We have studied diffuse interface models for compressible multi-phase flows undergoing phase transitions (modelling e.g. water and water vapor), we have worked on the derivation of new models as well as on the stability analysis of a large class of models that have a Hamiltonian structure. In addition to the challenges already present in single phase flows (learn more ), one has to deal with non-convexity of the energy in multiphase flows. We have also constructed numerical methods that preserve structural properties such as energy dissipation and we have used our stability estimates to provide a priori and a posteriori error estimates for numerical schemes.
We use similar models for phase transitions in elastic solids and for the modelling of fracture propagation.
