Hybrid Solver for the Radiative Transport Equation Using Finite Volume and Discontinuous Galerkin

TL;DR

This paper introduces a hybrid spatial discretization method combining DG and FV techniques for the radiative transport equation, improving accuracy and efficiency in scattering-dominated regimes.

Contribution

It presents a novel hybrid discretization strategy that reduces memory and computational costs while maintaining accuracy, with natural hybridization in space and angle.

Findings

Efficient hybrid method outperforms uniform DG in scattering regimes.

Reduces memory usage and computational time.

Demonstrates effectiveness on Cartesian grids with discrete ordinates.

Abstract

We propose a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster computational time than a uniform DG discretization. In addition, the underlying splitting allows naturally for hybridization in both space and angle. Numerical results are given to demonstrate the efficiency of the hybrid approach in the context of discrete ordinate angular discretizations and Cartesian spatial grids.