A New Diffusing-Vortex Numerical Scheme

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A diffusing-vortex method, for solving the two-dimensional incompressibl Navier-Stokes equation, will be extended and applied to the external incompressible viscous flow over a generally smooth blunt body. The numerical advantages over other Langrangian vortex methods will be further demonstrated by reducing total CPU time and by avoiding cut-off procedures. The new approach, which is an approximate expression of the Green's function of the diffusion equation, will be constructed for a general two-dimensional smooth contour at a high Reynolds number. A benchmark case, the cylinder problem will be used to examine the accuracy of the code and the effect of spatial mesh length and time step length on computational results. The proposed finite difference analysis based on the diffusing vortex method can be applied to the unsteady imcompressible viscous flow past two dimensional geometry typical of circular, elliptic, and other type of cylinders with CPU time less than vortex method by one order of magnitude.