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

TL;DR

This paper introduces an iterative numerical method for computing conformal mappings and their inverses, specifically applied to water wave problems over complex topographies, validated against established benchmarks.

Contribution

The paper presents a novel iterative approach for conformal mapping and its inverse, tailored for water wave simulations over uneven terrains.

Findings

Method achieves high accuracy compared to Schwarz-Christoffel toolbox

Provides a reliable numerical alternative for inverse conformal mapping

Applicable to complex water wave 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.