Work

Entropy stable hydrostatic reconstruction schemes for shallow water systems

Year: 2025

Type: article

Abstract: In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite volume scheme and combine it with entropy conservative fluxes and suitable numerical dissipation to preserve an entropy inequality in the semi-discrete case. We then combine the novel hydrostatic reconstruction with a collocated nodal split-form discontinuous Galerkin spectral element method, extending the method to high-order and curvilinear meshes. The high-order method incorporates an additional positivity-limiter and is blended with a compatible subcell finite volume method to maintain well-balancedness at wet/dry fronts. We prove entropy stability, well-balancedness, and positivity-preservation for both methods. Numerical results for the high-order method validate the theoretical findings and demonstrate the robustness of the scheme. • New hydrostatic reconstruction method for multilayer SWEs, including wet/dry fronts. • Formulation of entropy stable, well-balanced and positivity-preserving schemes. • Extension to high-order and curvilinear meshes using discontinuous Galerkin method.

Source: Journal of Computational Physics

DOI: 10.1016/j.jcp.2025.113802

Authors: Patrick Ersing, Sven Goldberg, Andrew R. Winters

Institutions: Linköping University, Deutsches Zentrum für Luft- und Raumfahrt e. V. (DLR)

Language: English

Topic: Computational Fluid Dynamics and Aerodynamics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,980

Funder: Vetenskapsrådet