| The vortex method has the adaptive characteristic of Lagrange, such an the high precision, advantage of handling boundary condition and DNS of N-S equations, which make it outstanding comparing other methods. The particle vortex method is mainly used to solve the unsteady flow and the complicated flow. The most popular vortex method now is particle strength exchange method. But the vortex method is mainly used in uncompressive fluid, many scholars improve it to solve the compressive flow but there is few convincing result. Recently some scholars put forward an improved vortex method named dilating vortex particle method to simulate the compressive fluid. The results are satisfied.Based on the particle strength exchange method and the dilating vortex particle method, this thesis have simulated the flow past two tandem cylinders under un compressive flow and the co-rotating of vortexes under compressive flow. The main research contents are as following:(1) The particle strength exchange method is used to study the incompressible flow past a pair of tandem cylinders at Re=200 and Re=300. Deferent separation distances between the cylinders are considered to investigate the influence of separation distances. The results show that there is a critical distance between the tandem cylinders beyond which the flow will change dramatically, and the critical distance will diminish as the Reynolds number rises;(2) The dilating vortex particle method is used to study the co-rotating of two and three vortexes. The results show that:for two vortexes, the effect of the Mach number is not evident; if the vortexes have the same circulation but very different radiuses, and the vortex with low Mach number will absorb the vortex with high Mach number; for three vortexes, the co-rotating process is affected by the original arrange of the vortexes.
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