The extended Discontinuous Galerkin method for two-phase flows with evaporation

In this work, we present an extended Discontinuous Galerkin method for simulating transient, incompressible two-phase flows, which include heat transfer and thermally driven evaporation at the interface of single-component systems. This expands our previous work to include the consideration of non-material interfaces and a coupling between velocities and temperature gradients at the interface. The phase boundary is represented by the zero-set of a level set function, while effects due to surface tension are treated by the Laplace-Beltrami formulation. This sharp interface model allows for a sub-grid accurate representation of the solution fields. By using compactly supported polynomial solutions, discontinuities at the interface can be sharply represented without employing additional reconstruction schemes. The approach is validated through well-known evaporation test cases. This includes two 1D test cases, known as Stefan and Sucking problem, a 2D film boiling and finally the 3D growth of a vapor bubble, known as Scriven test case.