Algorithm of Incompressible Flow Simulation for Massively Parallel Computer in Small Granularity

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Massively parallel computers of distributed memories which consist of more than several hundreds processors become popular when a huge scale of numerical simulations are carried out. The standard algorithm for incompressible flow such as SIMPLE and MAC,so-called "de-coupled algorithm", cannot keep the large value of parallel efficiency as the number of processors increases and the granularity becomes small. This research proposes that the coupled method, which solves momentum equations and continuity equation simultaneously, is very effective for massive parallel computing even in small granularity.The reason why this coupled method is suitable for massively parallel computing is the small occupation of the overhead time for communications between processors. The another reason is the simplicity of algorithm because the main part is to solve a small matrix in each cell of control volume.The results of coupled algorithm are as follows. In the calculations of two-dimensional circular cyl … More inder whose grid number is 256x128, the speed-up factor becomes 235,374 and 491 as the number of processors increases to 256,512 and 1024 respectively, which means that the efficiency of parallel algorithm decreases to 92,73 and 48%. It is found that the adequate performance is derived in the coupled method even if the number of grid points, that is, granularity, is very small such as 128,64 and 32. For example, the efficiency of 50% for the very small granularity of 32 grid points is surprisingly large comparing with around 10% in the standard algorithm of SIMPLE.The similar results are confirmed in the other flows of two- and three-dimensional rectangular cylinder. The final simulation of three-dimensional circular cylinder is carried out with this developed code, in which it is confirmed that the Karman vortex appears behind a obstacle and its structure is very similar to the exact one. This code will be developed to a huge simulation of LES which is a future solver for the design, and furthermore to "a real time simulator" with more than one million processors. Less