期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 43, 期 3, 页码 B759-B783出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1318031
关键词
front capturing; asymptotic preserving; radiative transfer equation; nonlinearity
资金
- Science Challenge Project [TZ2016002]
- NSFC [NSFC11871340, NSFC91330203]
- NSF-DMS [1903420]
- NSF CAREER-DMS [1846854]
- University of Minnesota
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1903420] Funding Source: National Science Foundation
The translation discusses an asymptotic preserving scheme for the gray radiative transfer equation, introducing an auxiliary variable to solve an implicit nonlinear system and using a three-stage update. The method preserves accurate simulation results in both the nonlinear diffusion limit and the free streaming limit.
We develop an asymptotic preserving scheme for the gray radiative transfer equation. Two asymptotic regimes are considered: one is a diffusive regime described by a nonlinear diffusion equation for the material temperature; the other is a free streaming regime with zero opacity. To alleviate the restriction on time step and capture the correct front propagation in the diffusion limit, an implicit treatment is crucial. However, this often involves a large-scale nonlinear iterative solver as the spatial and angular dimensions are coupled. Our idea is to introduce an auxiliary variable that leads to a redundant system, which is then solved with a three-stage update: prediction, correction, and projection. The benefit of this approach is that the implicit system is local to each spatial element, independent of angular variable, and thus only requires a scalar Newton's solver. We also introduce a spatial discretization with a compact stencil based on even-odd decomposition. Our method preserves both the nonlinear diffusion limit with correct front propagation speed and the free streaming limit, with a hyperbolic CFL condition.
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