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978-3-8439-1944-9, Reihe Strömungsmechanik

Claudia Günther
A Cartesian Cut-Cell Method for Flows in Complex Geometries with Forced Boundary Motion

220 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2014), Softcover, A5

Zusammenfassung / Abstract

In this thesis, a versatile, robust, and accurate approach for the numerical simulation of compressible viscous flow problems in arbitrarily complex geometries with forced boundary motion is developed. The geometry may consist of multiple independently moving parts that are allowed to interact, i.e., to approach closely, overlap, or induce topological changes. The overall method is designed for superior robustness and stability and enables a simple and quick problem setup. A Cartesian grid embedded boundary flow solver forms the basis of this approach. For a robust and flexible representation and reconstruction of the moving embedded boundaries, a level-set based approach is employed.

The use of component based geometry is a key idea of the concept. Multiple level-set functions that are solved separately represent different moving interfaces. A fast assembly procedure provides a combined level-set function, which contains all relevant information for the reconstruction of the interfaces of the flow grid. This allows a consistent and accurate treatment of overlapping interfaces and topological changes.

The Cartesian cut-cell flow solver handles complex intersection patterns without limitations. A detailed description of the cut cell generation process for arbitrary cut cells is provided. The information that corresponds to the different components of the geometry stored in the individual level-set functions can be incorporated to generate a higher order boundary representation in the vicinity of multiple interfaces. Two different finite volume discretizations for fixed and moving interfaces are extended to allow the computation of all types of cut cells that can be generated by the novel approach.

To enable the use of adaptive meshes, two separate hierarchically refined grids are used for the flow solution and the interface capturing. The adaptation of the flow grid to the current position of the embedded interfaces is done by means of the combined level-set function.

Detailed studies show the robustness and accuracy of the method up to arbitrarily small cut cells. The accuracy of the intersection information that is reconstructed from the level set representation and the computational efficiency of the level-set based interface reconstruction are studied. The ability of the current method to handle technically relevant setups is demonstrated for the flow in two- and three-dimensional piston engine geometries.