Discontinuous Galerkin methods for incompressible multi-phase flows

• Applicant: Dr.-Ing. Florian Kummer
• Subject Area: Fluid Mechanics ; Software Engineering and Programming Languages
• Term: from 2012 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 230990002

In many technical applications, for instance in internal combustion engines or turbines, multi-phase flows play an important role. These are flows containing at least two different liquids or gases which do not dissolve, for instance oil in water or water in air. Technically relevant examples are the atomization of liquid fuels by injection nozzels or liquid sheet breakup; other areas are e.g. evaporation processes.The numerical simulation of such flows is still an actively researched topic. Especially the numerical representation of the density jump and the implied discontinuities in the velocity and pressure field are numerically challenging.Within this project, multi-phase solvers which are based on the discontinuous Galerkin (DG) method will be developed. The DG method will be extended in a way so that it is capable of representing the density jump within a numerical cell. By doing so, the high precision (i.e. the high error convergence order) of the original DG method could be extended to multi-phase flow problems.The basic ingredients of the extended DG method have already been implemented in BoSSS; within the first part of the project, two multi-phase flow solvers with different time discretization schemes will be implemented. We suggest one multi-phase method that is based on SIMPLE and another one which is based on the projection method. The second part of the project addresses the performance-optimization of the methods which have been developed in the first part. These include an optimization of the algorithms as well as software-optimization. Especially, we plan to port computationally expensive parts of the BoSSS-code to so-called `Graphics Processing Units’ (GPU’s) which are becoming more and more popular for high-performance computing.Within the third part of the project, some relevant applications should be simulated. This includes, for instance, primary jet breakup (nozzle injectors), droplet dynamics and premixed combustion.

• DFG Programme: Research Fellowships
• International Connection: USA
• Hosts: Professor Parviz Moin; Professor Dr. Tim Warburton