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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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 440; p. 117932
Main Authors: Epshteyn, Yekaterina, Narayan, Akil, Yu, Yinqian
Format: Journal Article
Language:English
Published: Elsevier B.V 15.05.2025
Subjects:
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
Online Access:Get full text
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Summary: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