The SHTC-Model and Multiphase Flows

The modeling, analysis and numerical treatment of multiphase fluid dynamics provide several challenging problems treated in the past as well as in very recent literature. Recently interest in the works by Godunov, Müller, Ruggeri, Romenski and their co-authors is growing. In particular Godunov and Romenski suggest an approach which leads to symmetric hyperbolic systems which are derived from physical principles, i.e. symmetric hyperbolic and thermodynamic consistent models (SHTC). These hyperbolic models are capable of describing multiphase fluid dynamics including heat conduction and viscosity which are typically second order effects. In this project we want to combine the expertise on these models provided by Prof. Romenski and Prof. Dumbser with our expertise on sharp interface models. This project includes different goals related to the diverse aspects of the topic. One main problem is to discuss the Riemann problem for a barotropic submodel of the main model provided by Romenski. With this we obtain further analytical insight and additionally can verify numerical methods.
A further aim is to reveal the connection between the diffuse and the sharp interface two-phase flows considered in this context.

The modeling, analysis and numerical treatment of multiphase fluid dynamics provide several challenging problems treated in the past as well as in very recent literature. Recently interest in the works by Godunov, Müller, Ruggeri, Romenski and their co-authors is growing. In particular Godunov and Romenski suggest an approach which leads to symmetric hyperbolic systems which are derived from physical principles, i.e. symmetric hyperbolic and thermodynamic consistent models (SHTC). These hyperbolic models are capable of describing multiphase fluid dynamics including heat conduction and viscosity which are typically second order effects. In this project we want to combine the expertise on these models provided by Prof. Romenski and Prof. Dumbser with our expertise on
sharp interface models. This project includes different goals related to the diverse aspects of the topic. One main problem is to discuss the Riemann problem for a barotropic submodel of the main model provided by Romenski. With this we obtain further analytical insight and additionally can verify numerical methods. A further aim is to reveal the connection between the diffuse and the sharp interface two-phase flows considered in this context.