StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer
This work provides a simple, efficient numerical method for radiative transfer simulations, which is important for computational physics and engineering applications.
The authors present a second-order accurate finite difference scheme for solving spherical harmonics moment equations (P_N and SP_N) of radiative transfer, achieving efficient solutions for problems with ten million degrees of freedom in seconds using Matlab.
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.