terra::fv::hex::operators::FCTPredictorKernel< ScalarT > Struct Template Reference

Kokkos kernel for the explicit low-order predictor and antidiffusive flux assembly. More...

#include <fct_advection_diffusion.hpp>

Public Types
using	ScalarType = ScalarT
using	Vec3 = dense::Vec< ScalarT, 3 >
using	GH = fct_detail::GeometryHelper< ScalarT >

Public Member Functions
void	operator() (const int id, const int x, const int y, const int r) const

Public Attributes
grid::Grid3DDataVec< ScalarT, 3 >	grid_
grid::Grid2DDataScalar< ScalarT >	radii_
grid::Grid4DDataVec< ScalarT, 3 >	cell_centers_
grid::Grid4DDataVec< ScalarT, 3 >	vel_grid_
grid::Grid4DDataScalar< ScalarT >	T_old_
	\(T^n\): scalar at time level \(n\) (ghost layers must be filled).
grid::Grid4DDataScalar< ScalarT >	T_L_
	\(T^L\): low-order predictor output.
grid::Grid5DDataScalar< ScalarT >	antidiff_
	\(\tilde{f}_{ij}\): pre-scaled antidiff flux per face, shape \([\ldots, 6]\).
ScalarT	dt_
	Time step \(\Delta t\).
ScalarT	diffusivity_
	Physical diffusivity \(\kappa \geq 0\); set to 0 for pure advection.
bool	subtract_divergence_ = true
	Whether to subtract the discrete divergence error \(T_i\,\nabla\cdot\mathbf{u}\).
Optional volumetric source term \f$f\f$ [T/time]
Source values per cell. A null (default-constructed) view means no source. The explicit predictor adds \(\Delta t \cdot f_i\) to \(T_i^L\) after the upwind/diffusion update. Physical units: same as \(T\) per unit time.
grid::Grid4DDataScalar< ScalarT >	source_
bool	has_source_ = false

Static Public Attributes
static constexpr int	num_neighbors = GH::num_neighbors

Detailed Description

template<typename ScalarT>
struct terra::fv::hex::operators::FCTPredictorKernel< ScalarT >

Kokkos kernel for the explicit low-order predictor and antidiffusive flux assembly.

In a single pass over each cell \(i\) this kernel:

1. Calls GeometryHelper::compute_geometry to obtain the face-normal velocity fluxes \(\beta_{ij}\), the cell volume \(M_{ii}\), and the area-weighted face normals \(\mathbf{S}_f^{(j)}\) for all 6 neighbours.
2. Computes the low-order predictor (first-order upwind + two-point diffusion):

   \[ T_i^L = T_i^n - \frac{\Delta t}{M_{ii}} \left[ \beta_{ii}^+\,T_i^n + \sum_j \beta_{ij}^-\,T_j^n + \sum_j \kappa\, \frac{|\mathbf{S}_f^{(j)}|^2} {(\mathbf{x}_j-\mathbf{x}_i)\cdot\mathbf{S}_f^{(j)}} (T_i^n - T_j^n) \right], \]

   where \(\beta^+ = \max(\beta,0)\) and \(\beta^- = \min(\beta,0)\).
3. Stores the pre-scaled antidiffusive flux for face \(j\):

   \[ \tilde{f}_{ij} = \frac{\Delta t}{M_{ii}}\,\frac{|\beta_{ij}|}{2}\,(T_i^n - T_j^n). \]

   Physical diffusion is not included in \(\tilde{f}_{ij}\) — only purely advective antidiffusion enters the Zalesak limiter.

Note

Ghost layers of \(T^n\) (and of cell_centers_) must be filled before launch.

The kernel is Kokkos-portable (CUDA/HIP/OpenMP/Serial).

Template Parameters

ScalarT

Floating-point scalar type.

Member Typedef Documentation

GH

template<typename ScalarT >

using terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::GH = fct_detail::GeometryHelper< ScalarT >

ScalarType

template<typename ScalarT >

using terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::ScalarType = ScalarT

Vec3

template<typename ScalarT >

using terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::Vec3 = dense::Vec< ScalarT, 3 >

Member Function Documentation

operator()()

template<typename ScalarT >

void terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::operator() ( const int  id, const int  x, const int  y, const int  r  ) const

inline

Member Data Documentation

antidiff_

template<typename ScalarT >

grid::Grid5DDataScalar< ScalarT > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::antidiff_

\(\tilde{f}_{ij}\): pre-scaled antidiff flux per face, shape \([\ldots, 6]\).

cell_centers_

template<typename ScalarT >

grid::Grid4DDataVec< ScalarT, 3 > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::cell_centers_

diffusivity_

template<typename ScalarT >

ScalarT terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::diffusivity_

Physical diffusivity \(\kappa \geq 0\); set to 0 for pure advection.

dt_

template<typename ScalarT >

ScalarT terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::dt_

Time step \(\Delta t\).

grid_

template<typename ScalarT >

grid::Grid3DDataVec< ScalarT, 3 > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::grid_

has_source_

template<typename ScalarT >

bool terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::has_source_ = false

num_neighbors

template<typename ScalarT >

constexpr int terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::num_neighbors = GH::num_neighbors

staticconstexpr

radii_

template<typename ScalarT >

grid::Grid2DDataScalar< ScalarT > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::radii_

source_

template<typename ScalarT >

grid::Grid4DDataScalar< ScalarT > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::source_

subtract_divergence_

template<typename ScalarT >

bool terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::subtract_divergence_ = true

Whether to subtract the discrete divergence error \(T_i\,\nabla\cdot\mathbf{u}\).

When true (default), the correction \(-T_i\,(\sum_j \beta_{ij})/M_{ii}\) is applied, converting the conservative form \(\nabla\cdot(\mathbf{u}T)\) into the advective form \(\mathbf{u}\cdot\nabla T\). This is the physically correct equation for temperature. When \(\nabla\cdot\mathbf{u} = 0\) the correction is exactly zero and costs nothing.

T_L_

template<typename ScalarT >

grid::Grid4DDataScalar< ScalarT > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::T_L_

\(T^L\): low-order predictor output.

T_old_

template<typename ScalarT >

grid::Grid4DDataScalar< ScalarT > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::T_old_

\(T^n\): scalar at time level \(n\) (ghost layers must be filled).

vel_grid_

template<typename ScalarT >

grid::Grid4DDataVec< ScalarT, 3 > terra::fv::hex::operators::FCTPredictorKernel< ScalarT >::vel_grid_

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The documentation for this struct was generated from the following file:

• fct_advection_diffusion.hpp