![](bg1.png)
New Depth-averaged Non-hydrostatic Hydrodynamic Model
for Flows over a Slope
Z Jing
1
, H Q Cao
2, *
, H P Luo
3
, W L Zhai
4
and K F Zhao
5
Basin Water Environmental Research Dept., Changjiang River Scientific, Research
Institute, Wuhan 430010, China
Corresponding author and e-mail: H Q Cao, 673844316@qq.com
Abstract. Compared to the hydrostatic hydrodynamic model, the non-hydrostatic
hydrodynamic model can accurately simulate flows which have obvious vertical accelerations.
This paper proposes a non-hydrostatic hydrodynamic model. The horizontal momentum
equation is obtained by integrating the Navier-Stokes equations from the bottom to the free
surface. The vertical momentum equation is approximated by the Keller-box scheme. A non-
hydrostatic correction method is used to solve the model equations. The proposed model is
verified using measurements from a solitary wave experiment, and good consistency is
reported. The results show that the proposed model is an effective tool for simulation of
coastal engineering.
1. Introduction
The propagation of sea waves over a slope involves a series of complex physical processes such as
wave refraction, wave diffraction, and shoaling. Many mathematical models were used to analyze the
prototype experiments of wave propagation and transformation, including the Boussinesq-type
equation [1], potential flow model, and non-hydrostatic hydrodynamic model.
Compared to hydrostatic models, non-hydrostatic models consider the effect of dynamic pressure,
and are thus appropriate for situations with significant vertical acceleration. Thus non-hydrostatic
models are particularly well-suited to grasping the discipline of complex flow movement. Managing
the dynamic pressure variable is the key to successful non-hydrostatic modeling. In most non-
hydrostatic models, it is assumed that the pressure of the surface grid conforms to the hydrostatic
distribution and the dynamic pressure variables are placed at the center of the surface grid [2, 3].
Thus these models don’t completely deviate from the hydrostatic assumption.
To solve the problem, this paper proposes a novel non-hydrostatic hydrodynamic model. Based on
a non-hydrostatic correction method, the horizontal momentum equation is obtained by integrating
the Navier-Stokes equations from the bottom to the free surface. The vertical momentum equation is
approximated by Keller-box scheme. The validity of the model was verified by a solitary wave
experiment.
2. Mathematical model
To improve the hydrostatic hydrodynamic model, the pressure term in the 3D Navier-Stokes (N-S)
equations is separated into hydrostatic and non-hydrostatic components. The horizental momentum
Jing, Z., Cao, H., Luo, H., Zhai, W. and Zhao, K.
New Depth-averaged Non-hydrostatic Hydrodynamic Model for Flows over a Slope.
In Proceedings of the International Workshop on Environmental Management, Science and Engineering (IWEMSE 2018), pages 133-139
ISBN: 978-989-758-344-5
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
133