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An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation
Author(s) -
Stelling G.,
Zijlema M.
Publication year - 2003
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.595
Subject(s) - free surface , hydrostatic equilibrium , mechanics , finite difference , flow (mathematics) , reynolds number , computational fluid dynamics , finite difference method , pressure gradient , hydrostatic pressure , mathematics , grid , dispersion (optics) , physics , mathematical analysis , geometry , optics , turbulence , quantum mechanics
A numerical technique is presented for the approximation of vertical gradient of the non‐hydrostatic pressure arising in the Reynolds‐averaged Navier–Stokes equations for simulating non‐hydrostatic free‐surface flows. It is based on the Keller‐box method that take into account the effect of non‐hydrostatic pressure with a very small number of vertical grid points. As a result, the proposed technique is capable of simulating relatively short wave propagation, where both frequency dispersion and non‐linear effects play an important role, in an accurate and efficient manner. Numerical examples are provided to illustrate this; accurate wave characteristics are already achieved with only two layers. Copyright © 2003 John Wiley & Sons, Ltd.