scalar_burgers_2d.cpp

// Copyright 2018-2025 the samurai's authors
// SPDX-License-Identifier:  BSD-3-Clause

#include <xtensor/xfixed.hpp>

#include <samurai/algorithm.hpp>
#include <samurai/bc.hpp>
#include <samurai/field.hpp>
#include <samurai/io/hdf5.hpp>
#include <samurai/io/restart.hpp>
#include <samurai/mr/adapt.hpp>
#include <samurai/mr/mesh.hpp>
#include <samurai/samurai.hpp>
#include <samurai/stencil_field.hpp>
#include <samurai/subset/node.hpp>

#include <filesystem>
namespace fs = std::filesystem;

template <class Field>
void init(Field& u)
{
    auto mesh = u.mesh();
    u.resize();
    samurai::for_each_cell(
        mesh,
        [&](auto& cell)
        {
            auto center               = cell.center();
            constexpr double radius   = 0.1;
            constexpr double x_center = 0.5;
            constexpr double y_center = 0.5;

            if (((center[0] - x_center) * (center[0] - x_center) + (center[1] - y_center) * (center[1] - y_center)) <= radius * radius)
            {
                u[cell] = 1;
            }
            else
            {
                u[cell] = 0;
            }

            constexpr double x_center2 = 0.2;
            constexpr double y_center2 = 0.2;
            if (((center[0] - x_center2) * (center[0] - x_center2) + (center[1] - y_center2) * (center[1] - y_center2)) <= radius * radius)
            {
                u[cell] = -1;
            }
        });
}

template <class Field>
void flux_correction(double dt, const std::array<double, 2>& k, const Field& u, Field& unp1)
{
    using mesh_t              = typename Field::mesh_t;
    using mesh_id_t           = typename mesh_t::mesh_id_t;
    using interval_t          = typename mesh_t::interval_t;
    constexpr std::size_t dim = Field::dim;

    auto mesh = u.mesh();

    for (std::size_t level = mesh.min_level(); level < mesh.max_level(); ++level)
    {
        xt::xtensor_fixed<int, xt::xshape<dim>> stencil;

        stencil = {
            {-1, 0}
        };

        auto subset_right = samurai::intersection(samurai::translate(mesh[mesh_id_t::cells][level + 1], stencil),
                                                  mesh[mesh_id_t::cells][level])
                                .on(level);

        subset_right(
            [&](const auto& i, const auto& index)
            {
                auto j          = index[0];
                const double dx = mesh.cell_length(level);

                unp1(level,
                     i,
                     j) = unp1(level, i, j)
                        + dt / dx
                              * (samurai::upwind_scalar_burgers_op<dim, interval_t>(level, i, j).right_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i + 1, 2 * j).right_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i + 1, 2 * j + 1).right_flux(k, u));
            });

        stencil = {
            {1, 0}
        };

        auto subset_left = samurai::intersection(samurai::translate(mesh[mesh_id_t::cells][level + 1], stencil),
                                                 mesh[mesh_id_t::cells][level])
                               .on(level);

        subset_left(
            [&](const auto& i, const auto& index)
            {
                auto j          = index[0];
                const double dx = mesh.cell_length(level);

                unp1(level,
                     i,
                     j) = unp1(level, i, j)
                        - dt / dx
                              * (samurai::upwind_scalar_burgers_op<dim, interval_t>(level, i, j).left_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i, 2 * j).left_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i, 2 * j + 1).left_flux(k, u));
            });

        stencil = {
            {0, -1}
        };

        auto subset_up = samurai::intersection(samurai::translate(mesh[mesh_id_t::cells][level + 1], stencil), mesh[mesh_id_t::cells][level])
                             .on(level);

        subset_up(
            [&](const auto& i, const auto& index)
            {
                auto j          = index[0];
                const double dx = mesh.cell_length(level);

                unp1(level,
                     i,
                     j) = unp1(level, i, j)
                        + dt / dx
                              * (samurai::upwind_scalar_burgers_op<dim, interval_t>(level, i, j).up_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i, 2 * j + 1).up_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i + 1, 2 * j + 1).up_flux(k, u));
            });

        stencil = {
            {0, 1}
        };

        auto subset_down = samurai::intersection(samurai::translate(mesh[mesh_id_t::cells][level + 1], stencil),
                                                 mesh[mesh_id_t::cells][level])
                               .on(level);

        subset_down(
            [&](const auto& i, const auto& index)
            {
                auto j          = index[0];
                const double dx = mesh.cell_length(level);

                unp1(level,
                     i,
                     j) = unp1(level, i, j)
                        - dt / dx
                              * (samurai::upwind_scalar_burgers_op<dim, interval_t>(level, i, j).down_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i, 2 * j).down_flux(k, u)
                                 - 0.5 * samurai::upwind_scalar_burgers_op<dim, interval_t>(level + 1, 2 * i + 1, 2 * j).down_flux(k, u));
            });
    }
}

template <class Field>
void save(const fs::path& path, const std::string& filename, const Field& u, const std::string& suffix = "")
{
    auto mesh   = u.mesh();
    auto level_ = samurai::make_field<std::size_t, 1>("level", mesh);

    if (!fs::exists(path))
    {
        fs::create_directory(path);
    }

    samurai::for_each_cell(mesh,
                           [&](const auto& cell)
                           {
                               level_[cell] = cell.level;
                           });

    samurai::save(path, fmt::format("{}{}", filename, suffix), mesh, u, level_);
    samurai::dump(path, fmt::format("{}_restart{}", filename, suffix), mesh, u);
}

int main(int argc, char* argv[])
{
    auto& app = samurai::initialize("Finite volume example for the scalar Burgers equation in 2d using multiresolution", argc, argv);

    constexpr size_t dim = 2;
    using Config         = samurai::MRConfig<dim>;

    // Simulation parameters
    xt::xtensor_fixed<double, xt::xshape<dim>> min_corner = {0., 0.};
    xt::xtensor_fixed<double, xt::xshape<dim>> max_corner = {1., 1.};
    std::array<double, 2> k{
        {sqrt(2.) / 2., sqrt(2.) / 2.}
    };
    double Tf  = 0.1;
    double cfl = 0.05;
    double t   = 0.;
    std::string restart_file;

    // Multiresolution parameters
    std::size_t min_level = 4;
    std::size_t max_level = 10;
    double mr_epsilon     = 2.e-4; // Threshold used by multiresolution
    double mr_regularity  = 1.;    // Regularity guess for multiresolution
    bool correction       = false;

    // Output parameters
    fs::path path        = fs::current_path();
    std::string filename = "FV_scalar_burgers_2d";
    std::size_t nfiles   = 1;

    app.add_option("--min-corner", min_corner, "The min corner of the box")->capture_default_str()->group("Simulation parameters");
    app.add_option("--max-corner", max_corner, "The max corner of the box")->capture_default_str()->group("Simulation parameters");
    app.add_option("--velocity", k, "The velocity of the Burgers equation")->capture_default_str()->group("Simulation parameters");
    app.add_option("--cfl", cfl, "The CFL")->capture_default_str()->group("Simulation parameters");
    app.add_option("--Ti", t, "Initial time")->capture_default_str()->group("Simulation parameters");
    app.add_option("--Tf", Tf, "Final time")->capture_default_str()->group("Simulation parameters");
    app.add_option("--restart-file", restart_file, "Restart file")->capture_default_str()->group("Simulation parameters");
    app.add_option("--min-level", min_level, "Minimum level of the multiresolution")->capture_default_str()->group("Multiresolution");
    app.add_option("--max-level", max_level, "Maximum level of the multiresolution")->capture_default_str()->group("Multiresolution");
    app.add_option("--mr-eps", mr_epsilon, "The epsilon used by the multiresolution to adapt the mesh")
        ->capture_default_str()
        ->group("Multiresolution");
    app.add_option("--mr-reg",
                   mr_regularity,
                   "The regularity criteria used by the multiresolution to "
                   "adapt the mesh")
        ->capture_default_str()
        ->group("Multiresolution");
    app.add_option("--with-correction", correction, "Apply flux correction at the interface of two refinement levels")
        ->capture_default_str()
        ->group("Multiresolution");
    app.add_option("--path", path, "Output path")->capture_default_str()->group("Output");
    app.add_option("--filename", filename, "File name prefix")->capture_default_str()->group("Output");
    app.add_option("--nfiles", nfiles, "Number of output files")->capture_default_str()->group("Output");
    SAMURAI_PARSE(argc, argv);

    const samurai::Box<double, dim> box(min_corner, max_corner);
    samurai::MRMesh<Config> mesh;

    auto u = samurai::make_field<double, 1>("u", mesh);

    if (restart_file.empty())
    {
        mesh = {box, min_level, max_level};
        init(u);
    }
    else
    {
        samurai::load(restart_file, mesh, u);
    }

    samurai::make_bc<samurai::Dirichlet<1>>(u, 0.);

    double dt            = cfl * mesh.cell_length(max_level);
    const double dt_save = Tf / static_cast<double>(nfiles);

    auto unp1 = samurai::make_field<double, 1>("unp1", mesh);

    auto MRadaptation = samurai::make_MRAdapt(u);
    MRadaptation(mr_epsilon, mr_regularity);
    save(path, filename, u, "_init");

    std::size_t nsave = 1;
    std::size_t nt    = 0;

    while (t != Tf)
    {
        MRadaptation(mr_epsilon, mr_regularity);

        t += dt;
        if (t > Tf)
        {
            dt += Tf - t;
            t = Tf;
        }

        std::cout << fmt::format("iteration {}: t = {}, dt = {}", nt++, t, dt) << std::endl;

        samurai::update_ghost_mr(u);
        unp1.resize();
        unp1 = u - dt * samurai::upwind_scalar_burgers(k, u);
        flux_correction(dt, k, u, unp1);

        std::swap(u.array(), unp1.array());

        if (t >= static_cast<double>(nsave + 1) * dt_save || t == Tf)
        {
            const std::string suffix = (nfiles != 1) ? fmt::format("_ite_{}", nsave++) : "";
            save(path, filename, u, suffix);
        }
    }
    samurai::finalize();
    return 0;
}