A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume method

Abstract

This paper describes and compares two vorticity-based integral approaches for the solution of the incompressible Navier-Stokes equations. Either a Lagrangian vortex particle method or ail Eulerian finite Volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot-Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of ail iteration scheme connected with the well-established panel method. In the early stages of development of flows around ail impulsively started circular cylinder, and past ail impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity-based methods. Copyright (c) 2005 John Wiley & Sons, Ltd.