A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs

作者：Jin, Shi; Xiu, Dongbin^*; Zhu, Xueyu

来源：Journal of Scientific Computing, 2016, 67(3): 1198-1218.

DOI：10.1007/s10915-015-0124-2

• Uncertainty quantification
• Hyperbolic balance laws
• Well-balanced schemes
• Generalized polynomial chaos
• Stochastic Galerkin

We propose a generalized polynomial chaos based stochastic Galerkin methods for scalar hyperbolic balance laws with random geometric source terms or random initial data. This method is well-balanced (WB), in the sense that it captures the stochastic steady state solution with high order accuracy. The framework of the stochastic WB schemes is presented in details, along with several numerical examples to illustrate their accuracy and effectiveness. The goal of this paper is to show that the stochastic WB scheme yields a more accurate numerical solution at steady state than the non-WB ones.

• 出版日期2016-6
• 单位上海交通大学