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

Abstract

We present a simple method to solve spherical harmonics moment systems, such as the the time-dependent $P_N$ and $S{P}_N$ 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.

arXiv comment28 pages, 7 figures; StaRMAP code available at http://www.math.temple.edu/~seibold/research/starmap

References in corpus (1)

• Asymptotic Derivation and Numerical Investigation of Time-Dependent Simplified Pn Equations

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