### Speaker

Mr
Sean McGovern
(Forschungszentrum Juelich)

### Description

Given the context of distributed parallelism, the purpose of this contribution is to consider a solution procedure to the classical Stefan phase change problem, an example of a free boundary problem. In the Stefan problem, the interface between water and ice moves through a domain as the ice melts due to a heat source. As an example of an interface problem, we choose to apply the level set method to implicitly track the evolution of the ice/water interface. The diffusive temperature equation must be solved over the whole domain while an evolving interface separates regions endowed with different material properties, i.e. specific heat of water and ice. The Gibbs-Thomson relation gives the discontinuity in the temperature field at the interface and the interface velocity is given by the jump in the heat flux.
To solve this kind of coupled nonlinear problem, we can 1) evolve the interface and 2) solve the temperature equation iteratively. The first is a hyperbolic advection equation and the second is parabolic. As is well-known, these require different solution tactics. We consider a setup for which an analytical solution exists.
The approach remains pedagogical as I would like to package this as a possible tutorial step.

### Primary author

Mr
Sean McGovern
(Forschungszentrum Juelich)