Research Topic

Discontinuous Galerkin Simulation of Multiphase Flows with Interfacial Equations

Numerical simulation of a first order surface PDE on a cut sphere

The objective of this research project chair of fluid dynamics at TU Darmstadt is the development of a highly accurate numerical solver for the computation of multiphase flows including phase interfaces and interfacial transport equations. In particular, our first aim focuses on the transport equation for surface active agents, known as surfactants.

Our solver is based on Discontinuous Galerkin (DG) methods that have been established rather successfully by now in the treatment of hyperbolic conservation laws, for combining the advantage of a local flux evaluation with an O(h^p) discretization error. In this way, we intend to extend the DG library BoSSS that has been developed in our working group since 2008 for the simulation of single and two phase incompressible and compressible flows.

In this context, the numerical treatment of a possibly moving interface as well as interfacial conservation equations remains a challenging task, involving a simultaneous tracking of the interface position and solution of both the flow field and the interfacial equations, possibly with additional jump conditions. The numerical representation of the interface is currently implemented by a level set method where re-initialization may be applied on demand. An extended DG method is proposed to compute surface and volume integrals accurately for those cells which are split by the phase interface. Furthermore, non-smooth basis functions allow for a sharp delimitation between different fluid properties.

The interfacial equations are solved by embedding the interface, a two-dimensional manifold, into a three-dimensional manifold by projecting the respective quantities onto a narrow band located near the interface and employing an extrinsic formulation of the surface differential operators. A problem re-formulation by conservation laws is currently under construction and is planned to be coupled with this approach in future.

Altogether, the suitable choice of methods in combination with DG should avoid serious shortcomings of classical schemes, for instance mass deficit at the interface or artificially induced flows due to numerical errors in computation of surface curvature.

Key Research Area

Fluid Dynamics, Scientific Computing


Christina Kallendorf



L1|01 331, Petersenstr. 30

D-64287 Darmstadt



+49 6151 16 - 24401 or 24402


+49 6151 16 - 24404




kallendorf (at) fdy.tu...

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