An iterative method to compute conformal mappings and their inverses in the context of water waves over topographies

Abstract: An iterative numerical method to compute the conformal mapping in the context of propagating water waves over uneven topographies is investigated. The map flattens the fluid domain onto a canonical strip in which computations are performed. The accuracy of the method is tested by using the MATLAB Schwarz-Christoffel toolbox mapping as a benchmark. Besides, we give a numerical alternative to compute the inverse of the conformal map.