Efficient High Accuracy Simulation for Euler and MHD Flow in Complex Geometries

• Applicant: Professor Dr. Claus-Dieter Munz
• Subject Area: Fluid Mechanics
• Term: from 2006 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 27134793

A considerable amount of recent interest in science and engineering revolves around being able to simulate flows with a high level of accuracy. Finite volume schemes (FV-schemes) are amongst the most well-used schemes for such flow simulations. The standard FV-schemes for complex geometries especially based on unstructured grids are second order accurate. However, second order accuracy can be shown to be very inadequate, when the simulation of highly unsteady phenomena is required for long times or over long distances. The present proposal, which is a collaboration between research groups in the USA and Germany, seeks to improve this situation by employing Discontinuous Galerkin (DG) based algorithms of arbitrary accuracy in space and time. These schemes give the high order accuracy even on distorted unstructured grids. An important aspect of the first funding period is to improve the shock-capturing properties for high order DG schemes.Beside the simulation of fluid flow based on the Euler equation our interest also extends to the simulation of flows interacting with electro-magnetic phenomena. Here, additional requirements have to be fulfilled by the numerical method - the divergence-free property for the magnetic field and the charge conservation. In this proposal two strategies are being followed: a special space discretization method by the US group and a general a posteriori divergence cleaning strategy by the German group. The test problems and the applications of the methods developed cover typical shock problems in aerodynamics as well as in astrophysics and space physics. The divergence corrections will also be used in the simulation of pulsed plasma dynamic thrusters.

• DFG Programme: Research Grants