Commit 6c762d38 authored by incardon's avatar incardon

Adding equation unit test

parent a74e6600
/*
* 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_
#define BOOST_TEST_DYN_LINK
#include <boost/test/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"
constexpr unsigned int x = 0;
constexpr unsigned int y = 1;
constexpr unsigned int z = 2;
constexpr unsigned int V = 0;
BOOST_AUTO_TEST_SUITE( eq_test_suite )
//! [Definition of the system]
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};
//! [Definition of the system]
//! [Definition of the equation of the system in the bulk and at the boundary]
// 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
//! [Definition of the equation of the system in the bulk and at the boundary]
template<typename solver_type,typename lid_nn> void lid_driven_cavity_2d()
{
Vcluster<> & v_cl = create_vcluster();
if (v_cl.getProcessingUnits() > 3)
return;
//! [lid-driven cavity 2D]
// 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());
//! [lid-driven cavity 2D]
//! [Copy the solution to grid]
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 += "_";
//! [Copy the solution to grid]
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_ */
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