Phase transitions in thermoelasticity and compressible fluids

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This project deals with dynamic phase transition problems arising in shape memory alloys developing microstructure, in compressible fluids undergoing gas-liquid-transitions, or during the formation of neutron stars in astrophysics. The mathematical sharp-interface model for all these phenomena are systems of hyperbolic-elliptic conservation laws. A locally adaptive finite volume method (FVM) to solve the conservation laws in 2D/3D will be developed. The novel approach is to evolve the phase boundary by a level set (LS) technique. The code will be validated on test problems, embedded into a parallel environment, and applied to specific problems. The method will be analyzed with respect to stability and convergence.