ISBN 9783843946414

978-3-8439-4641-4, Reihe Ingenieurwissenschaften

Nico Krais
Moving Mesh Methods and Wall Modelling for Discontinuous Galerkin Schemes

259 Seiten, Dissertation Universität Stuttgart (2020), Hardcover, A5

Zusammenfassung / Abstract

This work deals with the extension of the high-order discontinuous Galerkin solver Flexi towards several important aspects for future computational fluid dynamics applications: Moving meshes, the incorporation into fluid-structure interaction frameworks and wall-modelled large eddy simulations. The efficient use of high-order methods is an important building block in the way towards large eddy simulations in engineering applications. Many relevant problems deal with moving boundaries, and in this thesis the equations are cast in the arbitrary Lagrangian Eulerian framework to handle arbitrary moving meshes. The discontinuous Galerkin spectral element method is derived on moving grids, both in the standard form and for split forms. Those can be used to incorporate additional conservation properties into the set of equations, and efficiently reduce aliasing problems in underresolved situations.

In numerical experiments it is shown that the scheme on moving meshes retains high-order accuracy in both space and time, and that no spurious oscillations are introduced by discretely fulfilling the geometric conservation law. The parallel efficiency and the performance compared to static methods is also investigated, as large scale computations require efficient use of the available resources. The resulting scheme is coupled with a structural solver in a partitioned algorithm to enable fluid-structure-interaction computations. To enable simulations at realistic Reynolds numbers, a way to model the inner part of the boundary layer is shown and implemented in the discontinuous Galerkin flow solver.