burgers.h

//
// Created by chen on 2021/11/30.
//

#ifndef BURGERS_BURGERS_H
#define BURGERS_BURGERS_H
#include <iostream>
#include <string>
#include <Eigen/Dense>
using std::endl;
using std::cout;
using std::string;
using namespace Eigen;


const int N = 3;
const int Nv = N + 1;
const int K = 8;
const double xmin = -1;
const double xmax = 1;
const double CFL = 0.75;
const double epsilon = 0.1;
const double FinalTime = 1.5;

namespace RK4 {
    const unsigned int N_t = 5;
    double const rk4a[N_t] = {0.0,
                              -567301805773.0 / 1357537059087.0,
                              -2404267990393.0 / 2016746695238.0,
                              -3550918686646.0 / 2091501179385.0,
                              -1275806237668.0 / 842570457699.0};

    double const rk4b[N_t] = {1432997174477.0 / 9575080441755.0,
                              5161836677717.0 / 13612068292357.0,
                              1720146321549.0 / 2090206949498.0,
                              3134564353537.0 / 4481467310338.0,
                              2277821191437.0 / 14882151754819.0};

    double const rk4c[N_t] = {0.0,
                              1432997174477.0 / 9575080441755.0,
                              2526269341429.0 / 6820363962896.0,
                              2006345519317.0 / 3224310063776.0,
                              2802321613138.0 / 2924317926251.0};
}

void MeshGen1D(const double &xmin, const double &xmax, const int &K, VectorXd &VX);

void GeometricFactors1D(const MatrixXd &x, const MatrixXd &Dr,
                        MatrixXd &rx, MatrixXd &J);
MatrixXd BurgersRHS1D(const double &time,
                  const MatrixXd &Dr, const MatrixXd &rx,
                  const MatrixXd &nx, const MatrixXd &LIFT,
                  const MatrixXd &Fscale, const MatrixXd &u) ;
#endif //BURGERS_BURGERS_H