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978-3-8439-1232-7, Reihe Strömungsmechanik

Henning Sauerland
An XFEM Based Sharp Interface Approach for Two-Phase and Free-Surface Flows

159 Seiten, Dissertation Rheinisch-Westfälische Technische Hochschule Aachen (2013), Softcover, A5

Zusammenfassung / Abstract

The aim of this thesis is the development of a flexible and accurate numerical approach for the simulation of industrially relevant three-dimensional two-phase and free-surface flow problems. The Navier-Stokes equations are discretized using a stabilized finite element method on hexahedral meshes. A flexible description of the interface is achieved by means of the level set method. Due to the implicit interface description, topological changes of the phases are readily manageable. In a two-phase flow setup, generally, discontinuities in the flow field can be observed across the phase interface. The extended finite element method (XFEM) is applied in this work in order to accurately account for the jumps in the pressure field by including a sign-enrichment to the approximation space. Thereby, discontinuities in the pressure field can be considered for without requiring that the mesh aligns with the interface. Additionally, an adaptive mesh refinement approach is applied in the vicinity of the interface. This improves the accuracy of the level set representation and allows to account for high gradients near the interface, e.g., in the velocity field. The robustness and accuracy of the proposed approach is systematically investigated for different enrichment schemes and time-integration schemes. Test cases with and without surface tension, on moving or stationary meshes, are studied and compared to interface tracking results when possible.

The usage of large computing clusters is inevitable for the simulation of industrial two-phase or free-surface flows. Therefore, the developed framework considers parallelization strategies and employs iterative solution approaches to deal with the resulting large system of equations. Nevertheless, the XFEM is often prone to ill-conditioning of the global system matrix, which reduces the performance of iterative solution techniques significantly. Approximation properties and iterative solver performance are systematically compared for different approaches which should improve the conditioning—stable XFEM, preconditioning and blocking of degrees of freedom.