期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 41, 期 3, 页码 A1500-A1526出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1196297
关键词
kinetic transport equations; diffusion limit; positive-preserving schemes; asymptotic-preserving schemes; finite difference methods
资金
- U.S. Department of Energy, under the SCGSR program [DE-AC05-06OR23100]
- Office of Advanced Scientific Computing Research and performed at the Oak Ridge National Laboratory [DE-AC05-00OR22725]
We present a positive-and asymptotic-preserving numerical scheme for solving linear kinetic transport equations that relax to a diffusive equation in the limit of infinite scattering. The proposed scheme is developed using a standard spectral angular discretization and a classical micro-macro decomposition. The three main ingredients are a semi-implicit temporal discretization, a dedicated finite difference spatial discretization, and realizability limiters in the angular discretization. Under mild assumptions, the scheme becomes a consistent numerical discretization for the limiting diffusion equation when the scattering cross-section tends to infinity. The scheme also preserves positivity of the particle concentration on the space-time mesh and therefore fixes a common defect of spectral angular discretizations. The scheme is tested on the well-known line source benchmark problem with the usual uniform material medium as well as a medium composed of different materials that are arranged in a checkerboard pattern. We also tested the scheme on a Riemann problem with a nonuniform material medium. The observed order of space-time accuracy of the proposed scheme is reported.
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