HeatConduction.H

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//
// This implements a basic heat conduction method in Alamo.
// The partial differential equation to be solved is
//
// .. math::
//
//    \frac{\partial T}{\partial t} = \alpha\,\Delta T
//
// where :math:`T` is temperature, :math:`t` is time, and :math:`alpha` 
// is the thermal diffusivity.
// Integration is performed explicitly in time using forward Euler, and
// differentiation is performed using the finite difference method.
//
 
#ifndef INTEGRATOR_HEATCONDUCTION_H // Include guards
#define INTEGRATOR_HEATCONDUCTION_H // 
 
// AMReX Includes
#include "AMReX_Array4.H"
#include "AMReX_GpuComplex.H"
#include "AMReX_MFIter.H"
#include <AMReX.H>
#include <AMReX_ParallelDescriptor.H>
#include <AMReX_ParmParse.H>
#include <AMReX_TimeIntegrator.H>
 
// Alamo Includes
#include "Set/Base.H"
#include "Integrator.H"
#include "IO/ParmParse.H"
#include "Integrator/Integrator.H"
#include "BC/Constant.H"
#include "BC/Expression.H"
#include "IC/IC.H"
#include "IC/Sphere.H"
#include "IC/Constant.H"
#include "IC/Expression.H"
#include "Numeric/Stencil.H"
#include "Operator/Spectral/FFT.H"
 
namespace Integrator
{
class HeatConduction : virtual public Integrator
{
public:
    static constexpr const char* name = "heatconduction";
 
 
    // Empty constructor
    HeatConduction(int a_nghost = 2) : 
        Integrator(),
        number_of_ghost_cells(a_nghost)
    {}
 
    // Constructor that triggers parse
    HeatConduction(IO::ParmParse& pp) : HeatConduction()
    {
        Parse(*this, pp);
    }
 
    virtual ~HeatConduction()
    {
        delete ic;
        delete bc;
    }
 
    // The Parse function initializes the HeatConduction object using
    // a parser, pp. 
    // Note that this is a static function, which means it does not have
    // direct access to member variables. Instead, it initializes the variables
    // inside the argument, "value", and so all references to member items are
    // prefixed by "value."
    static void Parse(HeatConduction& value, IO::ParmParse& pp)
    {
        // Diffusion coefficient :math:`\alpha`.
        //   *This is an example of a required input variable -
        //    - program will terminate unless it is provided.*
        pp.query_required(  "heat.alpha", value.alpha,
                            Unit::ThermalDiffusivity());
        
        // Criterion for mesh refinement.
        //   *This is an example of a default input variable.
        //    The default value is provided here, not in the 
        //    definition of the variable.*
        pp.query_default(   "heat.refinement_threshold", value.refinement_threshold, "0.01_K", 
                            Unit::Temperature());
 
        // Initial condition type.
        pp.select_default<IC::Constant,IC::Sphere,IC::Expression>(  "ic",value.ic,value.geom, 
                                                                    Unit::Temperature());
 
        // Select BC object for temperature
        pp.select_default<BC::Constant,BC::Expression>( "bc.temp",value.bc,1,
                                                        Unit::Temperature());
 
        // Select between using a realspace solve or the spectral method
        pp.query_validate("method",value.method,{"realspace","spectral"});
 
        // Register the temperature and old temperature fields.
        // temp_mf and temp_old_mf are defined near the bottom of this Header file.
        value.RegisterNewFab(   value.temp_mf, value.bc, value.number_of_components, 
                                value.number_of_ghost_cells, "Temp", true);
        if (value.method == "realspace")
        {
            value.RegisterNewFab(   value.temp_old_mf, value.bc, value.number_of_components, 
                                    value.number_of_ghost_cells, "Temp_old", false);
        }
    }
 
protected:
 
    // Use the ic object to initialize the temperature field
    void Initialize(int lev)
    {
        ic->Initialize(lev, temp_mf);
        if (method == "realspace") ic->Initialize(lev, temp_old_mf);
    }
 
    // Integrate the heat equation
    void Advance(int lev, Set::Scalar time, Set::Scalar dt)
    {
        // If we are solving using the spectral method, go there instead.
        if (method == "spectral")
        {
            AdvanceSpectral(lev,time,dt);
            return;
        }
 
        // Swap the old temp fab and the new temp fab so we use
        // the new one.
        std::swap(*temp_mf[lev], *temp_old_mf[lev]);
 
        // Create the time integrator object
        amrex::TimeIntegrator timeintegrator(*temp_old_mf[lev], time);
        
        // Calculate the "RHS" of the function.
        // If using forward Euler, the RHS would be
        //    T_new = T_old + dt * RHS
        timeintegrator.set_rhs([&](amrex::MultiFab & rhs_mf, amrex::MultiFab & temp_mf, const Set::Scalar /*time*/)
        {
            // Get the cell size corresponding to this level
            const Set::Scalar* DX = geom[lev].CellSize();
 
            // Iterate over all of the patches on this level
            for (amrex::MFIter mfi(temp_mf, amrex::TilingIfNotGPU()); mfi.isValid(); ++mfi)
            {
                // Get the box (index dimensions) for this patch
                const amrex::Box &bx = mfi.tilebox();
 
                // Get an array-accessible handle to the data on this patch.
                Set::Patch<const Set::Scalar>  temp     = temp_mf.array(mfi);
                Set::Patch<Set::Scalar>        rhs      = rhs_mf.array(mfi);
 
                // Iterate over the grid on this patch
                amrex::ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k)
                {
                    // Do the physics!
                    // Note that Numeric::Laplacian is an inlined function so there is no overhead.
                    // You can calculate the derivatives yourself if you want.
                    rhs(i, j, k) = alpha * Numeric::Laplacian(temp, i, j, k, 0, DX);
                });
            }
        });
        
        // We must update the boundaries here and apply boundary conditions 
        timeintegrator.set_post_stage_action([&](amrex::MultiFab & stage_mf, Set::Scalar time) 
        {
            bc->FillBoundary(stage_mf,0,1,time,0);   
            stage_mf.FillBoundary(true);
        });
 
        // Do the update
        timeintegrator.advance(*temp_old_mf[lev], *temp_mf[lev], time, dt);
    }
 
 
#ifdef ALAMO_FFT
    void
    AdvanceSpectral(int lev, Set::Scalar /*time*/, Set::Scalar dt)
    {
        Operator::Spectral::FFT fft(geom,refRatio(),lev);
        amrex::FabArray<amrex::BaseFab<Set::Complex>> Temp_hat = fft.MakeSpectralFab();
        fft.Forward(*temp_mf[lev], Temp_hat);
 
        for (amrex::MFIter mfi(Temp_hat, amrex::TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            const amrex::Box &bx = mfi.tilebox();
            amrex::Array4<Set::Complex> const & T_hat =  Temp_hat.array(mfi);
 
            fft.ParallelFor(bx, [=] AMREX_GPU_DEVICE(int m, int n, int p, Set::Scalar lap) {
                    T_hat(m,n,p) *= exp( - alpha * dt * lap);
                });
        }
        fft.Backward(Temp_hat, *temp_mf[lev]);
    }
#else
    void
    AdvanceSpectral(int, Set::Scalar, Set::Scalar)
    {
        Util::Abort(INFO,"Alamo must be configured with --fft");
    }
#endif
 
 
    // Tag cells for mesh refinement based on temperature gradient
    void TagCellsForRefinement(int lev, amrex::TagBoxArray& a_tags, Set::Scalar /*time*/, int /*ngrow*/)
    {
        if (method=="spectral") return;
 
        // Get cell dimensions as done above.
        const Set::Scalar* DX = geom[lev].CellSize();
        // Calculate the diagonal.
        Set::Scalar dr = sqrt(AMREX_D_TERM(DX[0] * DX[0], +DX[1] * DX[1], +DX[2] * DX[2]));
 
        // Iterate over the patches on this level
        for (amrex::MFIter mfi(*temp_mf[lev], amrex::TilingIfNotGPU()); mfi.isValid(); ++mfi)
        {
            // Get the box and handles as done above.
            const amrex::Box& bx = mfi.tilebox();
            amrex::Array4<char>         const& tags = a_tags.array(mfi);
            amrex::Array4<Set::Scalar>  const& temp = (*temp_mf[lev]).array(mfi);
 
            // Iterate over the grid as done above.
            amrex::ParallelFor(bx, [=] AMREX_GPU_DEVICE(int i, int j, int k)
            {
                // Calculate the temperature gradient.
                Set::Vector grad = Numeric::Gradient(temp, i, j, k, 0, DX);
 
                // Is the gradient * cell_size too big? If so, then
                // mark this cell as needing refinement.
                if (grad.lpNorm<2>() * dr > refinement_threshold)
                    tags(i, j, k) = amrex::TagBox::SET;
            });
        }
    }
 
protected:
    Set::Field<Set::Scalar> temp_mf;         // Temperature field variable (current timestep)
    Set::Field<Set::Scalar> temp_old_mf;     // Temperature field variable (previous timestep)
 
    std::string method; // determine whether to use realspace or spectral method
 
private:
 
    //
    // Definition of parameters set only at instantiation by
    // constructors. 
    //
    const int number_of_components = 1;      // Number of components
    const int number_of_ghost_cells = 2;     // Number of ghost cells
 
    //
    // Definition of user-determined variables.
    //
    // Instantiate all variables to NAN if possible.
    // Default values may be set in Parse using query_default.
    //
 
    Set::Scalar alpha = NAN;                 // Thermal diffusivity
    Set::Scalar refinement_threshold = NAN ; // Criterion for cell refinement
 
    //
    // Definition of user-determined pointer variables.
    //
    // These should be set to nullptr. Make sure that they are deleted
    // in the ~HeatConduction destructor.
    //
 
    IC::IC<Set::Scalar>* ic = nullptr;                    // Object used to initialize temperature field
    BC::BC<Set::Scalar>* bc = nullptr;       // Object used to update temp field boundary ghost cells
};
} // namespace Integrator
#endif