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

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...

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Vydáno v:Computer methods in applied mechanics and engineering Ročník 440; s. 117932
Hlavní autoři: Epshteyn, Yekaterina, Narayan, Akil, Yu, Yinqian
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 15.05.2025
Témata:
Energy conservative schemes
Energy stable schemes
Entropy flux pair
Stochastic Galerkin
Stochastic shallow water equations
Structure-preserving
Energy conservative schemes
Stochastic Galerkin
Structure-preserving
Entropy flux pair
Stochastic shallow water equations
Energy stable schemes
ISSN:0045-7825
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Shrnutí: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.
ISSN:0045-7825
DOI:10.1016/j.cma.2025.117932