期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 345, 期 -, 页码 224-244出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2017.05.027
关键词
Uncertainty quantification; Quasilinear hyperbolic system; Stochastic Galerkin methods; Generalized polynomial chaos; Symmetrically hyperbolic; Operator splitting
资金
- National Natural Science Foundation of China [91330205, 11421101, 91630310]
- AFOSR [FA95501410022]
- DARPA [N660011524053]
- NSF [DMS-1418771]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1656459] Funding Source: National Science Foundation
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.
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