Solving phase change problems using stabilized finite elements with improved interfacial conditions

Here we present a mathematically consistent numerical technique for solving two-phase problems involving phase-change processes such as evaporation and condensation. We use a stabilized finite element method on hybrid meshes for solving compressible Navier-Stokes equations and correctly account for the jump conditions across the interface (derived from conservation laws) using discontinuous interpolations. The interface is tracked explicitly using the arbitrary Lagrangian-Eulerian (ALE) description in which the mesh at the interface is required to move with the interface. A penalty approach is used to weakly ensure continuity of tangential velocity components and to explore various jump conditions for temperature. The rate of phase change is evaluated using thermodynamic variables at the interfaces and kinetic interfacial parameters determined from molecular dynamics simulations.