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	A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
	Wu, Kailiang ; Tang, Huazhong ; Xiu, Dongbin
	2017
关键词	Uncertainty quantification Quasilinear hyperbolic system Stochastic Galerkin methods Generalized polynomial chaos Symmetrically hyperbolic Operator splitting PARTIAL-DIFFERENTIAL-EQUATIONS FINITE-VOLUME SCHEMES RANDOM INPUT DATA EULER EQUATIONS GAS-DYNAMICS COLLOCATION METHOD POLYNOMIAL CHAOS QUANTIFICATION SIMULATIONS PROPAGATION
英文摘要	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. (C) 2017 Elsevier Inc. All rights reserved.; National Natural Science Foundation of China [91330205, 11421101, 91630310]; AFOSR [FA95501410022]; DARPA [N660011524053]; NSF [DMS-1418771]; SCI(E); ARTICLE; 224-244; 345
语种	英语
出处	SCI
出版者	JOURNAL OF COMPUTATIONAL PHYSICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/470865]
专题	数学科学学院 工学院
推荐引用方式 GB/T 7714	Wu, Kailiang,Tang, Huazhong,Xiu, Dongbin. A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty. 2017-01-01.

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