A method of numerical conformal mapping of bounded regions with a rectilinear slit

This paper presented a numerical method based on the charge simulation method for calculating conformal mappings from the bounded multiply connected regions with a rectilinear slit onto the first category canonical slit domains. First, we proposed utilizing a pre-map function to expand a rectilinear slit in the bounded multiply connected regions. Second, to address pathologically constrained equation systems, we proposed a conjugate gradient squared (CGS) method combined with LU decomposition. Third, the conformal mappings were applied to simulate spiral point vortex bypass flow in regions with a rectilinear slit. Finally, numerical experiments validated the correctness of the mapping, the method's superiority, and its effectiveness in spiral point vortex bypass flow simulations.