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

TL;DR

This paper introduces advanced stochastic IMEX schemes for transport equations with uncertainties, achieving higher accuracy and relaxed stability conditions in multiscale diffusive regimes, demonstrated through theoretical analysis and numerical tests.

Contribution

It presents novel stochastic Galerkin schemes with IMEX discretization and diffusion-based penalties, improving stability and efficiency for multiscale transport problems with randomness.

Findings

Higher order accuracy achieved with IMEX schemes.

Relaxed hyperbolic CFL stability condition in diffusive regimes.

Numerical demonstrations confirm asymptotic-preserving property and efficiency.

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.