4. Vorticity Redistribution Method

In this chapter we will describe our new redistribution method to handle diffusion in vortex computations. As we explained at the start of chapter 1, our method is designed to handle any distribution of vortices. Hence, we make no a priori assumptions about the relative locations of the vortices, or the number of vortices surrounding any given vortex in our mathematical formulation of the method in section 4.1. The physical meaning of the equations is discussed in section 4.2. A general justification of our approach is presented in section 4.3. Further theoretical justification can be found in the comparison with other methods in chapter 9. That the method converges is shown analytically and numerically in chapters 5 to 8.