CRKSPH-compatible discretization of the SUPG and SAAF transport equations

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.