Journal article
Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings
Journal of computational physics, Vol.289(C), pp.35-52
05/15/2015
DOI: 10.1016/j.jcp.2015.02.023
Abstract
In this paper we develop a set of stochastic numerical schemes for hyperbolic and transport equations with diffusive scalings and subject to random inputs. The schemes are asymptotic preserving (AP), in the sense that they preserve the diffusive limits of the equations in discrete setting, without requiring excessive refinement of the discretization. Our stochastic AP schemes are extensions of the well-developed deterministic AP schemes. To handle the random inputs, we employ generalized polynomial chaos (gPC) expansion and combine it with stochastic Galerkin procedure. We apply the gPC Galerkin scheme to a set of representative hyperbolic and transport equations and establish the AP property in the stochastic setting. We then provide several numerical examples to illustrate the accuracy and effectiveness of the stochastic AP schemes. (C) 2015 Elsevier Inc. All rights reserved.
Details
- Title: Subtitle
- Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings
- Creators
- Shi Jin - University of Wisconsin–MadisonDongbin Xiu - University of UtahXueyu Zhu - University of Utah
- Resource Type
- Journal article
- Publication Details
- Journal of computational physics, Vol.289(C), pp.35-52
- DOI
- 10.1016/j.jcp.2015.02.023
- ISSN
- 0021-9991
- eISSN
- 1090-2716
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Number of pages
- 18
- Grant note
- 91330203 / National Science Foundation of China 1107291: RNMS / NSF FA9300-14-C-2502 / AFOSR DESC0011615 / DOE
- Language
- English
- Date published
- 05/15/2015
- Academic Unit
- Mathematics
- Record Identifier
- 9984240772602771
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