Extension of the gridless vortex method into the compressible flow regime

Abstract

This paper proposes an extension of the gridless vortex method into the compressible flow regime. The proposed method consists of tracking particles in the flow that carry vorticity, divergence, temperature and density. The particle velocity is given by the Helmholtz decomposition law, which is approximated using the trapezoid rule. The evolution equations for the particle vorticity, divergence, temperature and density are evaluated using finite differences or least squares approximations for all derivatives. The method is applied to an isentropic model problem and compared to solutions obtained using an Eulerian scheme. Difficulties with the least squares approximation and with boundary conditions are discussed.

This article was chosen from selected Proceedings of the 4th International Workshop on Vortex Flows and Related Numerical Methods (UC Santa-Barbara, 17-20 March 2002) ed E Meiburg, G H Cottet, A Ghoniem and P Koumoutsakos.