A semi-implicit finite difference method for non-hydrostatic, free-surface flows

TLDR

The study focuses on the free‑surface Navier–Stokes equations on irregular domains of arbitrary scale. The authors analyze a semi‑implicit finite difference model for non‑hydrostatic, free‑surface flows. They integrate the momentum, incompressibility, and free‑surface equations with a semi‑implicit algorithm that ensures mass conservation and unconditional stability against gravity wave speed, wind stress, vertical viscosity, and bottom friction. The algorithm outperforms recent quasi‑hydrostatic models in accuracy. © 1999 John Wiley & Sons, Ltd.

Abstract

In this paper a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. It is shown that the present algorithm is generally more accurate than recently developed models for quasi-hydrostatic flows. The governing equations are the free-surface Navier–Stokes equations defined on a general, irregular domain of arbitrary scale. The momentum equations, the incompressibility condition and the equation for the free-surface are integrated by a semi-implicit algorithm in such a fashion that the resulting numerical solution is mass conservative and unconditionally stable with respect to the gravity wave speed, wind stress, vertical viscosity and bottom friction. Copyright © 1999 John Wiley & Sons, Ltd.