期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 40, 期 2, 页码 A671-A696出版社
SIAM PUBLICATIONS
DOI: 10.1137/17M1120518
关键词
transport equation; radiative heat transfer; uncertainty quantification; asymptotic preserving; diffusion limit; stochastic Galerkin; implicit-explicit Runge-Kutta methods
资金
- NSF [DMS-1522184, DMS-1107291]
- NSFC [91330203]
- Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin, Madison
- Wisconsin Alumni Research Foundation
- GNCS-INDAM, Numerical Methods for Uncertainty Quantification in Hyperbolic and Kinetic Equations
For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based asymptotic-preserving stochastic Galerkin schemes that allow efficient computation for the problems that contain both uncertainties and multiple scales. Compared with previous methods for these problems, our new method uses the implicit-explicit time discretization to gain higher order accuracy, and by using a modified diffusion operator based penalty method, a more relaxed stability condition a hyperbolic, rather than parabolic, CFL stability condition is achieved in the case of a small mean free path in the diffusive regime. The stochastic asymptotic-preserving property of these methods will be shown asymptotically and demonstrated numerically, along with a computational cost comparison with previous methods.
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