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

Journal Article · Fri May 15 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2015.02.023· OSTI ID:22465624

Jin, Shi ^[1]; Xiu, Dongbin ^[2]; Zhu, Xueyu ^[2]

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1. Department of Mathematics, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240 (China)
2. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112 (United States)

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.

• OSTI ID: 22465624
• Journal Information: Journal of Computational Physics, Vol. 289; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ASYMPTOTIC SOLUTIONS
CHAOS THEORY
POLYNOMIALS
RANDOMNESS
STOCHASTIC PROCESSES
TRANSPORT THEORY