Meshless discretization of the discrete-ordinates transport equation with integration based on Voronoi cells

The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends on the position and extent of the kernels. The resolution of the integration automatically follows the particles and requires no manual adjustment. The discretization includes streamline-upwind Petrov-Galerkin stabilization to prevent oscillations and improve numerical conditioning. The angular quadrature is selectively refineable to increase angular resolution in chosen directions. The time discretization is done using backward Euler. The transport solve for each direction and the solve for the scattering source are both done using Krylov iterative methods. Results indicate first-order convergence in time and second-order convergence in space for linear reproducing kernels. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The time-dependent, gray, linear radiation transport equation is discretized using the meshless local Petrov-Galerkin method with reproducing kernels, integrated using a Voronoi tessellation that automatically adjusts resolution and includes streamline-upwind Petrov-Galerkin stabilization. The angular quadrature can be selectively refined for higher angular resolution, with results indicating first-order convergence in time and second-order convergence in space using Krylov iterative methods for solving transport and scattering source.