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978-3-8439-0126-0, Reihe Strömungsmechanik

Arne Taube
A High-Order Discontinuous Galerkin Scheme for Aerodynamic Applications in Industry

193 Seiten, Dissertation Universität Stuttgart (2011), Softcover, A5

Zusammenfassung / Abstract

The aim of the present work is the investigation of the space-time expansion discontinuous Galerkin (STE-DG) scheme and its building blocks - time discretization, adaptation and high-order shock capturing - with respect to aerodynamic applications in industry. This is done against the background of the ADIGMA project, whose aim is the promotion of innovative and adaptive higher order methods for the compressible Navier-Stokes equations.

The current DG scheme is explicit and arbitrary order accurate in space as well as time. Its time evolution is a single stage predictor-corrector approach. This leads to a very compact discretization. This locality and the space-time nature of the STE-DG discretization allow the introduction of local time steps and thus fundamentally change the usual time advancement during the simulation.

For two-dimensional simulations, the scheme's efficiency can be increased even further by making use an adaptation framework presented in this work. During the time dependent simulation, the mesh, the approximation order or both can be adjusted to the flow.

The high-order shock capturing is achieved with the aid of a two-step approach. First, shock cells are detected by a troubled cell indicator and then are dealt with by a cell-wise constant artificial viscosity. With the proper shock capturing settings for each individual test case, the scheme can capture a shock with increasing order within less grid cells until its full resolution within only one cell.

The scheme's features are demonstrated and validated with the aid of ADIGMA test cases. Different NACA0012 airfoil test case are used to evaluate the scheme's convergence, compare it to the DLR's TAU-Code and to test the adaptation framework. For the shock capturing, the results are compared to other high-order schemes and the interaction of the adaptation framework with the shock capturing is investigated.

Finally, the whole method is applied to the problem of two- and three-dimensional cavity flow. The energy drain resulting from the small scale flow features is modelled by a similar artificial viscosity, as it is used for shocks. The numerical results shown in this work are the first computations with the STE-DG scheme of an unsteady flow field close to turbulence. The results and the chosen path towards the large eddy simulation show good agreement with a rough estimate for the acoustic modes and therefore may serve as reference data for future simulations.