Discontinuous Galerkin methods for incompressible flow

Niklas Fehn, Benjamin Krank and Martin Kronbichler


Aiming at large-scale flow computations on modern supercomputers, the discontinuous Galerkin method is the only method that combines all of the following highly desired properties:

  • High-order capability
  • Geometric flexibility through arbitrary meshes and curved boundaries
  • Convective stabilization through consistent upwind fluxes
  • Efficiency on massively parallel high-performance computers

We have therefore developed a new code INDEXA (A high-order discontinuous Galerkin solver for turbulent incompressible flow towards the EXA scale) for incompressible laminar and turbulent flow based on the discontinuous Galerkin method. The code is based on tensor product elements in combination with a matrix-free implementation that is particularly efficient for high spatial polynomial degrees. We have evaluated the remarkable parallel efficiency of our code through scaling to the complete phase 1 of SuperMUC on 147,456 compute cores where we achieved a parallel speedup of a factor of 9 to 12 when increasing the computational resources by a factor of 18. For this achievement we won the "Extreme Scaling Award 2016 (Finalist)".

Among various benchmark flows, we have computed DNS of turbulent channel flow at Re_tau = 590 using 131 million degrees of freedom, which is visualized in the animation below.