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

作者：Wu, Kailiang; Tang, Huazhong^*; Xiu, Dongbin

来源：Journal of Computational Physics, 2017, 345: 224-244.

DOI：10.1016/j.jcp.2017.05.027

• Uncertainty quantification
• Quasilinear hyperbolic system
• Stochastic Galerkin methods
• Generalized polynomial chaos
• Symmetrically hyperbolic
• Operator splitting

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.

• 出版日期2017-9-15
• 单位北京大学; 湘潭大学