Abstract
A new shape derivative formula for singular contour integrals with logarithmic kernels is proposed. This formula yields a simple numerical scheme for computing vortex patch equilibria. Owing to its simplicity, any steady configuration of point vortices can be extended to that of vortex patches. As a test problem, a doubly periodic array of vortex patches is considered to show the efficiency of the new formula. Several non-trivial families of stationary vortex patch lattices are also presented.
| Original language | English |
|---|---|
| Pages (from-to) | 86-100 |
| Number of pages | 15 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 332 |
| DOIs | |
| State | Published - 2018/04 |
Keywords
- Free-boundary problem
- Lattice
- Shape derivative
- Vortex equilibria
- Vortex patch
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics