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978-3-8439-1771-1, Reihe Ingenieurwissenschaften
Mesh Curving Techniques for High Order Parallel Simulations on Unstructured Meshes
203 Seiten, Dissertation Universität Stuttgart (2014), Softcover, A5
In this work, the generation of high order curved three-dimensional hybrid meshes and its application are presented. Meshes with linear edges are the standard of today's state-of-the-art meshing software. Industrial applications typically imply geometrically complex domains, mostly described by curved domain boundaries.
To apply high order methods in this context, the geometry - in contrast to classical low order methods - has to be represented with a high order approximation, too.
The main idea here is to rely on existing linear mesh generators and provide additional information to produce high order curved elements.
A very promising candidate for future numerical solvers in computational fluid dynamics is the family of high order discontinuous Galerkin (DG) schemes. Elements couple only to direct face neighbors, and the discontinuity is resolved via numerical flux functions.
As the main focus of this work are curved elements, the different formulations and possible implementations of the DG scheme with non-linear element mappings are discussed in detail.
The main focus of this thesis is the generation of high order meshes. Several techniques to generate curved elements are described and their applicability to complex geometries is demonstrated.
One of the reasons making high order DG schemes attractive for the simulation of fluid dynamics is their parallel efficiency. As future applications in fluid dynamics comprise the resolution of three-dimensional unsteady effects and are increasingly complex, the simulations require more and more computing resources, and weak and strong scalability of the numerical method becomes extremely important.
In the last part of this thesis, the parallelization concept of the DG-SEM code Flexi is described in detail.
A new domain decomposition strategy based on space filling curves is introduced, and is shown to be simple and flexible. A thorough parallel performance analysis confirms that the overall implementation scales perfectly. Ideal speed-up is maintained for high polynomial degrees, up to the limit of one element per core.
As the DG scheme only communicates with direct neighbors, the same parallel efficiency is found on both cartesian meshes as well as fully unstructured meshes. The findings underline that the proposed Discontinuous Galerkin scheme exhibit a great potential for highly resolved simulations on current and future large scale parallel computer systems.