DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

Chen, Zheng; Liu, Liu; Mu, Lin

doi:10.1007/s10915-017-0439-2

Title: DG-IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

Journal Article · Wed May 03 00:00:00 EDT 2017 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-017-0439-2· OSTI ID:1356966

^[1]; Liu, Liu ^[2]; Mu, Lin ^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division
Univ. of Wisconsin, Madison, WI (United States). Department of Mathematics

In this paper, we consider the linear transport equation under diffusive scaling and with random inputs. The method is based on the generalized polynomial chaos approach in the stochastic Galerkin framework. Several theoretical aspects will be addressed. Additionally, a uniform numerical stability with respect to the Knudsen number ϵ, and a uniform in ϵ error estimate is given. For temporal and spatial discretizations, we apply the implicit–explicit scheme under the micro–macro decomposition framework and the discontinuous Galerkin method, as proposed in Jang et al. (SIAM J Numer Anal 52:2048–2072, 2014) for deterministic problem. Lastly, we provide a rigorous proof of the stochastic asymptotic-preserving (sAP) property. Extensive numerical experiments that validate the accuracy and sAP of the method are conducted.

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Research Organization:: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1356966

Journal Information:: Journal of Scientific Computing, Vol. 73, Issue 2-3; ISSN 0885-7474

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 9 works

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References (17)

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