Vortex Element Methods for Flow Simulation

Abstract

Publisher Summary This chapter focuses on vortex element methods for flow simulation. The vortex element methods allow recreating the physically relevant dynamics of two- and three-dimensional incompressible flows through the use of the Lagrangian or the Lagrangian-Eulerian description of the evolution of discretized vorticity fields. The most important accuracy condition in vortex methods is that the cores of neighboring vortex elements must, at all times, overlap. All remeshing efforts are, by and large, directed to fulfill this condition. It should be kept in mind, however, that the stretching of a segment, intensification of vorticity, constancy of the vortex core, distortion of the near-field velocity distribution due to the increase of the particles or nodes, and artificial dissipation may not all be commensurate with the need to maintain a nondivergent vorticity field. In fact, the accuracy of the calculations may be sacrificed by remeshing, particularly in regions of generation and high concentration of vorticity, due to the warping of the velocity and gradient spaces. This chapter describes evolution and applications of vortex element methods. Concepts related to contra flowing streams, quasi-two-dimensional cross flows, and general three-dimensional flows are also discussed in detail.