On Conservative and Nonconservative Two-Layer Shallow Water Equations | Sciact

On Conservative and Nonconservative Two-Layer Shallow Water Equations Научная публикация

Журнал

Journal of Computational Physics
ISSN: 0021-9991

Вых. Данные

Год: 2026, Номер: 569 (1), Номер статьи : 115471, Страниц : DOI: 10.1016/j.jcp.2026.115471

Ключевые слова

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

Авторы

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

Организации

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

Опубликована online:	5 окт. 2026 г.
Опубликована в печати:	10 окт. 2026 г.

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