diffusion.hpp

Go to the documentation of this file.

/// @file pde/diffusion.hpp
/// @brief Explicit Euler diffusion steps for 2D uniform grids.
///
/// diffusion_step_2d           -- u += coeff * ∆_periodic(u),  periodic BC
/// diffusion_step_2d_dirichlet -- u += coeff * ∆_dirichlet(u), Dirichlet BC
///
/// coeff = α·dt/h² where α is the diffusion coefficient.
///
/// Typical usage (viscosity in Navier-Stokes):
/// @code
///   const double coeff = dt * nu / (h * h);
///   num::pde::diffusion_step_2d(u_star, N, coeff, num::best_backend);
///   num::pde::diffusion_step_2d(v_star, N, coeff, num::best_backend);
/// @endcode
#pragma once
 
#include "pde/stencil.hpp"
#include "core/vector.hpp"
#include "core/policy.hpp"
 
namespace num::pde {
 
/// Explicit Euler diffusion step on a periodic 2D grid:
///   u += coeff * ∆_periodic(u)
///
/// @param u      NxN field vector (row-major)
/// @param N      Grid side length
/// @param coeff  Diffusion coefficient * dt / h² (e.g. nu*dt/h² for viscosity)
/// @param b      Backend for the axpy accumulation
inline void diffusion_step_2d(Vector& u, int N, double coeff,
                               Backend b = best_backend) {
    Vector lap(u.size());
    laplacian_stencil_2d_periodic(u, lap, N);
    axpy(coeff, lap, u, b);
}
 
/// Explicit Euler diffusion step with Dirichlet (zero) BCs:
///   u += coeff * ∆_dirichlet(u)
inline void diffusion_step_2d_dirichlet(Vector& u, int N, double coeff,
                                         Backend b = best_backend) {
    Vector lap(u.size());
    laplacian_stencil_2d(u, lap, N);
    axpy(coeff, lap, u, b);
}
 
} // namespace num::pde