A way to split the Navier-Stokes equations in the context of the vortex method

Abstract

SUMMARYA numerical scheme has been obtained rigorously from the initial-boundary value problem for the Navier± Stokes (NS) equations in the context of the vortex method. The technique is based on a transformation of the NS equation into a parabolic equation which has an exact solution. The numerical scheme is derived by expanding the exact solution in Taylor series in powers of a small time interval. Numerical implementation is developed with use of vortex particles to represent the vortex¯ow domain. The method is used to solve practical engineering problems. The technique can also incorporate turbulence modelling.