Gray Scott in 3D

Solving a gray scott-system

This example is just an extension of the 2D Gray scott example. Here we show how to solve a non-linear reaction diffusion system in 3D

In figure is the final solution of the problem

More or less this example is the adaptation of the previous example to 3D with the improvement of using stencil iterator.

Stencil iterator

Stencil iterator require that you define a stencil,

    static grid_key_dx<3> star_stencil_3D[7] = {{0,0,0},
                                                {0,0,-1},
                                                {0,0,1},
                                                {0,-1,0},
                                                {0,1,0},
                                                {-1,0,0},
                                                {1,0,0}};

once is defined it is possible get and use a stencil iterator

        auto it = Old.getDomainIteratorStencil(star_stencil_3D);

        while (it.isNext())
        {
            // center point
            auto Cp = it.getStencil<0>();

            // plus,minus X,Y,Z
            auto mx = it.getStencil<1>();
            auto px = it.getStencil<2>();
            auto my = it.getStencil<3>();
            auto py = it.getStencil<4>();
            auto mz = it.getStencil<5>();
            auto pz = it.getStencil<6>();

            // update based on Eq 2
            New.get<U>(Cp) = Old.get<U>(Cp) + uFactor * (
                                        Old.get<U>(mz) +
                                        Old.get<U>(pz) +
                                        Old.get<U>(my) +
                                        Old.get<U>(py) +
                                        Old.get<U>(mx) +
                                        Old.get<U>(px) -
                                        6.0*Old.get<U>(Cp)) +
                                        - deltaT * Old.get<U>(Cp) * Old.get<V>(Cp) * Old.get<V>(Cp) +
                                        - deltaT * F * (Old.get<U>(Cp) - 1.0);


            // update based on Eq 2
            New.get<V>(Cp) = Old.get<V>(Cp) + vFactor * (
                                        Old.get<V>(mz) +
                                        Old.get<V>(pz) +
                                        Old.get<V>(my) +
                                        Old.get<V>(py) +
                                        Old.get<V>(mx) +
                                        Old.get<V>(px) -
                                        6*Old.get<V>(Cp)) +
                                        deltaT * Old.get<U>(Cp) * Old.get<V>(Cp) * Old.get<V>(Cp) +
                                        - deltaT * (F+K) * Old.get<V>(Cp);

            // Next point in the grid
            ++it;
        }

The rest of the example remain the same with the exception that the code has been extended in 3D.

See Also

Solve equation

Finalize

Deinitialize the library

    openfpm_finalize();

Full code

#include "Grid/grid_dist_id.hpp"
#include "data_type/aggregate.hpp"
#include "timer.hpp"


constexpr int U = 0;
constexpr int V = 1;

constexpr int x = 0;
constexpr int y = 1;
constexpr int z = 2;


void init(grid_dist_id<3,double,aggregate<double,double> > & Old, grid_dist_id<3,double,aggregate<double,double> > & New, Box<3,double> & domain)
{
    auto it = Old.getDomainIterator();

    while (it.isNext())
    {
        // Get the local grid key
        auto key = it.get();

        // Old values U and V
        Old.template get<U>(key) = 1.0;
        Old.template get<V>(key) = 0.0;

        // Old values U and V
        New.template get<U>(key) = 0.0;
        New.template get<V>(key) = 0.0;

        ++it;
    }

    long int x_start = Old.size(0)*1.55f/domain.getHigh(0);
    long int y_start = Old.size(1)*1.55f/domain.getHigh(1);
    long int z_start = Old.size(1)*1.55f/domain.getHigh(2);

    long int x_stop = Old.size(0)*1.85f/domain.getHigh(0);
    long int y_stop = Old.size(1)*1.85f/domain.getHigh(1);
    long int z_stop = Old.size(1)*1.85f/domain.getHigh(2);

    grid_key_dx<3> start({x_start,y_start,z_start});
    grid_key_dx<3> stop ({x_stop,y_stop,z_stop});
    auto it_init = Old.getSubDomainIterator(start,stop);

    while (it_init.isNext())
    {
        auto key = it_init.get();

                Old.template get<U>(key) = 0.5 + (((double)std::rand())/RAND_MAX -0.5)/10.0;
                Old.template get<V>(key) = 0.25 + (((double)std::rand())/RAND_MAX -0.5)/20.0;

        ++it_init;
    }
}


int main(int argc, char* argv[])
{
    openfpm_init(&argc,&argv);

    // domain
    Box<3,double> domain({0.0,0.0},{2.5,2.5,2.5});
    
    // grid size
        size_t sz[3] = {128,128,128};

    // Define periodicity of the grid
    periodicity<3> bc = {PERIODIC,PERIODIC,PERIODIC};
    
    // Ghost in grid unit
    Ghost<3,long int> g(1);
    
    // deltaT
    double deltaT = 1;

    // Diffusion constant for specie U
    double du = 2*1e-5;

    // Diffusion constant for specie V
    double dv = 1*1e-5;

    // Number of timesteps
        size_t timeSteps = 5000;

    // K and F (Physical constant in the equation)
        double K = 0.053;
        double F = 0.014;

    grid_dist_id<3, double, aggregate<double,double>> Old(sz,domain,g,bc);

    // New grid with the decomposition of the old grid
    grid_dist_id<3, double, aggregate<double,double>> New(Old.getDecomposition(),sz,g);

    
    // spacing of the grid on x and y
    double spacing[3] = {Old.spacing(0),Old.spacing(1),Old.spacing(2)};

    init(Old,New,domain);

    // sync the ghost
    size_t count = 0;
    Old.template ghost_get<U,V>();

    // because we assume that spacing[x] == spacing[y] we use formula 2
    // and we calculate the prefactor of Eq 2
    double uFactor = deltaT * du/(spacing[x]*spacing[x]);
    double vFactor = deltaT * dv/(spacing[x]*spacing[x]);

    timer tot_sim;
    tot_sim.start();


    static grid_key_dx<3> star_stencil_3D[7] = {{0,0,0},
                                                {0,0,-1},
                                                {0,0,1},
                                                {0,-1,0},
                                                {0,1,0},
                                                {-1,0,0},
                                                {1,0,0}};


    for (size_t i = 0; i < timeSteps; ++i)
    {
        if (i % 300 == 0)
        {std::cout << "STEP: " << i << std::endl;}


        auto it = Old.getDomainIteratorStencil(star_stencil_3D);

        while (it.isNext())
        {
            // center point
            auto Cp = it.getStencil<0>();

            // plus,minus X,Y,Z
            auto mx = it.getStencil<1>();
            auto px = it.getStencil<2>();
            auto my = it.getStencil<3>();
            auto py = it.getStencil<4>();
            auto mz = it.getStencil<5>();
            auto pz = it.getStencil<6>();

            // update based on Eq 2
            New.get<U>(Cp) = Old.get<U>(Cp) + uFactor * (
                                        Old.get<U>(mz) +
                                        Old.get<U>(pz) +
                                        Old.get<U>(my) +
                                        Old.get<U>(py) +
                                        Old.get<U>(mx) +
                                        Old.get<U>(px) -
                                        6.0*Old.get<U>(Cp)) +
                                        - deltaT * Old.get<U>(Cp) * Old.get<V>(Cp) * Old.get<V>(Cp) +
                                        - deltaT * F * (Old.get<U>(Cp) - 1.0);


            // update based on Eq 2
            New.get<V>(Cp) = Old.get<V>(Cp) + vFactor * (
                                        Old.get<V>(mz) +
                                        Old.get<V>(pz) +
                                        Old.get<V>(my) +
                                        Old.get<V>(py) +
                                        Old.get<V>(mx) +
                                        Old.get<V>(px) -
                                        6*Old.get<V>(Cp)) +
                                        deltaT * Old.get<U>(Cp) * Old.get<V>(Cp) * Old.get<V>(Cp) +
                                        - deltaT * (F+K) * Old.get<V>(Cp);

            // Next point in the grid
            ++it;
        }


        // Here we copy New into the old grid in preparation of the new step
        // It would be better to alternate, but using this we can show the usage
        // of the function copy. To note that copy work only on two grid of the same
        // decomposition. If you want to copy also the decomposition, or force to be
        // exactly the same, use Old = New
        Old.copy(New);

        // After copy we synchronize again the ghost part U and V
        Old.ghost_get<U,V>();

        // Every 500 time step we output the configuration for
        // visualization
        if (i % 500 == 0)
        {
            Old.save("output_" + std::to_string(count));
            count++;
        }
    }
    
    tot_sim.stop();
    std::cout << "Total simulation: " << tot_sim.getwct() << std::endl;



    openfpm_finalize();


}