grid_and_dofs(); + void assemble_system(); + void solve(); + void output_results(const unsigned int timestep_number) const; + double compute_residual(); + void applying_bc(); + float get_random_number(); + + MPI_Comm mpi_communicator; + const unsigned int n_mpi_processes; + const unsigned int this_mpi_process; + ConditionalOStream pcout; + + Triangulation<2> triangulation; + FESystem<2> fe; + DoFHandler<2> dof_handler; + GridIn<2> gridin; + + PETScWrappers::MPI::SparseMatrix jacobian_matrix; + + double time; + const double final_time, time_step; + const double theta; + const double epsilon, tau, gamma, latent_heat, alpha, t_eq, a; //as given in Ref. [1] + + PETScWrappers::MPI::Vector conv_solution; //solution vector at last newton-raphson iteration + PETScWrappers::MPI::Vector old_solution; //solution vector at last time step + PETScWrappers::MPI::Vector solution_update; //increment in solution or delta solution + PETScWrappers::MPI::Vector system_rhs; //to store residual + Vector conv_solution_np, old_solution_np; //creating non parallel vectors to store data for easy access of old solution values by all processes + +}; + +// Initial values class +class InitialValues : public Function<2> +{ +public: + InitialValues(): Function<2>(2) + {} + virtual void vector_value(const Point<2> &p, + Vector & value) const override; +}; + + +#endif //KOBAYASHI_PARALLEL_PHASEFIELDSOLVER_H diff --git a/Crystal_Growth_Phase_Field_Model/README.md b/Crystal_Growth_Phase_Field_Model/README.md new file mode 100644 index 0000000..57840dc --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/README.md @@ -0,0 +1,42 @@ +Crystal solidification using phase field modeling +------------------------------------------ +### Overview +This code solves the solidification problem based in the famous work by Ryo Kobayashi (1993) [1]. +The model is based on the Allen-Cahn [2] phase field equation coupled with the transient heat +equation Though we have covered only the isotropic directional solidification from the paper in the +results, the same code can be modified and used for other types of solidification problems. Let us +quickly go through the governing equations and the boundary conditions solved in this problem. + +### Problem Definition +@f{align*}{ +\tau \frac{\partial p}{\partial t} = \nabla \cdot( \left(\epsilon^2\right)\nabla p) + p(1-p)(p-\frac{1}{2}+m) \label{heateq} \\ +\frac{\partial T}{\partial t}=\nabla^2T+K\frac{\partial p}{\partial t} +@f} +where $m(t) = \frac{a}{\pi}\tan^{-1}(\gamma(T_e-T))$ + +The problem is subjected to the boundary conditions: +@f{align*}{ +p(0,y,t)= 1 \\ +T(0,y,t)= T_\gamma -\Delta T +@f} +and the initial conditions: +@f{align*}{ +p(x,y,0)= 0 \\ +T(x,y,0)= T_\gamma -\Delta T +@f} +Here, $\Delta T$ is the degree of undercooling. + +### Dendritic Growth +Using this code, we have reproduced one of the study from Koabayashi's work regarding the dendritic +behaviour during directional solidification. The latent heat parameter 'K' in the equation determines +the amount of heat released as the phase solidifies. If this value is high enough, we would observe an +unstable interface between the solid and liquid phase, which would lead to the formation of dendrites +as shown in these images. To assist this growth we need to add a random perterbation term +'$a \chi p (1-p)$' to the dynamic term of the phase field equation. + +![Screenshot](./doc/images/K=1v1.2v1.4.gif) + +### References +[1] Kobayashi, R. (1993). Modeling and numerical simulations of dendritic crystal growth. Physica D: Nonlinear Phenomena, 63(3–4), 410–423. https://doi.org/10.1016/0167-2789(93)90120-P + +[2] Allen, S. M., & Cahn, J. W. (1979). A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metallurgica, 27(6), 1085–1095. https://doi.org/10.1016/0001-6160(79)90196-2 diff --git a/Crystal_Growth_Phase_Field_Model/applying_bc.cpp b/Crystal_Growth_Phase_Field_Model/applying_bc.cpp new file mode 100644 index 0000000..b111f3d --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/applying_bc.cpp @@ -0,0 +1,29 @@ +#include "PhaseFieldSolver.h" + +void PhaseFieldSolver::applying_bc(){ + FEValuesExtractors::Scalar phase_parameter(0); + FEValuesExtractors::Scalar temperature(1); + + QGauss<2> quadrature_formula(fe.degree + 1); + FEValues<2> fe_values(fe, + quadrature_formula, + update_values | update_gradients | update_JxW_values); + + ComponentMask p_mask = fe.component_mask(phase_parameter); + ComponentMask t_mask = fe.component_mask(temperature); + + std::map boundary_values; + + // Prescribing p=1 at the left face (this will be maintained in the subsequent iterations when zero BC is applied in the Newton-Raphson iterations) + VectorTools::interpolate_boundary_values (dof_handler, + 1, + ConstantFunction<2>(1., 2), + boundary_values,p_mask); + + // To apply the boundary values only to the solution vector without the Jacobian Matrix and RHS Vector + for (auto &boundary_value : boundary_values) + old_solution(boundary_value.first) = boundary_value.second; + + old_solution.compress(VectorOperation::insert); + +} diff --git a/Crystal_Growth_Phase_Field_Model/assemble_system.cpp b/Crystal_Growth_Phase_Field_Model/assemble_system.cpp new file mode 100644 index 0000000..695c510 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/assemble_system.cpp @@ -0,0 +1,165 @@ +// +// Created by ubuntu on 1/23/21. +// + +#include "PhaseFieldSolver.h" +#include + +void PhaseFieldSolver::assemble_system() { + //Separating each variable as a scalar to easily call the respective shape functions + FEValuesExtractors::Scalar phase_parameter(0); + FEValuesExtractors::Scalar temperature(1); + + QGauss<2> quadrature_formula(fe.degree + 1); + FEValues<2> fe_values(fe, + quadrature_formula, + update_values | update_gradients | update_JxW_values); + + const unsigned int dofs_per_cell = fe.n_dofs_per_cell(); + const unsigned int n_q_points = quadrature_formula.size(); + FullMatrix cell_matrix(dofs_per_cell, dofs_per_cell); + + Vector cell_rhs(dofs_per_cell); + + //To copy values and gradients of solution from previous iteration + //Old Newton iteration + std::vector> old_newton_solution_gradients_p(n_q_points); + std::vector old_newton_solution_values_p(n_q_points); + std::vector> old_newton_solution_gradients_t(n_q_points); + std::vector old_newton_solution_values_t(n_q_points); + //Old time step iteration + std::vector> old_time_solution_gradients_p(n_q_points); + std::vector old_time_solution_values_p(n_q_points); + std::vector> old_time_solution_gradients_t(n_q_points); + std::vector old_time_solution_values_t(n_q_points); + + std::vector local_dof_indices(dofs_per_cell); + jacobian_matrix.operator=(0.0); + system_rhs.operator=(0.0); + + for (const auto &cell : dof_handler.active_cell_iterators()){ + if (cell->subdomain_id() == this_mpi_process) { + cell_matrix = 0; + cell_rhs = 0; + + fe_values.reinit(cell); + + //Copying old solution values + fe_values[phase_parameter].get_function_values(conv_solution_np,old_newton_solution_values_p); + fe_values[phase_parameter].get_function_gradients(conv_solution_np,old_newton_solution_gradients_p); + fe_values[temperature].get_function_values(conv_solution_np,old_newton_solution_values_t); + fe_values[temperature].get_function_gradients(conv_solution_np,old_newton_solution_gradients_t); + fe_values[phase_parameter].get_function_values(old_solution_np,old_time_solution_values_p); + fe_values[phase_parameter].get_function_gradients(old_solution_np,old_time_solution_gradients_p); + fe_values[temperature].get_function_values(old_solution_np,old_time_solution_values_t); + fe_values[temperature].get_function_gradients(old_solution_np,old_time_solution_gradients_t); + + for (unsigned int q = 0; q < n_q_points; ++q){ + double khi = get_random_number(); + //Old solution values + double p_on = old_newton_solution_values_p[q]; //old newton solution + auto grad_p_on = old_newton_solution_gradients_p[q]; + double p_ot = old_time_solution_values_p[q]; //old time step solution + auto grad_p_ot = old_time_solution_gradients_p[q]; + double t_on = old_newton_solution_values_t[q]; + auto grad_t_on = old_newton_solution_gradients_t[q]; + double t_ot = old_time_solution_values_t[q]; + auto grad_t_ot = old_time_solution_gradients_t[q]; + for (unsigned int i = 0; i < dofs_per_cell; ++i){ + //Shape Functions + double psi_i = fe_values[phase_parameter].value(i,q); + auto grad_psi_i = fe_values[phase_parameter].gradient(i,q); + double phi_i = fe_values[temperature].value(i,q); + auto grad_phi_i = fe_values[temperature].gradient(i,q); + for (unsigned int j = 0; j < dofs_per_cell; ++j){ + //Shape Functions + double psi_j = fe_values[phase_parameter].value(j,q); + auto grad_psi_j = fe_values[phase_parameter].gradient(j,q); + double phi_j = fe_values[temperature].value(j,q); + auto grad_phi_j = fe_values[temperature].gradient(j,q); + + double mp = psi_i*(tau*psi_j); + double kp = grad_psi_i*(std::pow(epsilon,2)*grad_psi_j); + double m = (alpha/M_PI)*std::atan(gamma*(t_eq - t_on)); + double t1 = (1-p_on)*(p_on-0.5+m); + double t2 = -(p_on)*(p_on-0.5+m); + double t3 = (p_on)*(1-p_on); + double nl_p = psi_i*((t1+t2+t3)*psi_j); + //Adding random noise at the interface + nl_p -= a*khi*psi_i*((1.0 - 2*(p_on))*psi_j); + double f1_p= mp + time_step*theta*kp - time_step*theta*nl_p; // doh f1 by doh p (first Jacobian terms) + + double t4 = (p_on)*(1-p_on)*(-(alpha*gamma/(M_PI*(1+std::pow((gamma*(t_eq-t_on)),2))))); + double nl_t = psi_i*(t4*phi_j); + double f1_t = -time_step*theta*nl_t; // doh f1 by doh t (second Jacobian terms) + + double mpt = phi_i*(latent_heat*psi_j); + double f2_p = -mpt; // doh f2 by doh p (third Jacobian terms) + + double mt = phi_i*(phi_j); + double kt = grad_phi_i*(grad_phi_j); + double f2_t = mt + time_step*theta*kt; // doh f2 by doh t (fourth Jacobian terms) + + //Assembling Jacobian matrix + cell_matrix(i,j) += (f1_p + f1_t + f2_p + f2_t)*fe_values.JxW(q); + + } + //Finding f1 and f2 at previous iteration for rhs vector + double mp_n = psi_i*(tau*p_on); + double kp_n = grad_psi_i*(std::pow(epsilon,2)*grad_p_on); + double m_n = (alpha/M_PI)*std::atan(gamma*(t_eq-t_on)); + double nl_n = psi_i*((p_on)*(1-p_on)*(p_on-0.5+m_n)); + double mp_t = psi_i*(tau*p_ot); + double kp_t = grad_psi_i*(tau*grad_p_ot); + double m_t = (alpha/M_PI)*std::atan(gamma*(t_eq-t_ot)); + double nl_t = psi_i*(p_ot)*(1-p_ot)*(p_ot-0.5+m_t); + //Adding random noise at the interface + nl_n -= psi_i*(a*khi*(p_on)*(1-p_on)); + nl_t -= psi_i*(a*khi*(p_ot)*(1-p_ot)); + + double f1n = mp_n + time_step*theta*kp_n - time_step*theta*nl_n - mp_t + time_step*(1-theta)*kp_t - time_step*(1-theta)*nl_t; //f1 at last newton iteration + + double mt_n = phi_i*(t_on); + double kt_n = grad_phi_i*(grad_t_on); + double mpt_n = phi_i*(latent_heat*p_on); + double mt_t = phi_i*(t_ot); + double kt_t = grad_phi_i*(grad_t_ot); + double mpt_t = phi_i*(latent_heat*p_ot); + + double f2n = mt_n + time_step*theta*kt_n - mpt_n - mt_t + time_step*(1-theta)*kt_t + mpt_t; //f2 at last newton iteration + + //Assembling RHS vector + cell_rhs(i) -= (f1n + f2n)*fe_values.JxW(q); + } + } + + cell->get_dof_indices(local_dof_indices); + for (unsigned int i = 0; i < dofs_per_cell; ++i) + { + for (unsigned int j = 0; j < dofs_per_cell; ++j) + jacobian_matrix.add(local_dof_indices[i], + local_dof_indices[j], + cell_matrix(i, j)); + system_rhs(local_dof_indices[i]) += cell_rhs(i); + } + } + } + + jacobian_matrix.compress(VectorOperation::add); + system_rhs.compress(VectorOperation::add); + + //Applying zero BC + std::map boundary_values; + VectorTools::interpolate_boundary_values(dof_handler, + 1, + Functions::ZeroFunction<2>(2), + boundary_values); + MatrixTools::apply_boundary_values(boundary_values, + jacobian_matrix, + solution_update, + system_rhs, false); + + jacobian_matrix.compress(VectorOperation::insert); + + system_rhs.compress(VectorOperation::insert); +} diff --git a/Crystal_Growth_Phase_Field_Model/doc/author b/Crystal_Growth_Phase_Field_Model/doc/author new file mode 100644 index 0000000..1664ae4 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/doc/author @@ -0,0 +1 @@ +Umair Hussain diff --git a/Crystal_Growth_Phase_Field_Model/doc/builds-on b/Crystal_Growth_Phase_Field_Model/doc/builds-on new file mode 100644 index 0000000..248ace4 --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/doc/builds-on @@ -0,0 +1 @@ +step-15 step-17 step-23 diff --git a/Crystal_Growth_Phase_Field_Model/doc/dependencies b/Crystal_Growth_Phase_Field_Model/doc/dependencies new file mode 100644 index 0000000..c77076f --- /dev/null +++ b/Crystal_Growth_Phase_Field_Model/doc/dependencies @@ -0,0 +1 @@ +DEAL_II_WITH_CXX11 DEAL_II_WITH_MPI 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