Research Topic

DG Methods for multiphase problems

Problem Setting of premixed combustion: Unburned Phase (A), Bunrned Phase (B), Interface(I), laminar flame speed

In Premixed combustion, which occurs e.g. in Otto-engines, the chemical reaction occurs in a very narrow region, compared to any external length-scale.  Therefore, the flow can be modelled mathematically as an incompressible two-phase flow consisting of an burned and unburned phase. In this setting, the flame itself is described as a 2-dimensional, non-material interface (there is mass flux across the interface !), and the whole chemistry and physics of the flame is replaced by a model that just describes the burning velocity of the flame in its normal direction.

Because of the jumps in velocity and pressure, its usually very difficult to capture the situation described above with a classical numerical scheme.The solution we come up with consists of the following ingredients:

  1. A Level Set method to capture the movement of the front, which is actually quite standart;
  2. The major novel development is an extended DG method, that is capeable of resolving the shocks desribed above with sub-cell accuracy. While the Level Set desribes the position of the front, the extended DG method is capeable of fullfilling the jump conditions for velocity and pressure at the interface.

Recent Results

Preliminary results for premixed combustion: The white circle contains burned gas; The flame burns outwards, displacing the unburned mixture and pushing it through the "exhaust" on left and right.

Key Research Area

Multi-Physics; Discontinouos Galerking (DG) Methods, Numerical Methods for Multiphase Methods, including Level Set Methods and Extended DG;


Florian Kummer


Dolivostraße 15

D-64293 Darmstadt



+49 6151 16 - 24401 or 24402


+49 6151 16 - 24404


(at) ...

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