Seminars

The Stefan problem is a macroscopic phase transition problem with a moving interface between the two phases, originally established for solid and liquid water. Changing the liquid phase to a rarefied gas to investigate corresponding sublimation or deposition processes requires careful modeling and poses numerical challenges. Some applications include industrial pharmaceutical freeze-drying and planetary science.

This talk will cover the derivation of non-equilibrium thermodynamic equations for the interface with the help of the kinetic theory of gases. The resulting macroscopic coupling conditions depend on the Knudsen and Mach numbers. They align well for comparison with classical conditions and allow identifying the equilibrium limit. Furthermore, an introduction to the R13 equations for modeling rarefied gases in the transition regime will be presented.

The numerical solver has specific requirements to capture all potential rarefaction effects. As these effects usually manifest first at boundaries, the region around the interface must be resolved as accurately as possible. Existing numerical strategies for phase-transition problems are thus revisited and adapted. A front-tracking strategy with exact remeshing enables the precise imposition of interface conditions. Preliminary examples demonstrate the capabilities of the resulting solver for the classical problem.