Conformal Mapping in 2D Coulombic Potential Problems

For physical systems governed by Coulombic potential in 2D, one can set up the problem in complex plane and use the freedom of conformal mappings to help solve the problem. In this talk I will mention some examples following this idea and focus on the example of a uniform flow past two close-to-touching discs. By using the method of image charges combined with conformal transformations in the numerical calculation of the potential, we can reach a solution with high accuracy and stability more efficiently compared to existing methods.