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.

This paper proposes a novel numerical scheme based on an improved charge simulation method for computing conformal mappings of bounded multiply connected domains. The core of the method reformulates the mapping problem into a constraint system constructed via charge simulation. This system is then solved efficiently using the symmetric successive over-relaxation incomplete Cholesky conjugate gradient method, which is particularly well-suited for handling the ill-conditioned systems inherent to such problems. Numerical experiments show that our method achieves significantly higher accuracy and improved convergence rates compared to the conventional Gauss-Seidel iteration. The results confirm the robustness and practical potential of the proposed framework, establishing it as an efficient and reliable tool for computing conformal mappings of domains with high connectivity and complex geometry.