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

Kokkos kernel that computes the Zalesak nodal correction factors \(R_i^+\) and \(R_i^-\) from the low-order predictor \(T^L\) and the antidiffusive fluxes. More...

#include <fct_advection_diffusion.hpp>

Public Types
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::Grid4DDataScalar< ScalarT >	T_L_
	\(T^L\) with ghost layers filled.
grid::Grid5DDataScalar< ScalarT >	antidiff_
	\(\tilde{f}_{ij}\): pre-scaled antidiff fluxes.
grid::Grid4DDataScalar< ScalarT >	R_plus_
	Output: \(R_i^+\) correction factor.
grid::Grid4DDataScalar< ScalarT >	R_minus_
	Output: \(R_i^-\) correction factor.

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

Detailed Description

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

Kokkos kernel that computes the Zalesak nodal correction factors \(R_i^+\) and \(R_i^-\) from the low-order predictor \(T^L\) and the antidiffusive fluxes.

Per cell \(i\) (summing over all 6 neighbours \(j \in \mathcal{N}(i)\)):

Positive/negative flux sums:

\[ P_i^+ = \sum_{j:\,\tilde{f}_{ij} > 0} \tilde{f}_{ij}, \qquad P_i^- = \sum_{j:\,\tilde{f}_{ij} < 0} \tilde{f}_{ij}. \]

Local extrema of the low-order solution:

\[ T_i^{\max} = \max(T_i^L,\;T_j^L\;\forall j \in \mathcal{N}(i)), \qquad T_i^{\min} = \min(T_i^L,\;T_j^L\;\forall j \in \mathcal{N}(i)). \]

Room to grow/shrink:

\[ Q_i^+ = T_i^{\max} - T_i^L \geq 0, \qquad Q_i^- = T_i^{\min} - T_i^L \leq 0. \]

Correction factors (Zalesak 1979, eq. 13–14):

\[ R_i^+ = \begin{cases} \min\!\left(1,\;\dfrac{Q_i^+}{P_i^+}\right) & P_i^+ > 0 \\ 1 & \text{otherwise} \end{cases}, \qquad R_i^- = \begin{cases} \min\!\left(1,\;\dfrac{Q_i^-}{P_i^-}\right) & P_i^- < 0 \\ 1 & \text{otherwise} \end{cases}. \]

Note

Ghost layers of \(T^L\) must be filled before launch so that \(T_j^L\) for boundary-adjacent cells is available.

Template Parameters

ScalarT

Floating-point scalar type.

Member Typedef Documentation

GH

template<typename ScalarT >

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

Member Function Documentation

operator()()

template<typename ScalarT >

void terra::fv::hex::operators::FCTLimiterKernel< 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::FCTLimiterKernel< ScalarT >::antidiff_

\(\tilde{f}_{ij}\): pre-scaled antidiff fluxes.

num_neighbors

template<typename ScalarT >

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

staticconstexpr

R_minus_

template<typename ScalarT >

grid::Grid4DDataScalar< ScalarT > terra::fv::hex::operators::FCTLimiterKernel< ScalarT >::R_minus_

Output: \(R_i^-\) correction factor.

R_plus_

template<typename ScalarT >

grid::Grid4DDataScalar< ScalarT > terra::fv::hex::operators::FCTLimiterKernel< ScalarT >::R_plus_

Output: \(R_i^+\) correction factor.

T_L_

template<typename ScalarT >

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

\(T^L\) with ghost layers filled.

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

• fct_advection_diffusion.hpp