Staff

In recent years, my colleagues and I have developed the so-called extended discontinuous Galerkin (XDG) method, which enables the highly accurate simulation of flows with all types of embedded interfaces and boundary surfaces.

These boundary surfaces can be, for example, a moving geometry such as the rotor of a wind turbine. Another type of boundary surface is the transition from a liquid to a gaseous fluid. This is known as a mathematical discontinuity.

Such a discontinuity occurs in the density, which can change by a factor of 1000 or more during the transition from liquid to gaseous. However, discontinuities are not only limited to density; since all variables are coupled with each other in such a complex problem, discontinuities also occur in almost all flow variables (velocity, pressure).

For such technically highly relevant flows, “normal” DG methods have the disadvantage that they typically lose their accuracy advantage. The XDG method completely eliminates these disadvantages. Over the last few years, we have successfully applied the XDG method to a variety of fluid dynamic problems. Examples include multiphase flows, fluid-structure interaction, combustion, particle-laden flows and supersonic flows with compression shocks.