An improved depth‐averaged nonhydrostatic shallow water model with quadratic pressure approximation

Abstract

SummaryPhase‐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.

Nonhydrostatic Numerical Modeling of Fixed and Mobile Barred Beaches: Limitations of Depth-Averaged Wave Resolving Models around Sandbars

“…The reported model limitations of XBNH and XBNH+ may be generalized to any similar nonhydrostatic 2D model (e.g., REEF3D-SFLOW of Wang et al 2020). The model user should be aware of such model limitations before applying it to real-world problems.…”

A Comparison of Different Wave Modelling Techniques in An Open-Source Hydrodynamic Framework

“…The governing equations for the non-hydrostatic shallow water module are derived from the mass and momentum conservation for an incompressible inviscid fluid. Following the quadratic assumption [46,47], the governing equations are written with depth-averaged variables:…”

“…From wave gauges 1 to 4, the x-coordinates are x = 19.8, 20.8, 21.8 and 22.1 m. The simulations are computed with four 2.7 GHz Intel Xeon E5 cores on Mac Pro for REEF3D::FNPF and REEF3D::SFLOW and 128 2.1 GHz Intel E5-2683v4 cores on the supercomputer Fram. The grid convergence study for the three models REEF3D::CFD, REEF3D::SFLOW and REEF3D::FNPF were reported respectively by Bihs et al [1], Wang et al [47] and Bihs et al [51]. As a result, the dx = 0.005 m, dx = 0.005 m and dx = 0.005 m are used in the REEF3D::CFD, REEF3D::SFLOW and REEF3D::FNPF simulations respectively.…”

A Moment-Based Depth-Averaged K-ε Model for Predicting the True Turbulence Intensity over Bedforms

“…Both depth-averaged models and VAM flow models require the use of relevant turbulence models, mainly to work as closure equations for the mathematical differential terms resulting from the time averaging of the Navier Stocks equations and to capture the dominating length and velocity scales in the turbulence/eddy structure of the flow field [6][7][8][9][10][11][12]. The two-transport equations model (Rastogi and Rodi's k-ε model) is the standard turbulence closure model that was introduced early in 1978 for depth-averaged models [13].…”