Christoph Altmann

An Efficient High Performance Parallelization of a Discontinuous Galerkin Spectral Element Method

We describe an efficient parallelization strategy for the discontinuous Galerkin spectral element method, illustrated by a structured grid framework. Target applications are large scale DNS and LES calculations on massively parallel systems. Due to the simple and efficient formulation of the method, a parallelization aiming at one-element-per-processor calculations is feasible; a highly desired feature for emerging multi- and many-core architectures. We show scale-up tests on up to 131,000 processors.

Discontinuous Galerkin for High Performance Computational Fluid Dynamics (hpcdg)

In this paper we present selected ongoing computations, performed on HLRS clusters. Three efficient explicit Discontinuous Galerkin schemes, suitable for high performance calculations, are employed to perform direct numerical simulations of isotropic turbulence and turbulent channel flow, large eddy simulations of cavity-flows as well as hybrid simulations of aeroacoustic phenomena. The computations were performed on hundreds to thousands computer cores.

An Explicit Space-Time Discontinuous Galerkin Scheme with Local Time-Stepping for Unsteady Flows

The objective of our project is the development of high-order methods for the unsteady Euler and Navier Stokes equations. For this, we consider an explicit DG scheme formulated in a space-time context called the Space-Time Expansion DG scheme (STE-DG). Our focus lies on the improvement of two main aspects: Increase of efficiency in the temporal and spatial discretization by giving up the assumption that all grid cells run with the same time step and introducing local time-stepping and the shock capturing property, where we have adopted the artificial viscosity approach as described by Persson and Peraire to our STE-DG scheme. Thus, we try to resolve the shock within a few relatively large grid cells forming a narrow viscous profile by locally adding some amount of artificial viscosity.

On the Numerical Simulation of a Scramjet Intake using a Space-Time-Expansion Discontinuous Galerkin Scheme

During the last years, discontinuous Galerkin (DG) methods became a prominent candidate for high order calculations since they combine high order spatial accuracy with geometrical exibility and further involve e ective parallelization. Hence, these features make the DG methods particularly suitable for complex large scale computations of a wide range of applications. A main drawback of high order schemes, though, is that they can lead to spurious oscillations when discontinuities, e.g. shock waves, are present within the ow eld. In order to prevent such non-physical oscillations, a shock capturing mechanism is required to robustly approximate the shocks. In this context, we will discuss an e cient arti cial viscosity based shock capturing mechanism within the Space-Time-Expansion discontinuous Galerkin (STE-DG) framework and apply it to typical shock capturing test cases and further to the three-dimensional simulation of the intake ow of a scramjet with a freestream Mach number of 8. As we focus on the shock waves and their proper resolution in a high order DG computation in this work, the numerical investigations base upon the inviscid Euler equations.

An Explicit Discontinuous Galerkin Scheme with Divergence Cleaning for Magnetohydrodynamics

The explicit space-time expansion discontinuous Galerkin scheme (Gassner et al., J. Sci. Comp. 34(3):260–286, 2008) is applied for solving ideal and viscous magnetohydrodynamic equations. Based on a Taylor expansion in space and time about the barycenter of each cell at the old time level, this predictor-corrector strategy enables each cell to have its own time step whereas the high order of accuracy in time is retained. Thus, it may significantly speed up computations. The discontinuous Galerkin method together with the local time-stepping algorithm allows for an efficient local sub-cycling for a divergence cleaning using a hyperbolic transport correction (Dedner et al., J. Comput. Phys. 175(2):645–673, 2002). Convergence tests and test problems are performed to challenge the capabilities of the space-time expansion scheme.

Towards the Numerical Simulation of a Scram Jet Intake at High Mach Number

We describe the current progress of our project towards a numerical simulation of a scram-jet intake at high Mach number. We will outline why we have not yet reached our goals and need more computational time and resources. Nevertheless we present results of complex large-scale computations already performed on the HLRB II supercomputer that will hold as pioneering computations to enable the code for massively parallel computations on a very large number of processors and also describe discovered obstacles as well as the implemented solutions towards successful calculations.

A space-time expansion discontinuous Galerkin scheme with local time-stepping for the ideal and viscous MHD equations

In this paper, we present the extension of the space-time expansion discontinuous Galerkin to handle ideal and viscous magnetohydrodynamics (MHD) equations. The local time-stepping strategy that this scheme is capable of allows each cell to have its own time step whereas the high order of accuracy in time is retained. This may significantly speed up calculations. The diffusive flux is evaluated through a so-called diffusive generalized Riemann problem. The divergence constraint of the MHD equations is addressed, and a hyperbolic cleaning method is shown that can be enhanced by utilizing the local time-stepping framework. MHD problems such as the Orszag-Tang vortex or the magnetic blast problem are performed to challenge the capabilities of the proposed space-time expansion scheme.