A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
- HEDPS, CAPT & LMAM, School of Mathematical Sciences, Peking University, Beijing 100871 (China)
- Department of Mathematics, The Ohio State University, Columbus, OH 43210 (United States)
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.
- OSTI ID:
- 22701596
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 345; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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