Energy-stable staggered schemes for the Shallow Water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:401

Article

Duran, Arnaud¹  Vila, Jean-Paul^2,3  Baraille, Remy^2,3,4 

[1] Univ Claude Bernard Lyon 1 France, Inst Camille Jordan, Villeurbanne, France

[2] Univ Paul Sabatier Toulouse 3, Inst Math Toulouse, Toulouse, France

[3] INSA, Toulouse, France

[4] SHOM, Paris, France

关键词: Non-linear shallow water equations;    Energy dissipation;    Non-linear stability;    Staggered meshes;    Well-balanced methods;   

DOI  :  10.1016/j.jcp.2019.109051

来源: Elsevier

【 摘 要 】

We focus on the development and analysis of staggered schemes for the two-dimensional non-linear Shallow Water equations with varying bathymetry. Semi-implicit and fully explicit time-discretizations are proposed. Particular attention is paid on non-linear stability results, principally considered here through discrete energy dissipation arguments. To address such an issue, specific convective fluxes are employed, implying diffusive terms relying on the pressure gradient. In addition of providing an explicit control of the discrete energy budget, the method is shown to preserve motionless steady states as well as the positivity of the water height. These properties are still satisfied in a fully explicit context, provided an appropriate discretization of the pressure gradient. These stability results make the approach particularly robust and efficient, for both coastal flows and low-Froude number regimes. As a result, in addition of a great ease of implementation, the presented schemes meet the operational requirements attached to the simulation of large and small scale oceanic flows. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free