Combined boundary element and weighted finite difference method for water flow

摘要

In an earlier study, we had identified the boundary element and weighted finite difference methods used to analyze the saltwater wedge diffusion in groundwater (Kanoh et al. [1]). In this paper, we extend the methodology and propose a combined boundary element and weighted finite difference method for water flow. By using the weighted finite difference method (WFDM), the nonlinear flow, which includes convective diffusion and shallow water flow problems, can be accurately calculated. On the other hand, the boundary element method (BEM) is an excellent way to handle the moving boundary technique and intricate boundary conditions, such as an absorbing boundary of waves or a piston wave- maker motion boundary. These two methods were combined in an attempt to solve the large amplitude of wave motion and turbulent flow that was produced by the wave motion against a submerged breakwater. In order to apply the combined method described in the problem above, the following steps were followed: (1) The analytical region is divided into two sub- domains. (2) The first is an irrotational flow domain, in which the moving boundary technique and the intricate boundary conditions are managed by BEM (Kanoh et al, [2]). (3) The second is a turbulent flow domain, in which WFDM provides an accurate solution for the wave motion against a submerged breakwater. As the free surface changes its position, even in the turbulent region, WFDM is better to handle the moving boundary. The effect and accuracy of the alternative hybrid method are estimated by using experimental laboratory models.