time_refinement_study_reference.cpp

#include "time_refinement_study_reference.h"
#include "flow_solver/flow_solver_factory.h"
#include "flow_solver/flow_solver_cases/periodic_1D_unsteady.h"
#include "cmath"

namespace PHiLiP {
namespace Tests {

template <int dim, int nstate>
TimeRefinementStudyReference<dim, nstate>::TimeRefinementStudyReference(
        const PHiLiP::Parameters::AllParameters *const parameters_input,
        const dealii::ParameterHandler &parameter_handler_input)  
        : GeneralRefinementStudy<dim,nstate>(parameters_input, parameter_handler_input,
                GeneralRefinementStudy<dim,nstate>::RefinementType::timestep)  
        , reference_solution(this->calculate_reference_solution(parameters_input->flow_solver_param.final_time))
{}

template <int dim, int nstate>
Parameters::AllParameters TimeRefinementStudyReference<dim,nstate>::reinit_params_for_reference_solution(const int number_of_timesteps, const double final_time) const
{
    PHiLiP::Parameters::AllParameters parameters = *(this->all_parameters);

    const double dt = final_time/number_of_timesteps;     
    parameters.ode_solver_param.initial_time_step = dt;
    
    parameters.flow_solver_param.final_time = final_time;

    parameters.flow_solver_param.end_exactly_at_final_time = true;

    //Change to RK because at small dt RRK is more costly but doesn't impact solution much
    using ODESolverEnum = Parameters::ODESolverParam::ODESolverEnum;
    parameters.ode_solver_param.ode_solver_type = ODESolverEnum::runge_kutta_solver;

    this->pcout << "Using timestep size dt = " << dt << " for reference solution." << std::endl;

    return parameters;
}

template <int dim, int nstate>
dealii::LinearAlgebra::distributed::Vector<double> TimeRefinementStudyReference<dim,nstate>::calculate_reference_solution(
        const double final_time) const
{
    const int number_of_timesteps_for_reference_solution = this->all_parameters->time_refinement_study_param.number_of_timesteps_for_reference_solution;
    const Parameters::AllParameters params_reference = reinit_params_for_reference_solution(number_of_timesteps_for_reference_solution, final_time);
    std::unique_ptr<FlowSolver::FlowSolver<dim,nstate>> flow_solver_reference = FlowSolver::FlowSolverFactory<dim,nstate>::select_flow_case(&params_reference, this->parameter_handler);
    static_cast<void>(flow_solver_reference->run());
    
    this->pcout << "   Actual final time: " << flow_solver_reference->ode_solver->current_time << std::endl;

    return flow_solver_reference->dg->solution;
}

template <int dim, int nstate>
double TimeRefinementStudyReference<dim,nstate>::calculate_L2_error_at_final_time_wrt_reference(
            std::shared_ptr<DGBase<dim,double>> dg,
            const Parameters::AllParameters parameters, 
            const double final_time_actual
            ) const
{
    const double final_time_target = parameters.flow_solver_param.final_time;

    if (abs(final_time_target-final_time_actual)<1E-13){
        
        this->pcout << "Comparing to reference solution at target final_time = " << final_time_target << " ..."  << std::endl;

        //calculate L2 norm of error
        dealii::LinearAlgebra::distributed::Vector<double> cellwise_difference(this->reference_solution); 
        cellwise_difference.add(-1.0, dg->solution);
        const double L2_error = cellwise_difference.l2_norm();
        return L2_error;
    }else{
        //recompute reference solution at actual end time
        //intended to be used when using ode_solver = rrk_explicit_solver

        this->pcout << "    -------------------------------------------------------" << std::endl;
        this->pcout << "    Calculating reference solution at actual final_time = " << final_time_actual << " ..."<<std::endl;
        this->pcout << "    -------------------------------------------------------" << std::endl;
        const dealii::LinearAlgebra::distributed::Vector<double> reference_solution_actual = calculate_reference_solution(final_time_actual);

        dealii::LinearAlgebra::distributed::Vector<double> cellwise_difference(reference_solution_actual); 
        cellwise_difference.add(-1.0, dg->solution);
        const double L2_error = cellwise_difference.l2_norm();
        return L2_error;
    }
    
}

template <int dim, int nstate>
std::tuple<double,int> TimeRefinementStudyReference<dim,nstate>::process_and_write_conv_tables(std::shared_ptr<FlowSolver::FlowSolver<dim,nstate>> flow_solver, 
            const Parameters::AllParameters params, 
            double L2_error_old, 
            std::shared_ptr<dealii::ConvergenceTable> convergence_table,
            int refinement,
            const double expected_order) const
{
    int testfail = 0;

    //pointer to flow_solver_case for computing energy
    std::unique_ptr<FlowSolver::Periodic1DUnsteady<dim, nstate>> flow_solver_case = std::make_unique<FlowSolver::Periodic1DUnsteady<dim,nstate>>(this->all_parameters);
    if (params.flow_solver_param.flow_case_type != Parameters::FlowSolverParam::FlowCaseType::periodic_1D_unsteady){
        this->pcout << "ERROR: the TimeRefinementStudyReference class is currently only valid " << std::endl
                    << "for flow_case_type = periodic_1D_unsteady. Aborting..." << std::endl;
        std::abort();
    }
    const double energy_initial = flow_solver_case->compute_energy(flow_solver->dg);
    const double final_time_actual = flow_solver->ode_solver->current_time;
    this->pcout << "   Actual final time: " << final_time_actual << std::endl;
    
    const int n_timesteps= flow_solver->ode_solver->current_iteration;

    //check L2 error
    const double L2_error = calculate_L2_error_at_final_time_wrt_reference(
            flow_solver->dg, 
            params, 
            final_time_actual);
    this->pcout << "Computed error is " << L2_error << std::endl;

    const double dt =  params.ode_solver_param.initial_time_step;
    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("final_time", final_time_actual );
    convergence_table->set_precision("final_time", 16);
    convergence_table->add_value("n_timesteps", n_timesteps);
    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);
    
    const double energy_end = flow_solver_case->compute_energy(flow_solver->dg);
    const double energy_change = energy_initial - energy_end;
    convergence_table->add_value("energy_change", energy_change);
    convergence_table->set_precision("energy_change", 16);
    convergence_table->evaluate_convergence_rates("energy_change", "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 order_tolerance = 0.1;
    if (refinement > 0) {
        double L2_error_conv_rate = -log(L2_error_old/L2_error)/log(this->refine_ratio);
        this->pcout << "Order at " << refinement << " is " << L2_error_conv_rate << std::endl;
        if (abs(L2_error_conv_rate - expected_order) > order_tolerance){
            testfail = 1;
            this->pcout << "Expected convergence order was not reached at refinement " << refinement <<std::endl;
        }
    }

    return std::make_tuple(L2_error, testfail);
}


template <int dim, int nstate>
int TimeRefinementStudyReference<dim, nstate>::run_test() const
{
    const double expected_order = this->all_parameters->ode_solver_param.rk_order;

    int testfail = this->run_refinement_study_and_write_result(this->all_parameters, expected_order);
    return testfail;
}

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