Numerical simulation of axisymmetric viscous flows by means of a particle method

A vortex particle method for the simulation of axisymmetric viscous flow is presented. The flow is assumed to be laminar and incompressible. The Navier-Stokes equations are expressed in an integral velocity-vorticity formulation. The inviscid scheme is based on Nitsche's method for axisymmetric vortex sheets. Meanwhile, two techniques are proposed for dealing with the viscous term. The first uses an integral Green's function method while the second is based on a diffusion velocity approach. Both are obtained by extension of existing methods for 2D flows. The problem of satisfying boundary conditions along the axis of symmetry is specifically addressed. The problem is solved by using cut-off functions that are derived from the Green's function of the axisymmetric diffusion equation. The scheme is applied to simulate the evolution of vortex rings at intermediate Reynolds number. The processes of entrainment and wake formation are evident in the calculations, as well as the extension of the support of vorticity due to viscous diffusion. (C) 1999 Academic Press.