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An arbitrary Lagrangian-Eulerian \(\sigma\) (ALES) model with non-hydrostatic pressure for shallow water flows. (English) Zbl 0967.76065
From the summary: We develop an arbitrary Lagrangian-Eulerian model in the \(\sigma\) coordinate system (ALES) for shallow water flows, based on the unsteady Reynolds averaged Navier-Stokes equations. Unlike the conventional \(\sigma\) coordinate system, non-hydrostatic pressure is incorporated together with the effect of moving free surface, giving a general scheme. The standard \(k-\varepsilon\) turbulence model is used to calculate the eddy viscosity. Wave flows over bars are appropriate test cases for which experimental data are available, and comparisons are favourable. The model is also applied to the problem of wave and wave/current flows over a trench.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
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