Geodesic
Explicit numerical algorithm for non-hydrostatic fluid dynamics equations based on the CABARET scheme
Matematičeskoe modelirovanie, Tome 35 (2023) no. 5, pp. 62-86

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The article presents a non-hydrostatic model of the dynamics of a stratified slightly compressible fluid with a free-surface. An explicit scheme CABARET-NH (CABARET Non-Hydrostatic) for the numerical solution of the constructed system of differential equations in mixed Eulerian-Lagrangian coordinates based on the balance-characteristic scheme of the CABARET class is described. The well-balanced property of the numerical scheme is proved. The results of calculations of the free-surface oscillation problem are presented.
Keywords: non-hydrostatic model, Eulerian-Lagrangian coordinates, weakly compressible fluid, hyperbolic type equations, free-surface, conservative-characteristic schemes. 
@article{MM_2023_35_5_a4,
     author = {V. Goloviznin and Petr Mayorov and Pavel Mayorov and A. Solovjev and N. Afanasiev},
     title = {Explicit numerical algorithm for non-hydrostatic fluid dynamics equations based on the {CABARET} scheme},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {62--86},
     publisher = {mathdoc},
     volume = {35},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2023_35_5_a4/}
}
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V. Goloviznin; Petr Mayorov; Pavel Mayorov; A. Solovjev; N. Afanasiev. Explicit numerical algorithm for non-hydrostatic fluid dynamics equations based on the CABARET scheme. Matematičeskoe modelirovanie, Tome 35 (2023) no. 5, pp. 62-86. http://geodesic.mathdoc.fr/item/MM_2023_35_5_a4/