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

doi:10.1007/s42967-023-00249-x

Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (1): 325-339.doi: 10.1007/s42967-023-00249-x

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

Zheng Chen¹, Lin Mu²

1. Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, Dartmouth, 02747, MA, USA;
2. Department of Mathematics, University of Georgia, Athens, 30602, GA, USA

收稿日期:2022-07-20 修回日期:2022-12-16 发布日期:2024-04-16
通讯作者: Zheng Chen,E-mail:zchen2@umassd.edu;Lin Mu,E-mail:linmu@uga.edu E-mail:zchen2@umassd.edu;linmu@uga.edu
基金资助:
Mu is partially supported by the Simons Foundation: Collaboration Grants. Chen is partially supported by the AFOSR grant FA9550-18-1-0383.

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

Zheng Chen¹, Lin Mu²

1. Department of Mathematics, University of Massachusetts Dartmouth, 285 Old Westport Road, Dartmouth, 02747, MA, USA;
2. Department of Mathematics, University of Georgia, Athens, 30602, GA, USA

Received:2022-07-20 Revised:2022-12-16 Published:2024-04-16
Contact: Zheng Chen,E-mail:zchen2@umassd.edu;Lin Mu,E-mail:linmu@uga.edu E-mail:zchen2@umassd.edu;linmu@uga.edu
Supported by:
Mu is partially supported by the Simons Foundation: Collaboration Grants. Chen is partially supported by the AFOSR grant FA9550-18-1-0383.

摘要/Abstract

摘要： 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.

关键词: Stochastic Galerkin scheme, linear transport equations, generalized polynomial approach, stochastic asymptotic-preserving property

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.

Key words: Stochastic Galerkin scheme, linear transport equations, generalized polynomial approach, stochastic asymptotic-preserving property

Zheng Chen, Lin Mu. High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings[J]. Communications on Applied Mathematics and Computation, 2024, 6(1): 325-339.

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

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

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