Conformal mapping and efficient boundary element method without boundary elements for fast vortex particle simulations

In this paper, a revitalization of conformal mapping methods applied to fluid flows in two dimensions is proposed. The present work addresses several important issues concerning their application for vortex particle flow solvers. Difficulties of past conformal based method are reviewed. One difficulty concerns the ability of a mapping procedure to represent complicated shapes. The present paper improves past algorithms to be able to map new shapes, including multiply connected domains. A new fast procedure allows transferring a set of points in the mapped simplified plane to the complicated domain and vice versa. After a mapping construction, it is demonstrated how basic exact solutions to potential flow problems with vortices can be put in a new form which provides a faster and more accurate computation than with distributed singularity methods.