StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer

TL;DR

StaRMAP introduces a second-order staggered grid finite difference method for solving spherical harmonics moment equations in radiative transfer, offering high efficiency and simplicity for large-scale problems.

Contribution

The paper presents a novel, simple, and efficient second-order staggered grid scheme for spherical harmonics moment systems, applicable to arbitrary moment order N.

Findings

Able to solve problems with ten million degrees of freedom in seconds

The scheme achieves second-order accuracy without TVD or realizability limiters

Open-source code enables reproducibility of all test results

Abstract

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $SP_N$ equations, of radiative transfer. The method, which works for arbitrary moment order $N$, makes use of the specific coupling between the moments in the $P_N$ equations. This coupling naturally induces staggered grids in space and time, which in turn give rise to a canonical, second-order accurate finite difference scheme. While the scheme does not possess TVD or realizability limiters, its simplicity allows for a very efficient implementation in Matlab. We present several test cases, some of which demonstrate that the code solves problems with ten million degrees of freedom in space, angle, and time within a few seconds. The code for the numerical scheme, called StaRMAP (Staggered grid Radiation Moment Approximation), along with files for all presented test cases, can be downloaded so that all results can be reproduced by the reader.