A coupling VOF/embedded boundary method to model two phase flows on arbitrary solid surfaces: Application to phase change

We present in this work a hybrid VOF/embedded boundary method allowing to model two phase flows in presence of solid with arbitrary shapes.

The method relies on the coupling of two methods: the Volume of fluid (VOF) dedicated to two phase flow and the embedded boundary desingned to sharply resolve arbitrary solid geometries.

A non trivial coupling of these two approaches is presented in details within our framework accounting for the solving of partial differential equation with Cartesian structured grids and possible adaptive quad/octree spatial discretization.

First, we have proposed a geometrical contact angle model to ensure the boundary condition when the fluid-fluid interface intersects a solid surface and the hybrid method has been validated with several test cases namely the spreading of a droplet on a cylinder or the capillary rise problem.

The ability of our method to resolve contact line for different solid geometries is also demonstrated in either static or dynamical situations.

The hybrid VOF/embedded boundary method is also use to tackle phase change problems with a physcial application: the freezing droplet. To simulate the phase change, we solve the heat equation and an additional set of equations (level-set) is solved to allow the solid to move.