Extended discontinuous Galerkin Methods - Multiphase and Beyond by Dr. Florian Kummer (TU Darmstadt)

This presentation focuses on the development and application of Extended Discontinuous Galerkin (XDG) methods, initially motivated by the need to accurately simulate incompressible multiphase flows, such as interactions between oil and water or air bubbles in liquids. Addressing multiphase flows often presents significant challenges, particularly when dealing with abrupt changes in parameters like density and viscosity, and the pressure variations due to surface tension. The XDG method addresses these issues by offering high-accuracy approximations and solutions for such discontinuous phenomena.

The XDG-method is designed to obtains solutions, resp. approximations to such discontinuous problems with a high order of accuracy. Here, the fluid interface is embedded within a Cartesian background mesh. The discontinuous finite elements, defined on the background mesh are extended in a fashion so that they are capable of approximating singularities (e.g., jumps and kinks) in the pressure and the velocity field with a high order of accuracy.

This talk aims to provide a comprehensive overview of the XDG methodology, highlighting essential aspects such as stabilization techniques and the agglomeration of small cut cells. Furthermore, the discussion extends to exploring the application potential of XDG methods in areas beyond their conventional scope, inviting a broader understanding of their versatility and effectiveness in complex flow simulations.

About the Author:

Career Path:

•    2015 – now: Research group leader at the Chair of Fluid Dynamics (FDY), TU Darmstadt• responsible for multi-phase research group and software development
•    2014 – 2015: Visiting Scholar at the Department of Computational and Applied Mathematics (CAAM), Rice University
•    2013 – 2014: Research Associate at Center for Turbulence Research (CTR), Stanford University
•    2006 – 2012 Research Staff at Chair of Fluid Dynamics (FDY), TU Darmstadt (PhD Student, Postdoc)
•    2000 – 2006: Studies of Technical Mathematics, University of Innsbruck

Research interests:

•    Development of numerical methods
o    Mostly focused on extended methods (XDG)
o    Special emphasis on multiphase flows
•    High Performance Computing
o    Iterative Solvers for indefinite, unsymmetric systems
•    Application of Continuous Integration Practices for Scientific Software Development.