eq_unit_test.hpp

/*
 * eq_unit_test.hpp
 *
 *  Created on: Oct 13, 2015
 *      Author: i-bird
 */

#ifndef OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_EQ_UNIT_TEST_HPP_
#define OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_EQ_UNIT_TEST_HPP_

#include "Laplacian.hpp"
#include "FiniteDifference/eq.hpp"
#include "FiniteDifference/sum.hpp"
#include "FiniteDifference/mul.hpp"
#include "Grid/grid_dist_id.hpp"
#include "Decomposition/CartDecomposition.hpp"
#include "Vector/Vector.hpp"
#include "Solvers/umfpack_solver.hpp"
#include "data_type/aggregate.hpp"
#include "FiniteDifference/FDScheme.hpp"

BOOST_AUTO_TEST_SUITE( eq_test_suite )


struct lid_nn
{
    // dimensionaly of the equation (2D problem 3D problem ...)
    static const unsigned int dims = 2;

    // number of fields in the system v_x, v_y, P so a total of 3
    static const unsigned int nvar = 3;

    // boundary conditions PERIODIC OR NON_PERIODIC
    static const bool boundary[];

    // type of space float, double, ...
    typedef float stype;

    // type of base grid, it is the distributed grid that will store the result
    // Note the first property is a 2D vector (velocity), the second is a scalar (Pressure)
    typedef grid_dist_id<2,float,aggregate<float[2],float>,CartDecomposition<2,float>> b_grid;

    // type of SparseMatrix, for the linear system, this parameter is bounded by the solver
    // that you are using, in case of umfpack it is the only possible choice
    typedef SparseMatrix<double,int> SparseMatrix_type;

    // type of Vector for the linear system, this parameter is bounded by the solver
    // that you are using, in case of umfpack it is the only possible choice
    typedef Vector<double> Vector_type;

    // Define that the underline grid where we discretize the system of equation is staggered
    static const int grid_type = STAGGERED_GRID;
};

const bool lid_nn::boundary[] = {NON_PERIODIC,NON_PERIODIC};



// Constant Field
struct eta
{
    typedef void const_field;

    static float val()  {return 1.0;}
};

// Convenient constants
constexpr unsigned int v[] = {0,1};
constexpr unsigned int P = 2;
constexpr unsigned int ic = 2;

// Create field that we have v_x, v_y, P
typedef Field<v[x],lid_nn> v_x;
typedef Field<v[y],lid_nn> v_y;
typedef Field<P,lid_nn> Prs;

// Eq1 V_x

typedef mul<eta,Lap<v_x,lid_nn>,lid_nn> eta_lap_vx;
typedef D<x,Prs,lid_nn> p_x;
typedef minus<p_x,lid_nn> m_p_x;
typedef sum<eta_lap_vx,m_p_x,lid_nn> vx_eq;

// Eq2 V_y

typedef mul<eta,Lap<v_y,lid_nn>,lid_nn> eta_lap_vy;
typedef D<y,Prs,lid_nn> p_y;
typedef minus<p_y,lid_nn> m_p_y;
typedef sum<eta_lap_vy,m_p_y,lid_nn> vy_eq;

// Eq3 Incompressibility

typedef D<x,v_x,lid_nn,FORWARD> dx_vx;
typedef D<y,v_y,lid_nn,FORWARD> dy_vy;
typedef sum<dx_vx,dy_vy,lid_nn> ic_eq;


// Equation for boundary conditions

/* Consider the staggered cell
 *
         \verbatim

        +--$--+
        |     |
        #  *  #
        |     |
        0--$--+

      # = velocity(y)
      $ = velocity(x)
      * = pressure

        \endverbatim
 *
 *
 * If we want to impose v_y = 0 on 0 we have to interpolate between # of this cell
 * and # of the previous cell on y, (Average) or Avg operator
 *
 */

// Directional Avg
typedef Avg<x,v_y,lid_nn> avg_vy;
typedef Avg<y,v_x,lid_nn> avg_vx;

typedef Avg<x,v_y,lid_nn,FORWARD> avg_vy_f;
typedef Avg<y,v_x,lid_nn,FORWARD> avg_vx_f;

#define EQ_1 0
#define EQ_2 1
#define EQ_3 2


template<typename solver_type,typename lid_nn> void lid_driven_cavity_2d()
{
    Vcluster & v_cl = create_vcluster();

    if (v_cl.getProcessingUnits() > 3)
        return;


    // velocity in the grid is the property 0, pressure is the property 1
    constexpr int velocity = 0;
    constexpr int pressure = 1;

    // Domain, a rectangle
    Box<2,float> domain({0.0,0.0},{3.0,1.0});

    // Ghost (Not important in this case but required)
    Ghost<2,float> g(0.01);

    // Grid points on x=256 and y=64
    long int sz[] = {256,64};
    size_t szu[2];
    szu[0] = (size_t)sz[0];
    szu[1] = (size_t)sz[1];

    // We need one more point on the left and down part of the domain
    // This is given by the boundary conditions that we impose, the
    // reason is mathematical in order to have a well defined system
    // and cannot be discussed here
    Padding<2> pd({1,1},{0,0});

    // Distributed grid that store the solution
    grid_dist_id<2,float,aggregate<float[2],float>,CartDecomposition<2,float>> g_dist(szu,domain,g);

    // It is the maximum extension of the stencil
    Ghost<2,long int> stencil_max(1);

    // Finite difference scheme
    FDScheme<lid_nn> fd(pd, stencil_max, domain,g_dist);

    // Here we impose the equation, we start from the incompressibility Eq imposed in the bulk with the
    // exception of the first point {0,0} and than we set P = 0 in {0,0}, why we are doing this is again
    // mathematical to have a well defined system, an intuitive explanation is that P and P + c are both
    // solution for the incompressibility equation, this produce an ill-posed problem to make it well posed
    // we set one point in this case {0,0} the pressure to a fixed constant for convenience P = 0
    fd.impose(ic_eq(),0.0, EQ_3, {0,0},{sz[0]-2,sz[1]-2},true);
    fd.impose(Prs(),  0.0, EQ_3, {0,0},{0,0});

    // Here we impose the Eq1 and Eq2
    fd.impose(vx_eq(),0.0, EQ_1, {1,0},{sz[0]-2,sz[1]-2});
    fd.impose(vy_eq(),0.0, EQ_2, {0,1},{sz[0]-2,sz[1]-2});

    // v_x and v_y
    // Imposing B1
    fd.impose(v_x(),0.0, EQ_1, {0,0},{0,sz[1]-2});
    fd.impose(avg_vy_f(),0.0, EQ_2 , {-1,0},{-1,sz[1]-1});
    // Imposing B2
    fd.impose(v_x(),0.0, EQ_1, {sz[0]-1,0},{sz[0]-1,sz[1]-2});
    fd.impose(avg_vy(),1.0, EQ_2,    {sz[0]-1,0},{sz[0]-1,sz[1]-1});

    // Imposing B3
    fd.impose(avg_vx_f(),0.0, EQ_1, {0,-1},{sz[0]-1,-1});
    fd.impose(v_y(), 0.0, EQ_2, {0,0},{sz[0]-2,0});
    // Imposing B4
    fd.impose(avg_vx(),0.0, EQ_1,   {0,sz[1]-1},{sz[0]-1,sz[1]-1});
    fd.impose(v_y(), 0.0, EQ_2, {0,sz[1]-1},{sz[0]-2,sz[1]-1});

    // When we pad the grid, there are points of the grid that are not
    // touched by the previous condition. Mathematically this lead
    // to have too many variables for the conditions that we are imposing.
    // Here we are imposing variables that we do not touch to zero
    //

    // Padding pressure
    fd.impose(Prs(), 0.0, EQ_3, {-1,-1},{sz[0]-1,-1});
    fd.impose(Prs(), 0.0, EQ_3, {-1,sz[1]-1},{sz[0]-1,sz[1]-1});
    fd.impose(Prs(), 0.0, EQ_3, {-1,0},{-1,sz[1]-2});
    fd.impose(Prs(), 0.0, EQ_3, {sz[0]-1,0},{sz[0]-1,sz[1]-2});

    // Impose v_x Padding Impose v_y padding
    fd.impose(v_x(), 0.0, EQ_1, {-1,-1},{-1,sz[1]-1});
    fd.impose(v_y(), 0.0, EQ_2, {-1,-1},{sz[0]-1,-1});

    solver_type solver;
    auto x = solver.solve(fd.getA(),fd.getB());



    fd.template copy<velocity,pressure>(x,{0,0},{sz[0]-1,sz[1]-1},g_dist);

    std::string s = std::string(demangle(typeid(solver_type).name()));
    s += "_";


    g_dist.write(s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid");

#ifdef HAVE_OSX

    std::string file1 = std::string("test/") + s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_osx.vtk";
    std::string file2 = s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";

#else

    #if __GNUC__ == 6

    std::string file1 = std::string("test/") + s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC6.vtk";
    std::string file2 = s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";

    #elif __GNUC__ == 5

    std::string file1 = std::string("test/") + s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC5.vtk";
    std::string file2 = s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";

    #else

    std::string file1 = std::string("test/") + s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + "_test_GCC4.vtk";
    std::string file2 = s + "lid_driven_cavity_p" + std::to_string(v_cl.getProcessingUnits()) + "_grid_" + std::to_string(v_cl.getProcessUnitID()) + ".vtk";

    #endif


#endif

    std::cout << "File1: " << file1 << std::endl;
    std::cout << "File2: " << file2 << std::endl;

#ifndef SE_CLASS3

    // Check that match
    bool test = compare(file1,file2);
    BOOST_REQUIRE_EQUAL(test,true);

#endif

}

// Lid driven cavity, incompressible fluid

BOOST_AUTO_TEST_CASE(lid_driven_cavity)
{
    lid_driven_cavity_2d<umfpack_solver<double>,lid_nn>();
}

BOOST_AUTO_TEST_SUITE_END()

#endif /* OPENFPM_NUMERICS_SRC_FINITEDIFFERENCE_EQ_UNIT_TEST_HPP_ */