High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

Abstract

In this paper, we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs. To tackle the randomness in the problem, the stochastic Galerkin method of the generalized polynomial chaos approach has been employed. Besides, the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed. We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.

Keywords

Stochastic Galerkin scheme / linear transport equations / generalized polynomial approach / stochastic asymptotic-preserving property

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Funding

Simons Foundation; U.S. Air Force(FA9550-18-1-0383)