Decomposition Approach for Moving Interface Phenomenon

In many situations of hydrodynamic phenomenon, two-layer fluid is a dominant feature of fluid motion. Such two-layer fluid often contains jumps in the density across the interface of fluid domains. The interface of air and water or salt water and fresh water is obvious example [Tho68]. The density jump may be assumed to occur in an infinitesimally thin interface in the mixture. And, the behavior of such an interface is important to understand various hydrodynamic phenomena [DR81]. In our previous study, we developed the efficient numerical procedure which is able to simulate the time evolution of an interface between two fluids with different densities. The numerical solution procedure based on the sub-region boundary element method with the mixed Eulerian Lagrangian approach developed in the moving boundary problems in potential field [ST93]. Now, cluster computation by work stations or personal computers becomes available in many laboratories all over the world. Because of their potential for both high-performance and cost-effectiveness, cluster computing will attract much more attention of researches, and they will take the most important part in engineering computation in stead of vector computing in near future. Under this situation, investigation of parallel FEM algorithm [GDP83],[GASS93] based on the DDM is increasing. Recently, Kamiya et al. introduced DDM for the boundary element analysis in order to implement the parallel BEM computation [DM96],[KIK96]. They showed the utility of BEM analysis with domain decomposition scheme for some potential and elastic problems. In this paper, we propose a new boundary element procedure for the density stratified flow based on the domain decomposition method. The final system of equations for the whole region is obtained by adding the set of boundary integral equations of governing equation for each sub-domain in conjunction with compatibility and equilibrium conditions between their interfaces. The present study is an attempt to develop parallel computation procedure for the interface motion of the two-layer fluid in a rectangular region based on domain decomposition method and two sub-domain boundary element method.