Institute of Aerodynamics and Gas Dynamics>
- Discontinuous Galerkin (DG)
- Efficient time integration schemes for unsteady problems
- HP-Adaptation in space and time
- Compressible Turbulence Simulation (DNS, LES)
- Analysis of Numerical Methods
- Multi-Scale Numerics
- High performance computing (HPC)
Typically, numerical methods are designed and constructed for well resolved simulations. This shows itself in the expression of convergence order of a numerical scheme and the recent development trend to higher order accurate discretizations.The convergence of a scheme describes its behavior when the discretization is refined, i.e. better resolved. It can be shown that in the well resolved case, a high order accurate or even spectrally accurate discretization is always more efficient compared to their lower order variants.
The problem with those statements is, that it is implied that the exact solution is well approximated, i.e. well resolved. Thus, it is not clear how those methods behave in the aspired coarse resolution turbulence simulations and how their superior efficiency characteristics translates to the under-resolved case.
It is thus necessary to evaluate, investigate and analyze the behavior and the efficiency of numerical methods in the under-resolved case. Discontinuous Galerkin offers the perfect opportunity to compare low order with high order (or even spectrally) accurate discretizations as this can be basically controlled with the local polynomial degree N of the DG approximation.
All those investigations and developments are undertaken with a high performance computing setting in mind. The fundamental advantage of a discontinuous Galerkin approximation is its inherent parallel efficiency. To conserve the locality of the resulting multi-scale numerics and to maintain a superb parallel efficiency is the fundamental boundary condition for all developments.