Phase transitions in thermoelasticity and compressible fluids

• Applicant: Professor Dr. Dietmar Kröner
• Subject Area: Mathematics
• Term: from 2002 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5469304

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.

• DFG Programme: Research Units
• Subproject of: FOR 469: Nonlinear Partial Differential Equations: Theoretical and Numerical Analysis