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ISBN 9783843938358

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978-3-8439-3835-8, Reihe Ingenieurwissenschaften

David G. Flad
On the Use of Discontinuous Galerkin High Order Methods for Large Eddy Simulation

101 Seiten, Dissertation Universität Stuttgart (2018), Softcover, A5

Zusammenfassung / Abstract

High order discontinuous Galerkin spectral lement methods (DGSEM) are investigated towards their ability to be used for large eddy simulation (LES). LES requires the resolution of a wide range of scales, posing high demands on the numerical method used to solve the non-linear equations. DGSEM are a special implementation of nodal discontinuous Galerkin methods. The method is characterized by its low dissipation and good dispersion properties and known to be specifically efficient in terms of computational cost, while fully unstructured grids can be used. These properties make it attractive for the use in large eddy simulation. The current state of the art for large eddy simulation using these methods is to rely on the inherent dissipation of the upwind-based inter-cell fluxes to account for turbulence closure, so called no-model LES. For stable simulation when using high order methods, de-aliasing is usually needed. A recently introduced split flux formulation to obtain a skew-symmetric like formulation for DGSEM is examined for LES. It is shown to be the superior de-aliasing strategy for LES, due to its property of discretely preserving kinetic energy. No-model LES is shown to have a limitation in applicability to well resolved LES. For typically (industrially) used coarse LES resolutions results become in-accurate. It is shown that only by using kinetic energy preserving fluxes, good results in such cases are obtained when combined with an explicit LES closure and a low dissipation inter-cell flux (Roe's Riemann solver with low Mach fix). A novel LES closure tailored for the high order DGSEM is suggested. The closure is based on a dissipative filter with the filter shape non-linearly optimized for LES of homogeneous isotropic turbulence. The filter strength is defined by the highest mode kinetic energy content. The method is tested in the limit of Reynolds number towards infinity and for turbulent channel flow. It is found to be at least as good as the classical Smagorinsky-Lilly closure, while offering the potential of drastically reducing computational cost as it does not require the computation of second order derivatives.