An efficient curvilinear non‐hydrostatic model for simulating surface water waves

Abstract

An efficient curvilinear non‐hydrostatic free surface model is developed to simulate surface water waves in horizontally curved boundaries. The generalized curvilinear governing equations are solved by a fractional step method on a rectangular transformed domain. Of importance is to employ a higher order (either quadratic or cubic spline function) integral method for the top‐layer non‐hydrostatic pressure under a staggered grid framework. Model accuracy and efficiency, in terms of required vertical layers, are critically examined on a linear progressive wave case. The model is then applied to simulate waves propagating in a canal with variable widths, cnoidal wave runup around a circular cylinder, and three‐dimensional wave transformation in a circular channel. Overall the results show that the curvilinear non‐hydrostatic model using a few, e.g. 2–4, vertical layers is capable of simulating wave dispersion, diffraction, and reflection due to curved sidewalls. Copyright © 2010 John Wiley & Sons, Ltd.

Modelling coastal water waves using a depth-integrated, non-hydrostatic model with shock-capturing ability

“…The fractional step method is commonly used in developing non-hydrostatic models (Bradford, 2011;Choi et al, 2011;Stelling & Zijlema, 2003), though it only has a first-order accuracy in time. The method decomposes total pressure into hydrostatic and non-hydrostatic parts.…”

A horizontally curvilinear non‐hydrostatic model for simulating nonlinear wave motion in curved boundaries

“…In contrast with the previous model of Choi et al , which employed explicit velocities to calculate a new free surface level, the Crank–Nicholson discretization is applied to maintain second‐order consistency in the time domain, as follows: …”

“…In this section, we first examine the model's capability for simulating nonlinear waves in a 2D NWT, and compare our results with the numerical results of Choi et al . The developed model is then applied to the simulation of waves in a curved channel, focusing on the nonlinear evolution of Stokes waves in an intermediate water depth.…”

“…On the other hand, the integral method of Yuan and Wu using the top‐layer equation was built on the standard staggered (Arakawa C‐type) grid layout. Their method has been further improved by the use of a high‐order interpolation scheme .…”

“…In addition, the third‐order spatial upwind method is used in advection terms. The numerical accuracy of the model is compared with that of Choi et al for analytical solutions from a two‐dimensional (2D) numerical wave tank (NWT) with nonlinear Stokes waves over varying wave steepness, that is, aK = 0.1, 0.2, and 0.3, where a is the wave amplitude, and K is the wave number. To investigate nonlinear effects over wave steepness in a curved domain, the developed model is first applied to wave transformation in a semicircular channel, in which the wave dispersion is prevailed over by the reflection and diffraction of the wave train interacting with the sidewall.…”