Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings

JOURNAL OF COMPUTATIONAL PHYSICS

卷:289

Article

Jin, Shi^1,2,3  Xiu, Dongbin^4,5  Zhu, Xueyu⁴ 

[1] Shanghai Jiao Tong Univ, Dept Math, Inst Nat Sci, Shanghai 200240, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200240, Peoples R China

[3] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[4] Univ Utah, Sci Comp & Imaging Inst, Salt Lake City, UT 84112 USA

[5] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

关键词: Uncertainty quantification;    Hyperbolic systems;    Transport equations;    Diffusion limit;    Asympotic-preserving;    Generalized polynomial chaos;   

DOI  :  10.1016/j.jcp.2015.02.023

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free