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

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.

Hybrid Finite Element Method Based on Polygon-Quadtree Meshes for Heat Transfer and Thermal Elastic Analysis

A steady-state thermal hybrid element model is proposed to calculate particle-reinforced composites divided by an improved quadtree mesh.The functional of hybrid flux finite element method(HF-FEM)is constructed using the weighted residual method.This functional independently assumes a heat flux field in the cell domain and a temperature field along cell boundaries.The construction of a universal heat flux function is put forward,which is approximated by a complete polynomial,and the temperature at the cell boundary is obtained by linear interpolation.Also,the hybrid stress finite element method(HS-FEM)is constructed to solve the thermal stress.In this paper,an improved quadtree grid that can accurately describe the shape of elliptical inclusions is built.By comparing several numerical examples with the traditional FEM,it is demonstrated that the hybrid element of the thermal analysis proposed in this paper is practical.