In this paper, the development of a seamless system for parallel¯ow analysis using the``free-mesh method'', which is a kind of meshless method, is described. The system consists of two main parts: the computation of the global mass, advection, diffusion, gradient, and divergence matrices, and the time integration by the decoupled method with respect to velocity and pressure. This system is quite compatible with the parallel environment because the matrices are independently computed node-by-node without any node-element connectivity information, and furthermore because the fractional step method, with the interpolation functions for velocity and pressure being of equal order, is used with the conjugate gradient solver for the time integration. A parallel ef®ciency of approximately 83% was achieved for a large-scale problem with 480,000 degrees of freedom using 16 processors.
IntroductionIn recent years, large-scale computer simulations for incompressible¯ow have become more important for¯ows in nuclear reactors, around automobiles and buildings, air ow in rooms, and so on. Numerical methods such as the ®nite difference method (FDM), the ®nite element method (FEM), and the ®nite volume method (FVM) have been used to analyze such¯ows. In these methods, FEM has been successful for simulation due to its ability to analyze domains of arbitrary shape.Nowadays, the degrees of freedom in analysis models tend to be extremely large and the geometries of the method have become extremely complex. To deal with such models with limited computer memory size and in a reasonable computation time, two main problems must be solved. First, the computational time must be reduced, and second, the dif®culties of global mesh generation over the whole domain of analysis must be avoided. For the ®rst problem, ef®cient parallel methods, such as parallelization of the processing loops (Kennedy et al. 1994, Nakabayashi et al. 1996 and the domain decomposition method (DDM) (Glowinski et al. 1983, Yagawa andShioya 1993), are currently being studied for this purpose. The former method has essentially the same algorithm as the usual FEM. After the whole domain of analysis is decomposed to processors as subdomains, the all-element matrices in each subdomain and the values on the nodes and/or elements (e.g. the velocity and pressure) are computed by each processor with interprocessor communication. In the latter method, the ®nite-element analysis in each subdomain is performed separately by giving the tentative shared boundary conditions. After the analysis, the values on the adjacent shared boundaries are exchanged, and the boundary conditions are updated so as to correlate the values on the shared boundaries. And again, the analysis in each subdomain is carried out with the updated shared boundary conditions. This process continues until the values on the shared boundaries converge. Because the tentative boundary conditions are given, the ®nite-element analysis in each subdomain can be done separately. These approaches provide parallelization wi...