COMPUTING VORTICITY DIFFUSION WITH A MODIFIED "DONOR-ACCEPTOR" SCHEME AND THE INTEGRATION OF THE SCHEME INTO THE "VORTEX-IN-CELL" METHOD

A modernised scheme of splitting Navier-Stokes equations for the numerical method of "vortex-in-cell" is proposed. The method consists in introducing a minor parameter proportional to kinematic viscosity into the scheme. It allows finding the solution of the problem in the form of asymptotic series. An advection-diffusion problem of the Lamb-Ozeen vortex is considered for the verification of the proposed method. Computation results obtained by "donor-acceptor" (D-A) and MD-A methods are compared with an analytical solution of the advection-diffusion problem. The MD-A method is shown to be more suitable for low viscosity flow simulation. Unlike the D-A method, the MD-A method remains accurate in a wide range of space and time resolution.