CRKSPH-compatible discretization of the SUPG and SAAF transport equations

TL;DR

This paper introduces a novel discretization method for transport equations using reproducing kernels, ensuring compatibility with smoothed particle hydrodynamics and involving only kernel evaluations at nodes.

Contribution

It develops a new discretization approach for the self-adjoint angular flux and SUPG/SAAF equations using reproducing kernels, including a novel second derivative for diffusion terms.

Findings

Discretization is compatible with conservative reproducing kernel SPH.

The method involves only kernel evaluations at nodal centers.

A new second derivative for diffusion-like terms is derived.

Abstract

The self-adjoint angular flux and streamline-upwind Petrov-Galerkin transport equations are discretized using reproducing kernels with the collocation method to produce a discretization that is compatible with conservative reproducing kernel smoothed particle hydrodynamics. A novel second derivative is derived for the diffusion-like term in the self-adjoint angular flux equation. The resulting equations involve only evaluations of kernels and physical data at the nodal centers.