Speaker
Description
Our goal is the feedback stabilization of a two-dimensional two-phase Stefan problem coupled with (Navier-)Stokes equations. The Stefan problem can model solidification and melting of pure materials and gets its name from the purely algebraic Stefan condition which describes the coupling between the temperature of the material and its melting process.
After linearization and discretization, the stabilization problem results in a non-autonomous differential Riccati equation (DRE) with differential-algebraic structure. While the actual index of the resulting DAE needs further investigation, the problem features a structure that combines that of semi-explicit index-1 DAEs (resulting from the Stefan condition) and Stokes-type index-2 DAEs (resulting from the dynamics of the convection).
Moreover, the interface between the two phases in the domain evolves over time, which causes all coefficients of the resulting DRE to be time-varying. Thus, existing DRE solvers have to be adapted to this highly non-autonomous case which has significantly increased computational costs and memory requirements.
We present techniques to treat the specific structure of this coupled problem
in the solver for the DREs and show first results of the application of our feedback stabilization.
