On Conservative and Nonconservative Two-Layer Shallow Water Equations

On Conservative and Nonconservative Two-Layer Shallow Water Equations Full article

Journal

Journal of Computational Physics
ISSN: 0021-9991

Output data

Year: 2026, Number: 569 (1), Article number : 115471, Pages count : DOI: 10.1016/j.jcp.2026.115471

Tags

Two-layer shallow water equations; Conservative form; Nonconservative form; Well-balanced methods; Central-upwind schemes; Path-conservative central-upwind scheme

Authors

Kurganov Alexander ¹ , Na Mingye ² , V. Ostapenko Vladimir ³

Affiliations

1	Department of Mathematics and Shenzhen International Center for Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China
2	Department of Mathematics, Southern University of Science and Technology, Shenzhen, 518055, China
3	Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

In this paper, we propose a novel hybrid formulation of the two-layer shallow water (TLSW) equations. We use a special conservative system in the convexity domain Ωc of its total energy function, while outside this domain, we replace the conservative TLSW system with a standard nonconservative one. Both conservative and nonconservative TLSW systems contain the mass conservation laws in the liquid layers and the total momentum conservation law. As the fourth equation, the conservative system utilizes the vorticity conservation law at the interface of the liquid layers, while the nonconservative system relies on a nondivergent equation describing the momentum exchange between the layers. We numerically demonstrate that the discontinuous solutions of the nonconservative and hybrid TLSW systems may be generically different inside the convexity domain Ωc, and thus only the conservative system should be used in this domain. Keywords

Kurganov A. , Na M. , V. Ostapenko V.
On Conservative and Nonconservative Two-Layer Shallow Water Equations
Journal of Computational Physics. 2026. N569 (1). 115471 . DOI: 10.1016/j.jcp.2026.115471 OpenAlex

Published online:	Oct 5, 2026
Published print:	Oct 10, 2026

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