Explicit-implicit scheme CABARETI–NH for the equations of a weakly compressible fluid dynamics





non-hydrostatic model, Eulerian-Lagrangian coordinates, weakly compressible fluid, hyperbolic type equations, free-surface, conservative-characteristic schemes


In this paper, an explicit-implicit conservative-characteristic scheme CABARETI–NH (CABARET Implicit Non-Hydrostatic), based on the CABARET scheme, for a hyperbolised system of Navier–Stokes equations is considered. Implicitness along one spatial direction allows the time step on computational grids with a large aspect ratio of cells to be significantly increased. A hyperbolic sweep method is used to resolve the introduced implicit part of the scheme. This keeps the same level of computational efficiency as explicit schemes. The results of model validation on the laboratory experiment of three-dimensional gravitational flow of a stratified fluid are presented.

Author Biographies

Vasily M. Goloviznin

Petr A. Maiorov

Nikita A. Afanasiev

Pavel A. Maiorov

Andrey V. Solovjev


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How to Cite

Головизнин В.М., Майоров П.А., Афанасьев Н.А., Майоров П.А., Соловьев А.В. Explicit-Implicit Scheme CABARETI–NH for the Equations of a Weakly Compressible Fluid Dynamics // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2023. 24. 152-169. doi 10.26089/NumMet.v24r212



Methods and algorithms of computational mathematics and their applications