Energy stable and structure-preserving algorithms for the stochastic Galerkin system of 2D shallow water equations

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Yekaterina Epshteyn , Akil Narayan , Yinqian Yu
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引用次数: 0

Abstract

Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods for SWE are needed. Although some algorithms are well studied for deterministic SWE, more effort should be devoted to handling the SWE with uncertainty. In this paper, we incorporate uncertainty through a stochastic Galerkin (SG) framework, and building on an existing hyperbolicity-preserving SG formulation for 2D SWE, we construct the corresponding entropy flux pair, and develop structure-preserving, well-balanced, second-order energy conservative and energy stable finite volume schemes for the SG formulation of the two-dimensional shallow water system. We demonstrate the efficacy, applicability, and robustness of these structure-preserving algorithms through several challenging numerical experiments.
二维浅水方程随机Galerkin系统的能量稳定和结构保持算法
浅水方程(SWE)是流体动力学中基于非线性双曲偏微分方程的基本模型,对于研究广泛的地球物理和工程现象至关重要。因此,需要稳定、准确的SWE数值计算方法。虽然一些算法已经被很好地研究用于确定性SWE,但更多的工作应该投入到处理不确定性SWE上。本文通过随机Galerkin (SG)框架引入不确定性,在已有的二维SWE的保持双曲的SG公式的基础上,构造了相应的熵通量对,给出了二维浅水系统SG公式的保持结构、良好平衡、二阶能量守恒和能量稳定的有限体积格式。我们通过几个具有挑战性的数值实验证明了这些结构保持算法的有效性,适用性和鲁棒性。
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来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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