Kokkos kernel that computes the local maximum stable explicit dt for each FV cell. 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, ScalarT &local_min) const

Public Attributes
grid::Grid3DDataVec< ScalarT, 3 >	grid_

grid::Grid2DDataScalar< ScalarT >	radii_

grid::Grid4DDataVec< ScalarT, 3 >	cell_centers_

grid::Grid4DDataVec< ScalarT, 3 >	vel_grid_

ScalarT	diffusivity_

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

Detailed Description

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

Kokkos kernel that computes the local maximum stable explicit dt for each FV cell.

The low-order predictor \(T^L_i\) is stable if and only if

\[ \frac{\Delta t}{M_{ii}}\,\lambda_i \leq 1, \qquad \lambda_i = \sum_{j:\,\beta_{ij}<0} |\beta_{ij}| + \sum_j \kappa\,\frac{|\mathbf{S}_{f,j}|^2} {(\mathbf{x}_j-\mathbf{x}_i)\cdot\mathbf{S}_{f,j}} \]

(assumes subtract_divergence = true; the formula naturally coincides with the advective stability limit \(\sum_{j:\,\beta>0}\beta_{ij}\) for exactly divergence-free fields.)

For each cell the kernel outputs \(M_{ii}/\lambda_i\) (a time scale), so the global minimum is the largest dt that satisfies the stability criterion everywhere.

This accounts for:

Lateral face fluxes on irregular/small cells near pentagon vertices of the icosahedral grid — these are missed by the simpler \(h_\text{min,radial}/u_\text{max}\) estimate.
Non-orthogonal diffusion stencils, where \(|\mathbf{S}_f|^2/(\mathbf{dx}\cdot\mathbf{S}_f)\) can be much larger than \(1/h^2\).