New approach to an underwater discharge simulation using elliptic coordinates

In this study, a system of two equations is developed that allows the time evolution of the underwater spark channel to be calculated numerically from a given power input. The proposed mathematical model utilizes the elliptical coordinates. This approach has the advantage of considering the underwater spark as an expanding ellipsoid, which closely corresponds to experimental observations. Similar to spherical or cylindrical models, the proposed method considers only one spatial coordinate as a function of time, which simplifies the analysis. The predictions of this model are compared with the experimental results.