06POD_RBF.C

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 * In real Time Highly Advanced Computational Applications for Finite Volumes
 * Copyright (C) 2017 by the ITHACA-FV authors
-------------------------------------------------------------------------------
License
    This file is part of ITHACA-FV
 
    ITHACA-FV is free software: you can redistribute it and/or modify
    it under the terms of the GNU Lesser General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    ITHACA-FV is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    GNU Lesser General Public License for more details.
 
    You should have received a copy of the GNU Lesser General Public License
    along with ITHACA-FV. If not, see <http://www.gnu.org/licenses/>.
 
Description
    Example of NS-Stokes Reduction Problem for Turbulent Flow Case
SourceFiles
    06POD_RBF.C
\*---------------------------------------------------------------------------*/
#include "fvCFD.H"
#include "fvOptions.H"
#include "IOmanip.H"
#include "simpleControl.H"
#include "ITHACAutilities.H"
#include "Foam2Eigen.H"
#include "ITHACAstream.H"
#include "ITHACAPOD.H"
#include <Eigen/Dense>
#include <Eigen/SVD>
#include <Eigen/SparseLU>
#include "EigenFunctions.H"
#include <chrono>
#include "reductionProblem.H"
#include "steadyNS.H"
#include "SteadyNSTurb.H"
#include "ReducedSteadyNS.H"
#include "ReducedSteadyNSTurb.H"

class tutorial06 : public SteadyNSTurb
{
    public:
        explicit tutorial06(int argc, char* argv[])
            :
            SteadyNSTurb(argc, argv),
            U(_U()),
            p(_p()),
            nut(_nut())
        {}

        // Relevant Fields
        volVectorField& U;
        volScalarField& p;
        volScalarField& nut;
        void offlineSolve()
        {
            Vector<double> inl(0, 0, 0);
            List<scalar> mu_now(2);
 
            // if the offline solution is already performed read the fields
            if (offline)
            {
                ITHACAstream::read_fields(Ufield, U, "./ITHACAoutput/Offline/");
                ITHACAstream::read_fields(Pfield, p, "./ITHACAoutput/Offline/");
                ITHACAstream::read_fields(nutFields, nut, "./ITHACAoutput/Offline/");
 
                // if the offline stage is not completed then resume it
                if (Ufield.size() < mu.rows())
                {
                    Vector<double> Uinl(0, 0, 0);
                    label BCind = 0;
 
                    for (label i = Ufield.size(); i < mu.rows(); i++)
                    {
                        Uinl[0] = mu(i, 0);
                        Uinl[1] = mu(i, 1);
                        assignBC(_U(), BCind, Uinl);
                        counter = Ufield.size() + 1;
                        truthSolve("./ITHACAoutput/Offline/");
                    }
                }
            }
            else
            {
                Vector<double> Uinl(0, 0, 0);
                label BCind = 0;
 
                for (label i = 0; i < mu.rows(); i++)
                {
                    Uinl[0] = mu(i, 0);
                    Uinl[1] = mu(i, 1);
                    assignBC(_U(), BCind, Uinl);
                    truthSolve("./ITHACAoutput/Offline/");
                }
            }
        }

        void offlineSolve(Eigen::MatrixXd par, fileName folder)
        {
            Vector<double> inl(0, 0, 0);
            List<scalar> mu_now(2);
            Vector<double> Uinl(0, 0, 0);
            label BCind = 0;
 
            for (label i = 0; i < par.rows(); i++)
            {
                Uinl[0] = par(i, 0);
                Uinl[1] = par(i, 1);
                assignBC(_U(), BCind, Uinl);
                truthSolve(folder);
            }
        }
 
        void truthSolve(fileName folder)
        {
            Time& runTime = _runTime();
            fvMesh& mesh = _mesh();
            volScalarField& p = _p();
            volVectorField& U = _U();
            surfaceScalarField& phi = _phi();
            fv::options& fvOptions = _fvOptions();
            simpleControl& simple = _simple();
            IOMRFZoneList& MRF = _MRF();
            singlePhaseTransportModel& laminarTransport = _laminarTransport();
#include "NLsolveSteadyNSTurb.H"
            ITHACAstream::exportSolution(U, name(counter), folder);
            ITHACAstream::exportSolution(p, name(counter), folder);
            volScalarField _nut(turbulence->nut());
            ITHACAstream::exportSolution(_nut, name(counter), folder);
            Ufield.append((U).clone());
            Pfield.append((p).clone());
            nutFields.append((_nut).clone());
            counter++;
        }
};
 
int main(int argc, char* argv[])
{
    // Construct the tutorial06 object
    tutorial06 example(argc, argv);
    // Read parameters samples for the offline stage and the ones for the online stages
    word par_offline("./par_offline");
    word par_new("./par_online");
    Eigen::MatrixXd par_online = ITHACAstream::readMatrix(par_new);
    example.mu = ITHACAstream::readMatrix(par_offline);
    // Set the inlet boundaries where we have parameterized boundary conditions
    example.inletIndex.resize(2, 2);
    example.inletIndex(0, 0) = 0;
    example.inletIndex(0, 1) = 0;
    example.inletIndex(1, 0) = 0;
    example.inletIndex(1, 1) = 1;
    ITHACAparameters* para = ITHACAparameters::getInstance(example._mesh(),
                             example._runTime());
    // Read parameters from ITHACAdict file
    int NmodesU = para->ITHACAdict->lookupOrDefault<int>("NmodesU", 5);
    int NmodesP = para->ITHACAdict->lookupOrDefault<int>("NmodesP", 5);
    int NmodesSUP = para->ITHACAdict->lookupOrDefault<int>("NmodesSUP", 5);
    int NmodesNUT = para->ITHACAdict->lookupOrDefault<int>("NmodesNUT", 5);
    int NmodesProject = para->ITHACAdict->lookupOrDefault<int>("NmodesProject", 5);
    word stabilization = para->ITHACAdict->lookupOrDefault<word>("Stabilization",
                         "supremizer");
    // Perform The Offline Solve;
    example.offlineSolve();
    // Read the lift functions
    ITHACAstream::read_fields(example.liftfield, example.U, "./lift/");
    // Create the homogeneous set of snapshots for the velocity field
    example.computeLift(example.Ufield, example.liftfield, example.Uomfield);
    // Export the homogeneous velocity snapshots
    ITHACAstream::exportFields(example.Uomfield, "./ITHACAoutput/Offline",
                               "Uofield");
    // Perform a POD decomposition for the velocity, the pressure and the eddy viscosity
    ITHACAPOD::getModes(example.Uomfield, example.Umodes, example._U().name(),
                        example.podex,
                        example.supex, 0, NmodesProject);
    ITHACAPOD::getModes(example.Pfield, example.Pmodes, example.p().name(),
                        example.podex,
                        example.supex, 0, NmodesProject);
    ITHACAPOD::getModes(example.nutFields, example.nutModes, example._nut().name(),
                        example.podex,
                        example.supex, 0, NmodesProject);
 
    // Solve the supremizer problem based on the pressure modes
    if (stabilization == "supremizer")
    {
        example.solvesupremizer("modes");
    }
 
    // Compute the reduced order matrices
    // Get reduced matrices
    if (stabilization == "supremizer")
    {
        example.projectSUP("./Matrices", NmodesU, NmodesP, NmodesSUP,
                           NmodesNUT);
    }
    else if (stabilization == "PPE")
    {
        example.projectPPE("./Matrices", NmodesU, NmodesP, NmodesSUP,
                           NmodesNUT);
    }
 
    // Create an object of the turbulent class
    ReducedSteadyNSTurb pod_rbf(
        example);
    // Set value of the reduced viscosity and the penalty factor
    pod_rbf.nu = 1e-3;
    pod_rbf.tauU.resize(2, 1);
    // We create the matrix rbfCoeff which will store the values of the interpolation results for the eddy viscosity field
    Eigen::MatrixXd rbfCoeff;
    rbfCoeff.resize(NmodesNUT, par_online.rows());
 
    // Perform an online solve for the new values of inlet velocities
    for (label k = 0; k < par_online.rows(); k++)
    {
        Eigen::MatrixXd velNow(2, 1);
        velNow(0, 0) = par_online(k, 0);
        velNow(1, 0) = par_online(k, 1);
        pod_rbf.tauU(0, 0) = 0;
        pod_rbf.tauU(1, 0) = 0;
 
        if (stabilization == "supremizer")
        {
            pod_rbf.solveOnlineSUP(velNow);
        }
        else if (stabilization == "PPE")
        {
            pod_rbf.solveOnlinePPE(velNow);
        }
 
        rbfCoeff.col(k) = pod_rbf.rbfCoeff;
        Eigen::MatrixXd tmp_sol(pod_rbf.y.rows() + 1, 1);
        tmp_sol(0) = k + 1;
        tmp_sol.col(0).tail(pod_rbf.y.rows()) = pod_rbf.y;
        pod_rbf.online_solution.append(tmp_sol);
    }
 
    // Save the matrix of interpolated eddy viscosity coefficients
    ITHACAstream::exportMatrix(rbfCoeff, "rbfCoeff", "python",
                               "./ITHACAoutput/Matrices/");
    ITHACAstream::exportMatrix(rbfCoeff, "rbfCoeff", "matlab",
                               "./ITHACAoutput/Matrices/");
    // Save the online solution
    ITHACAstream::exportMatrix(pod_rbf.online_solution, "red_coeff", "python",
                               "./ITHACAoutput/red_coeff");
    ITHACAstream::exportMatrix(pod_rbf.online_solution, "red_coeff", "matlab",
                               "./ITHACAoutput/red_coeff");
    ITHACAstream::exportMatrix(pod_rbf.online_solution, "red_coeff", "eigen",
                               "./ITHACAoutput/red_coeff");
    pod_rbf.rbfCoeffMat = rbfCoeff;
    // Reconstruct and export the solution
    pod_rbf.reconstruct(true, "./ITHACAoutput/Reconstruction/");
    // Create an object of the laminar class
    reducedSteadyNS pod_normal(
        example);
    // Set value of the reduced viscosity and the penalty factor
    pod_normal.nu = 1e-3;
    pod_normal.tauU.resize(2, 1);
 
    // Perform an online solve for the new values of inlet velocities
    for (label k = 0; k < par_online.rows(); k++)
    {
        Eigen::MatrixXd vel_now(2, 1);
        vel_now(0, 0) = par_online(k, 0);
        vel_now(1, 0) = par_online(k, 1);
        pod_normal.tauU(0, 0) = 0;
        pod_normal.tauU(1, 0) = 0;
        pod_normal.solveOnline_sup(vel_now);
        Eigen::MatrixXd tmp_sol(pod_normal.y.rows() + 1, 1);
        tmp_sol(0) = k + 1;
        tmp_sol.col(0).tail(pod_normal.y.rows()) = pod_normal.y;
        pod_normal.online_solution.append(tmp_sol);
    }
 
    // Save the online solution
    ITHACAstream::exportMatrix(pod_normal.online_solution, "red_coeffnew", "python",
                               "./ITHACAoutput/red_coeffnew");
    ITHACAstream::exportMatrix(pod_normal.online_solution, "red_coeffnew", "matlab",
                               "./ITHACAoutput/red_coeffnew");
    ITHACAstream::exportMatrix(pod_normal.online_solution, "red_coeffnew", "eigen",
                               "./ITHACAoutput/red_coeffnew");
    // Reconstruct and export the solution
    pod_normal.reconstruct(true, "./ITHACAoutput/Lam_Rec/");
    // Solve the full order problem for the online velocity values for the purpose of comparison
    // if (ITHACAutilities::check_folder("./ITHACAoutput/Offline_check") == false)
    // {
    //     example.offlineSolve(par_online, "./ITHACAoutput/Offline_check/");
    //     ITHACAutilities::createSymLink("./ITHACAoutput/Offline_check");
    // }
    Info << "Computing Frobenius errors for velocity fields" << endl;
    Eigen::MatrixXd errFrobU = ITHACAutilities::errorFrobRel(example.Ufield,
                               pod_rbf.uRecFields);
    Info << "Computing Frobenius errors for pressure fields" << endl;
    Eigen::MatrixXd errFrobP =  ITHACAutilities::errorFrobRel(example.Pfield,
                                pod_rbf.pRecFields);
    Info << "Computing Frobenius errors for eddy viscosity fields" << endl;
    Eigen::MatrixXd errFrobNut =  ITHACAutilities::errorFrobRel(example.nutFields,
                                  pod_rbf.nutRecFields);
    ITHACAstream::exportMatrix(errFrobU, "errFrobU", "matlab",
                               "./ITHACAoutput/ErrorsFrob/");
    ITHACAstream::exportMatrix(errFrobP, "errFrobP", "matlab",
                               "./ITHACAoutput/ErrorsFrob/");
    ITHACAstream::exportMatrix(errFrobNut, "errFrobNut", "matlab",
                               "./ITHACAoutput/ErrorsFrob/");
    Info << "Computing L2 errors for velocity fields" << endl;
    Eigen::MatrixXd errL2U = ITHACAutilities::errorL2Rel(example.Ufield,
                             pod_rbf.uRecFields);
    Info << "Computing L2 errors for pressure fields" << endl;
    Eigen::MatrixXd errL2P =  ITHACAutilities::errorL2Rel(example.Pfield,
                              pod_rbf.pRecFields);
    Info << "Computing L2 errors for eddy viscosity fields" << endl;
    Eigen::MatrixXd errL2Nut =  ITHACAutilities::errorL2Rel(example.nutFields,
                                pod_rbf.nutRecFields);
    ITHACAstream::exportMatrix(errL2U, "errL2U", "matlab",
                               "./ITHACAoutput/ErrorsL2/");
    ITHACAstream::exportMatrix(errL2P, "errL2P", "matlab",
                               "./ITHACAoutput/ErrorsL2/");
    ITHACAstream::exportMatrix(errL2Nut, "errL2Nut", "matlab",
                               "./ITHACAoutput/ErrorsL2/");
    return 0;
}