An accurate and efficient finite‐difference algorithm for non‐hydrostatic free‐surface flow with application to wave propagation

TLDR

The paper presents a numerical technique to approximate the vertical gradient of non‑hydrostatic pressure in Reynolds‑averaged Navier–Stokes equations for simulating non‑hydrostatic free‑surface flows. The method uses a Keller‑box scheme that incorporates non‑hydrostatic pressure effects with only a few vertical grid points. The technique accurately and efficiently simulates short‑wave propagation, capturing frequency dispersion and nonlinear effects, with accurate wave characteristics achieved using only two vertical layers in numerical examples. © 2003 John Wiley & Sons, Ltd.

Abstract

Abstract 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.