ISBN 978-3-8439-3777-1

978-3-8439-3777-1, Reihe Ingenieurwissenschaften

Thomas Bolemann
Towards Industrialization of High-Order Discontinuous Galerkin Methods for Turbulent Flows

205 Seiten, Dissertation Universität Stuttgart (2018), Hardcover, A5

Zusammenfassung / Abstract

Discontinuous Galerkin methods have in recent years become increasingly popular in CFD, primarily for being highly suitable for multiscale problems. They combine high-order of accuracy with low dispersion and dissipation errors, making them ideal for scale-resolving simulations, such as Large Eddy Simulation. Due to their element-local nature, DG methods are very flexible and can efficiently utilize today's largest supercomputers. While DG methods were in the past predominantly used in science, the continuous adoption of LES in design processes has brought them into the focus of industry.

This work is based on the results from the European projects IDIHOM and TILDA which aimed to improve the industrial applicability of high-order methods in CFD. It further advances high-order DG methods for industrial scale-resolving simulations. This involves both, an efficient and robust numerical scheme and the provision of high-order mesh generation and post-processing capabilities, tailored for the needs of DG methods.

A particularly efficient variant of DG methods is presented, known as the discontinuous Galerkin Spectral Element Method. To reduce aliasing effects two counter measures are compared: explicit modal filtering and overintegration. Low-storage, explicit Runge-Kutta methods are employed for the time discretization and some promising many-stage variants are assessed with respect to their efficiency.

The implementation of the massively parallel integrated simulation framework FLEXI is presented, including strategies to improve the performance. With mesh generation and post-processing being key criteria for industrial applicability, a high-order mesh preprocessor for generating unstructured, curved meshes is presented, with support for non-conforming interfaces. Two post-processing tools to directly visualize high-order polynomial data are outlined: a proof-of-concept tool using a direct volume rendering approach, and an integrated visualization environment based on Paraview, providing a user-friendly, parallel visualization of large DG data sets. All parts of the simulation framework are publicly available and open source.

For demonstrating the framework's capabilities to efficiently simulate unsteady, turbulent flows, two LES of model problems are conducted:

a channel flow over streamwise periodic constrictions featuring separation and reattachment and a flat-plate mounted cylinder.