Geodesic
Pressure correction method for multi-layer open flow model and wave problems
Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 61-88

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This paper describes a pressure correction method for single- and multi-layer open flow models in $\sigma$-coordinates. The method does not require any complex procedures to solve the discretization of the Poisson equation and is distinguished by a high computational efficiency. The discretization of the Poisson equation is written in a matrix form, allowing its usage also in the case of basic function expansion of the depth pressure profile. Parabolic interpolation of the pressure profile is used for the free surface. The algorithm can be parallelized for GPU. The paper presents the results of algorithm verification where experimental data sensitive to the numerical dissipation of the calculation model was used. The described method can be applied to problems with discontinuous solutions. Iteration convergence is high including problems with dry-bed flooding.
Keywords: multi-layer model, free surface, fully non-hydrostatic, waves, three-dimensional flows, boundary-fitted coordinates. 
@article{MM_2017_29_6_a4,
     author = {V. A. Prokofyev},
     title = {Pressure correction method for multi-layer open flow model and wave problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {61--88},
     publisher = {mathdoc},
     volume = {29},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_6_a4/}
}
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V. A. Prokofyev. Pressure correction method for multi-layer open flow model and wave problems. Matematičeskoe modelirovanie, Tome 29 (2017) no. 6, pp. 61-88. http://geodesic.mathdoc.fr/item/MM_2017_29_6_a4/