412 research outputs found
Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit
We present a mathematical analysis of the asymptotic preserving scheme
proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334-368,
2008] for linear transport equations in kinetic and diffusive regimes. We prove
that the scheme is uniformly stable and accurate with respect to the mean free
path of the particles. This property is satisfied under an explicitly given CFL
condition. This condition tends to a parabolic CFL condition for small mean
free paths, and is close to a convection CFL condition for large mean free
paths. Ou r analysis is based on very simple energy estimates
StaRMAP - A second order staggered grid method for spherical harmonics moment equations of radiative transfer
We present a simple method to solve spherical harmonics moment systems, such
as the the time-dependent and equations, of radiative transfer.
The method, which works for arbitrary moment order , makes use of the
specific coupling between the moments in the 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.Comment: 28 pages, 7 figures; StaRMAP code available at
http://www.math.temple.edu/~seibold/research/starma
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