Development of a self-consistent, electrified shallow water model coupled with Poisson solver

The physics of charged liquid surface plays an important role in plasma-liquid interaction. It is known that instabilities can appear on such charged liquid surfaces due to the competition of electric field, surface tension, and gravity. We have developed a shallow water model that describes the dynamics of an electrified liquid surface. In this talk, we present the development of an electrified shallow water model that is coupled with an electrostatic Poisson solver with curved liquid boundaries. For the calculation of potential and the electric field profiles, the curved boundary condition is taken into account using a weighted least square interpolation method. The preliminary results show a good agreement for the electric field and potential between the numerical and analytical solutions of a hemispherical boss test. We will discuss the further development of the shallow water model and the investigation of the Tonks-Frankel instability observed with the developed model.