Numerical model of wave-current interaction based on unstructured quadtree grid for nearshore coastal waters

Abstract

According to the characteristics of complex topography, hydrology, sediment transport in coastal waters, the aim of this paper is to develop an implicit, depth-averaged 2-D numerical mode of coupling current and wave for coastal area. The hydrodynamic model is the two dimensional depth averaged non-linear shallow water equations with an unstructured non-staggered and multiple-level quadtree rectangular mesh with local refinement for important region. In this non-staggered system, primary variables u -, v -velocity, and water level are stored on the same set of grid points in order to simplify the program code, and fluxes at cell faces are determined using the Rhie and Chow’s momentum interpolation method to avoid spurious checkerboard oscillations. The discretized algebraic equations are solved iteratively using the GMRES method with ILUT preconditioning for speeding the computation. The Wave model is a two-dimensional spectral wave action model of taking into account the effect of wave breaking, shoaling, refraction, diffraction, wave-current interaction, bottom friction. The wave model readily provides the radiation stresses for the hydrodynamic model. The coupling model has been tested against measurement data for steady flow around a spur-dyke in a laboratory flume and tidal flows in Gironde Estuary, France and Grays Harbor, USA. The model reasonably well reproduces the temporal and spatial variations of water level, current speed and wave height observed in the measurements. It shows that the coupling current and wave model can simulate accurately the questions of tide and wave for complex domain, the modeling approach presented herein should be useful in engineering application and environmental protection for coastal area.