Coupling of wave and current numerical model with unstructured quadtree grid for nearshore coastal waters

Abstract

This paper presents 2D wave-current interaction model for evaluating nearly horizontal wave-induced currents in the surf-zone and coastal waters. The hydrodynamic model is the two-dimensional depth-averaged nonlinear shallow water equations by using an unstructured non-staggered and multiple-level quadtree rectangular mesh, this mesh information is stored in simple data structures and it is easy to obtain a locally high resolution for important region. The intercell fluxes are computed based on the HLL (Harten-Lax-van Leer) approximate Riemann solver with shock capturing capability for computing the dry-to-wet interface of coastal line. The effects of pressure and gravity are included in source term in the model, this treatment can simplify the computation and eliminate numerical imbalance between source and flux terms. The wave model readily provides the radiation stresses that represent the shortwave-averaged forces in a water column for the hydrodynamic model and the wave model takes into account the effect of wave-induced nearshore currents and water level. The coupling model is applied to verify different experimental cases and real life case of considering the wave-current interaction. The calculated results agree with analytical solution, experimental and field data. The results show that the modeling approach presented herein should be useful in simulating the nearshore processes in complicated natural coastal domains.wave-current interaction, unstructured quadtree grid, finite volume method, HLL approximate Riemann solver, wave action spectral model Citation:Zhang M L, Wu W M, Lin L H, et al. Coupling of wave and current numerical model with unstructured quadtree grid for nearshore coastal waters.

Numerical Simulation of Wave Transformation Using Spectral Wave Action Model

“…The spectral waves from the NOAA were input data at the model boundaries every 3 h. The computational domain is divided into 250×211 rectangle cells, which is quite non-uniform and the length of cells varied from 29 to 290 m, The mesh is refined around the jetties and near the channels. Figure 6 compares the computed and measured wave heights at stations 2, 3 and 6 [9]. According to the comparison at stations 2 and 3, one can find that the comparison between the observed and calculated consequence is generally good, those slightly discrepancies of wave height can be found in station 6.…”

Numerical Simulation of Salinity and Pollutant Transport in Estuary by Using a Depth Averaged 2D Model

“…The depth-averaged shallow water equations in the Cartesian coordinate system are written as [3,4] ( ) ( )…”

“…In this mesh, various levels of fine cells are placed close to in-stream structures or inlet areas where the flow gradients are high, while coarse grids are used in the low-gradient regions, as shown in Fig. 1, so that the computational mesh will be less complicated [3] .…”

“…6. The estuary is partially mixed and macrotidal, with a 12 hour and 25 minutes tidal lunar period and a tidal amplitude of 1.5-5 m at the mouth [3,9]. The simulation domain is about 80 km long, starting from the mouth to the Garonne River and the Dordogne River.…”

“…By coupling the hydrodynamic module with solving the diffusion equation time-to-time, a transport-diffusion model is constructed which provides a useful instrument to predict the depth-average concentration of pollution along the estuary once there are polluted sources spread out. Recently many 2-D mathematical models have been proposed basing on the shallow water equations and some are taken in to account various phenomenon [2,3]. In this study, a two-dimensional depth-averaged model can be used to simulate salinity and pollutant transport process in water body.…”