Fully dispersive nonlinear water wave model in curvilinear coordinates

Beji S. , NADAOKA K.

JOURNAL OF COMPUTATIONAL PHYSICS, cilt.198, ss.645-658, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 198 Konu: 2
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1016/j.jcp.2003.12.022
  • Sayfa Sayıları: ss.645-658


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.