Fully dispersive nonlinear water wave model in curvilinear coordinates


Beji S. , NADAOKA K.

JOURNAL OF COMPUTATIONAL PHYSICS, vol.198, no.2, pp.645-658, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 198 Issue: 2
  • Publication Date: 2004
  • Doi Number: 10.1016/j.jcp.2003.12.022
  • Title of Journal : JOURNAL OF COMPUTATIONAL PHYSICS
  • Page Numbers: pp.645-658

Abstract

A vertically integrated fully dispersive nonlinear wave model is expressed in curvilinear coordinates with non-orthogonal grids for the simulation of broad-banded nonlinear random water waves in regions of arbitrary geometry. The transformation is performed for both dependent and independent variables, hence an irregular physical domain is converted into a rectangular computational domain with contravariant velocities. Use of contravariant velocity components as dependent variables ensures easy and accurate satisfaction of the wall condition for lateral enclosures surrounding a physical domain, such as a coastal area, channel, or harbor. The numerical scheme is based on finite-difference approximations with staggered grids which results in implicit formulations for the momentum equations and a semi-explicit formulation for the continuity equation. Linear long wave propagation in a channel of varying cross-section and linear random wave propagation in a circular channel are presented as test cases for comparisons with the corresponding analytical solutions. Cnoidal and Stokes waves in a circular channel are also simulated as examples to nonlinear wave propagation within curved walls. (C) 2004 Elsevier Inc. All rights reserved.