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To: 3.1 Vortex methods for inviscid flows |
Vortex methods are numerical methods to solve the vorticity equation. In this chapter we will briefly describe the basic elements of the vortex methods. Further details and applications of vortex methods are given in survey articles by Clements and Maull [63], Graham [93], Leonard [125,126], Saffman [190], and Sarpkaya [193,195] and in conference proceedings [6,16,33,81,104,192,9]. The mathematical analysis of vortex methods can be found in articles by Anderson & Greengard [11], Chorin [47], Puckett [178], and Raviart [180], and also in the aforementioned conference proceedings.
The evolution of vorticity is due to convection and diffusion processes (see section 2.1 following (2.4)). It is easier to handle those two processes separately in a computation; to do so, at each time step of the computation the vorticity is first convected and then diffused. This basic idea is called the `viscous splitting algorithm', Chorin et al. [53], and Beale & Majda [19].
The handling of convection in vortex methods for viscous flows can be based on that for inviscid flows; hence, we first describe the vortex methods for inviscid flows in section 3.1. Then, in section 3.2 we formulate the vortex methods for viscous flows.