Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations
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DOI：
10.1016/j.jcp.2021.110901
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发表时间：
2021-04
期刊：
影响因子：
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通讯作者：
Dihan Dai;Y. Epshteyn;A. Narayan
中科院分区：
文献类型：
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作者：
Dihan Dai;Y. Epshteyn;A. Narayan
二维浅水系统的随机Galerkin公式可能会失去双曲性，从而改变原模型的性质。在这项工作中，我们提出了一个双曲保持随机Galerkin制定仔细选择多项式混沌近似的浅水方程中的非线性项。我们推导出一个充分条件，以保持双曲的随机Galerkin系统，它只需要一个有限的收集的正性条件的随机水的高度在选定的正交点在参数空间。基于我们对随机Galerkin公式的理论结果，我们发展了一个相应的平衡的保双曲中心迎风格式。我们证明了几个具有挑战性的数值试验的准确性和鲁棒性的新方案。
Stochastic Galerkin formulations of the two-dimensional shallow water systems parameterized with random variables may lose hyperbolicity, and hence change the nature of the original model. In this work, we present a hyperbolicity-preserving stochastic Galerkin formulation by carefully selecting the polynomial chaos approximations to the nonlinear terms in the shallow water equations. We derive a sufficient condition to preserve the hyperbolicity of the stochastic Galerkin system which requires only a finite collection of positivity conditions on the stochastic water height at selected quadrature points in parameter space. Based on our theoretical results for the stochastic Galerkin formulation, we develop a corresponding well-balanced hyperbolicity-preserving central-upwind scheme. We demonstrate the accuracy and the robustness of the new scheme on several challenging numerical tests.