| Issue |
ESAIM: M2AN
Volume 58, Number 2, March-April 2024
|
|
|---|---|---|
| Page(s) | 723 - 757 | |
| DOI | https://doi.org/10.1051/m2an/2024012 | |
| Published online | 19 April 2024 | |
Energy stable and structure-preserving schemes for the stochastic Galerkin shallow water equations
1
Department of Mathematics and Scientific Computing and Imaging (SCI) Institute, The University of Utah, Salt Lake City, UT 84112, USA
2
Department of Mathematics, The University of Utah, Salt Lake City, UT 84112, USA
* Corresponding author: akil@sci.utah.edu
Received:
9
October
2023
Accepted:
22
February
2024
The shallow water flow model is widely used to describe water flows in rivers, lakes, and coastal areas. Accounting for uncertainty in the corresponding transport-dominated nonlinear PDE models presents theoretical and numerical challenges that motivate the central advances of this paper. Starting with a spatially one-dimensional hyperbolicity-preserving, positivity-preserving stochastic Galerkin formulation of the parametric/uncertain shallow water equations, we derive an entropy-entropy flux pair for the system. We exploit this entropy-entropy flux pair to construct structure-preserving second-order energy conservative, and first- and second-order energy stable finite volume schemes for the stochastic Galerkin shallow water system. The performance of the methods is illustrated on several numerical experiments.
Mathematics Subject Classification: 35L65 / 35Q35 / 35R60 / 65M60 / 65M70 / 65M08
Key words: Stochastic Galerkin method / finite volume method / structure-preserving discretization / shallow water equations / hyperbolic systems of conservation law and balance laws
© The authors. Published by EDP Sciences, SMAI 2024
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