xref: /honee/qfunctions/numerics.h (revision 2a28a40b05596e8676ec98635f0ea5784ed7a63a)

// SPDX-FileCopyrightText: Copyright (c) 2017-2024, HONEE contributors.
// SPDX-License-Identifier: Apache-2.0 OR BSD-2-Clause

#include <ceed/types.h>
#include "utils.h"

/**
  @brief Calculate CFL for 3D spatial dimensions

  Defined as
  @f[
  \mathrm{CFL} = \Delta t \sqrt{\overline{g}_{jk} u_j u_k}
  @f]

  where \f$ \Delta t \f$ is the `timestep`, \f$ \overline{g}_{jk} \f$ is the element metric tensor `gij`, and \f$ u_j \f$ is the `velocity`.
  For best results, `gij` should be scaled to account for the reference element domain (often [-1,1] for Gaussian quadrature).

  @param[in] velocity Velocity
  @param[in] timestep Timestep
  @param[in] gij      Element metric tensor (should be scaled)
  @return    The CFL value for the element
**/
CEED_QFUNCTION_HELPER CeedScalar CalculateCFL_3D(const CeedScalar velocity[3], CeedScalar timestep, const CeedScalar gij[3][3]) {
  CeedScalar gij_uj[3] = {0.};

  MatVec3(gij, velocity, CEED_NOTRANSPOSE, gij_uj);
  return sqrt(Dot3(velocity, gij_uj)) * timestep;
}

/**
  @brief Calculate CFL for 2D spatial dimensions

  Defined as
  @f[
  \mathrm{CFL} = \Delta t \sqrt{\overline{g}_{jk} u_j u_k}
  @f]

  where \f$ \Delta t \f$ is the `timestep`, \f$ \overline{g}_{jk} \f$ is the element metric tensor `gij`, and \f$ u_j \f$ is the `velocity`.
  For best results, `gij` should be scaled to account for the reference element domain (often [-1,1] for Gaussian quadrature).

  @param[in] velocity Advection velocity
  @param[in] timestep Timestep
  @param[in] gij      Element metric tensor (should be scaled)
  @return    The CFL value for the element
**/
CEED_QFUNCTION_HELPER CeedScalar CalculateCFL_2D(const CeedScalar velocity[2], CeedScalar timestep, const CeedScalar gij[2][2]) {
  CeedScalar gij_uj[2] = {0.};

  MatVec2(gij, velocity, CEED_NOTRANSPOSE, gij_uj);
  return sqrt(Dot2(velocity, gij_uj)) * timestep;
}