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An improved depth‐averaged nonhydrostatic shallow water model with quadratic pressure approximation
Author(s) -
Wang Weizhi,
Martin Tobias,
Kamath Arun,
Bihs Hans
Publication year - 2020
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4807
Subject(s) - discretization , quadratic equation , benchmark (surveying) , nonlinear system , waves and shallow water , wave propagation , domain decomposition methods , relaxation (psychology) , dispersion (optics) , euler's formula , turbulence , scale (ratio) , mathematics , mechanics , mathematical analysis , geology , physics , geometry , optics , finite element method , psychology , social psychology , oceanography , geodesy , quantum mechanics , thermodynamics
Summary Phase‐resolved information is necessary for many coastal wave problems, for example, for the wave conditions in the vicinity of harbor structures. Two‐dimensional (2D) depth‐averaging shallow water models are commonly used to obtain a phase‐resolved solution near the coast. These models are in general more computationally effective compared with computational fluid dynamics software and will be even more capable if equipped with a parallelized code. In the current article, a 2D wave model solving the depth‐averaged continuity equation and the Euler equations is implemented in the open‐source hydrodynamic code REEF3D. The model is based on a nonhydrostatic extension and a quadratic vertical pressure profile assumption, which provides a better approximation of the frequency dispersion. It is the first model of its kind to employ high‐order discretization schemes and to be fully parallelized following the domain decomposition strategy. Wave generation and absorption are achieved with a relaxation method. The simulations of nonlinear long wave propagations and transformations over nonconstant bathymetries are presented. The results are compared with benchmark wave propagation cases. A large‐scale wave propagation simulation over realistic irregular topography is shown to demonstrate the model's capability of solving operational large‐scale problems.