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Title: A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty

Abstract

This paper is concerned with generalized polynomial chaos (gPC) approximation for first-order quasilinear hyperbolic systems with uncertainty. The one-dimensional (1D) hyperbolic system is first symmetrized with the aid of left eigenvector matrix of the Jacobian matrix. Then the gPC stochastic Galerkin method is applied to derive a provably symmetrically hyperbolic equations for the gPC expansion coefficients. The resulting deterministic gPC Galerkin system is discretized by a path-conservative finite volume WENO scheme in space and a third-order total variation diminishing Runge–Kutta method in time. The method is further extended to two-dimensional (2D) quasilinear hyperbolic system with uncertainty, where the symmetric hyperbolicity of the one-dimensional gPC Galerkin system is carried over via an operator splitting technique. Several numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed gPC stochastic Galerkin method.

Authors:
 [1];  [1];  [2];  [3]
  1. HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)
  2. (China)
  3. Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)
Publication Date:
OSTI Identifier:
22701596
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 345; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; MATHEMATICAL OPERATORS; MATRICES; ONE-DIMENSIONAL CALCULATIONS; RUNGE-KUTTA METHOD; STOCHASTIC PROCESSES; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Wu, Kailiang, Tang, Huazhong, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, and Xiu, Dongbin. A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.05.027.
Wu, Kailiang, Tang, Huazhong, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, & Xiu, Dongbin. A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. United States. doi:10.1016/J.JCP.2017.05.027.
Wu, Kailiang, Tang, Huazhong, School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province, and Xiu, Dongbin. Fri . "A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty". United States. doi:10.1016/J.JCP.2017.05.027.
@article{osti_22701596,
title = {A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty},
author = {Wu, Kailiang and Tang, Huazhong and School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan Province and Xiu, Dongbin},
abstractNote = {This paper is concerned with generalized polynomial chaos (gPC) approximation for first-order quasilinear hyperbolic systems with uncertainty. The one-dimensional (1D) hyperbolic system is first symmetrized with the aid of left eigenvector matrix of the Jacobian matrix. Then the gPC stochastic Galerkin method is applied to derive a provably symmetrically hyperbolic equations for the gPC expansion coefficients. The resulting deterministic gPC Galerkin system is discretized by a path-conservative finite volume WENO scheme in space and a third-order total variation diminishing Runge–Kutta method in time. The method is further extended to two-dimensional (2D) quasilinear hyperbolic system with uncertainty, where the symmetric hyperbolicity of the one-dimensional gPC Galerkin system is carried over via an operator splitting technique. Several numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed gPC stochastic Galerkin method.},
doi = {10.1016/J.JCP.2017.05.027},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 345,
place = {United States},
year = {2017},
month = {9}
}