Efficient Stochastic Asymptotic-Preserving IMEX Methods for Transport Equations with Diffusive Scalings and Random Inputs

2017/03/10 by Shi Jin, Hanqing Lu, Jin, Shi +3
Decision Sciences · Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1703.03841

openalex publication_date 2017/03/10 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01

Abstract

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 use the implicit-explicit (IMEX) 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 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 computational cost comparison with previous methods.

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