time_refinement_study.cpp

#include "time_refinement_study.h"
#include "flow_solver/flow_solver_factory.h"
#include "flow_solver/flow_solver_cases/periodic_1D_unsteady.h"
#include "flow_solver/flow_solver_cases/periodic_entropy_tests.h"
#include "physics/exact_solutions/exact_solution.h"
#include "cmath"
//#include "ode_solver/runge_kutta_ode_solver.h"

namespace PHiLiP {
namespace Tests {

template <int dim, int nstate>
TimeRefinementStudy<dim, nstate>::TimeRefinementStudy(
        const PHiLiP::Parameters::AllParameters *const parameters_input,
        const dealii::ParameterHandler &parameter_handler_input)  
        : TestsBase::TestsBase(parameters_input),
         parameter_handler(parameter_handler_input),
         n_time_calculations(parameters_input->time_refinement_study_param.number_of_times_to_solve),
         refine_ratio(parameters_input->time_refinement_study_param.refinement_ratio)
{}



template <int dim, int nstate>
Parameters::AllParameters TimeRefinementStudy<dim,nstate>::reinit_params_and_refine_timestep(int refinement) const
{
    PHiLiP::Parameters::AllParameters parameters = *(this->all_parameters);

    parameters.ode_solver_param.initial_time_step *= pow(refine_ratio,refinement);

    //For RRK, do not end at exact time because of how relaxation parameter convergence is calculated
    using ODESolverEnum = Parameters::ODESolverParam::ODESolverEnum;
    if (parameters.ode_solver_param.ode_solver_type == ODESolverEnum::rrk_explicit_solver){
        parameters.flow_solver_param.end_exactly_at_final_time = false;
    }

    return parameters;
}

template <int dim, int nstate>
double TimeRefinementStudy<dim,nstate>::calculate_Lp_error_at_final_time_wrt_function(std::shared_ptr<DGBase<dim,double>> dg, const Parameters::AllParameters parameters, double final_time, int norm_p) const
{
    //generate exact solution at final time
    std::shared_ptr<ExactSolutionFunction<dim,nstate,double>> exact_solution_function;
    exact_solution_function = ExactSolutionFactory<dim,nstate,double>::create_ExactSolutionFunction(parameters.flow_solver_param, final_time);
    this->pcout << "End time: " << final_time << std::endl;
    double Lp_error=0;
    int overintegrate = 10;

    int poly_degree = parameters.grid_refinement_study_param.poly_degree;
    dealii::Vector<double> difference_per_cell(dg->solution.size());

    dealii::VectorTools::NormType norm_type;
    if (norm_p == 1)       norm_type = dealii::VectorTools::L1_norm;
    else if (norm_p == 2)  norm_type = dealii::VectorTools::L2_norm;
    else if (norm_p<0)     norm_type = dealii::VectorTools::Linfty_norm;
    else {
        pcout << "Norm not defined. Aborting... " << std::endl;
        std::abort();
    }

    dealii::VectorTools::integrate_difference(dg->dof_handler,    
                                              dg->solution,
                                              *exact_solution_function,
                                              difference_per_cell,
                                              dealii::QGauss<dim>(poly_degree + overintegrate), //overintegrating
                                              norm_type);
    Lp_error = dealii::VectorTools::compute_global_error(*dg->triangulation,
                                                              difference_per_cell,
                                                              norm_type);
    return Lp_error;    
}

template <int dim, int nstate>
int TimeRefinementStudy<dim, nstate>::run_test() const
{
    
    const double final_time = this->all_parameters->flow_solver_param.final_time;
    const double initial_time_step = this->all_parameters->ode_solver_param.initial_time_step;
    const int n_steps = floor(final_time/initial_time_step);
    if (n_steps * initial_time_step != final_time){
        pcout << "WARNING: final_time is not evenly divisible by initial_time_step!" << std::endl
              << "Remainder is " << fmod(final_time, initial_time_step)
              << ". Consider modifying parameters." << std::endl;
    }

    int testfail = 0;

    dealii::ConvergenceTable convergence_table;
    double L2_error_old = 0;
    double L2_error_conv_rate=0;

    for (int refinement = 0; refinement < n_time_calculations; ++refinement){
        
        pcout << "\n\n---------------------------------------------" << std::endl;
        pcout << "Refinement number " << refinement << " of " << n_time_calculations - 1 << std::endl;
        pcout << "---------------------------------------------" << std::endl;

        const Parameters::AllParameters params = reinit_params_and_refine_timestep(refinement);
        std::unique_ptr<FlowSolver::FlowSolver<dim,nstate>> flow_solver = FlowSolver::FlowSolverFactory<dim,nstate>::select_flow_case(&params, parameter_handler);
        static_cast<void>(flow_solver->run());
        
        pcout << "Finished flowsolver " << std::endl;

        const double final_time_actual = flow_solver->ode_solver->current_time;
        
        //check Lp error
        const double L1_error = calculate_Lp_error_at_final_time_wrt_function(flow_solver->dg, params,final_time_actual, 1);
        const double L2_error = calculate_Lp_error_at_final_time_wrt_function(flow_solver->dg, params,final_time_actual, 2);
        const double Linfty_error = calculate_Lp_error_at_final_time_wrt_function(flow_solver->dg, params,final_time_actual, -1);
        pcout << "Computed errors are: " << std::endl
              << "    L1:      " << L1_error << std::endl
              << "    L2:      " << L2_error << std::endl
              << "    Linfty:  " << Linfty_error << std::endl;

        const double dt =  params.ode_solver_param.initial_time_step;
        const int n_timesteps= flow_solver->ode_solver->current_iteration;
        pcout << " at dt = " << dt << std::endl;


        if (this->all_parameters->ode_solver_param.runge_kutta_method == PHiLiP::Parameters::ODESolverParam::RK3_2_5F_3SStarPlus 
            && this->all_parameters->ode_solver_param.atol == 1e-4 && this->all_parameters->ode_solver_param.rtol == 1e-4 
            && this->all_parameters->time_refinement_study_param.number_of_times_to_solve == 1){
            double L2_error_expected = 2.14808703658e-5; 
            pcout << " Expected L2 error is: " << L2_error_expected << std::endl;
            if (L2_error > L2_error_expected + 1e-9 || L2_error < L2_error_expected - 1e-9){
                testfail = 1;
                pcout << "Expected L2 error for RK3(2)5F[3S*+] using an atol = rtol = 1e-4 was not reached " << refinement <<std::endl;
            }
        }
        
        convergence_table.add_value("refinement", refinement);
        convergence_table.add_value("dt", dt );
        convergence_table.set_precision("dt", 16);
        convergence_table.set_scientific("dt", true);
        convergence_table.add_value("L1_error",L1_error);
        convergence_table.set_precision("L1_error", 16);
        convergence_table.evaluate_convergence_rates("L1_error", "dt", dealii::ConvergenceTable::reduction_rate_log2, 1);
        convergence_table.add_value("L2_error",L2_error);
        convergence_table.set_precision("L2_error", 16);
        convergence_table.evaluate_convergence_rates("L2_error", "dt", dealii::ConvergenceTable::reduction_rate_log2, 1);
        convergence_table.add_value("Linfty_error",Linfty_error);
        convergence_table.set_precision("Linfty_error", 16);
        convergence_table.evaluate_convergence_rates("Linfty_error", "dt", dealii::ConvergenceTable::reduction_rate_log2, 1);
        
        using ODESolverEnum = Parameters::ODESolverParam::ODESolverEnum;
        if(params.ode_solver_param.ode_solver_type == ODESolverEnum::rrk_explicit_solver){
            //for burgers, this is the average gamma over the runtime
            const double gamma_aggregate_m1 = final_time_actual / (n_timesteps * dt)-1;
            convergence_table.add_value("gamma_aggregate_m1", gamma_aggregate_m1);
            convergence_table.set_precision("gamma_aggregate_m1", 16);
            convergence_table.set_scientific("gamma_aggregate_m1", true);
            convergence_table.evaluate_convergence_rates("gamma_aggregate_m1", "dt", dealii::ConvergenceTable::reduction_rate_log2, 1);
        }
 
        //Checking convergence order
        const double expected_order = params.ode_solver_param.rk_order;
        const double order_tolerance = 0.1;
        if (refinement > 0) {
            L2_error_conv_rate = -log(L2_error_old/L2_error)/log(refine_ratio);
            pcout << "L2 order at " << refinement << " is " << L2_error_conv_rate << std::endl;
            if (abs(L2_error_conv_rate - expected_order) > order_tolerance){
                testfail = 1;
                pcout << "Expected convergence order was not reached at refinement " << refinement <<std::endl;
            }
           
            // output current time refinement results to console 
            if (refinement < n_time_calculations-1 && pcout.is_active()) convergence_table.write_text(pcout.get_stream());
        }
        L2_error_old = L2_error;
    }

    //Printing and writing convergence table
    pcout << std::endl;
    if (pcout.is_active()) convergence_table.write_text(pcout.get_stream());

    std::ofstream conv_tab_file;
    const std::string fname = "temporal_convergence_table.txt";
    conv_tab_file.open(fname);
    convergence_table.write_text(conv_tab_file);
    conv_tab_file.close();

    return testfail;
}

#if PHILIP_DIM==1
    template class TimeRefinementStudy<PHILIP_DIM,PHILIP_DIM>;
#endif
} // Tests namespace
} // PHiLiP namespace