A Domain Decomposition Parallel Algorithm For Solving Boussinesq Equation

The numerical models based on Boussinesq equations could simulate nonlinear wave deformations in coastal shallow waters. So such models have been widely used in coastal engineering. In recent decades, there has been a great improvement in Boussinesq equation and discrete scheme. At the same time, however, it makes model solving more complicated, and increases the amount of computation. Singer-processor computers can not meet the need of practical engineering computation with their limit on the processing speed and the size of local memory and storage. For this reason, a domain decomposition method for solving Boussinesq equation parallelly is proposed in this paper.Firstly, in this paper, the improvement of dispersive property, dissipative property, shoaling for the Boussinesq type equations, and the development of parallel methods in CFD are reviewed. Then, classification of parallel methods, performance analysis methods, and MPI are introduced. In order to propose the parallel method, some introduction about the model considered in this paper, finite difference scheme, method of wave generation, treatment of boundary and the process of serial simulation are described.In this paper, domain decomposition method is adopted for the parallel strategy, and subdomains are coupled with each other through Schwarz iterations. The global solution domain is partitioned into several overlapping subdomains in x direction computation, while partitioned into several non-overlapping subdomains in y direction computation. However, in both direction computations, partioning is carried out along only one dirction, which makes direction changing is avoided. The parallel strategy proposed in paper is used to simulate three experimental models. Comparion between parallel results, serial results and experimental data shows that parallel model tallies closely with serial model, and both of them agree with experimental data, which means that the parallel strategy is correct. Speedup and efficiency of the parallel strategy, and the effect of the overlapping amount is also analyzed.