Smuda, Martin (2021):
Direct Numerical Simulation of Multi-Phase Flows using Extended Discontinuous Galerkin Methods. (Publisher's Version)
Darmstadt, Technische Universität,
DOI: 10.26083/tuprints-00017376,
[Ph.D. Thesis]
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Dissertationsschrift_Smuda_mitLizenz.pdf Copyright Information: CC BY 4.0 International - Creative Commons, Attribution. Download (7MB) | Preview |
Item Type: | Ph.D. Thesis | ||||
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Status: | Publisher's Version | ||||
Title: | Direct Numerical Simulation of Multi-Phase Flows using Extended Discontinuous Galerkin Methods | ||||
Language: | English | ||||
Abstract: | The scientific study of multi-phase flows is a challenging task for analytical and experimental works. Thus, sophisticated and specialized numerical methods are in need for the direct numerical simulation of such problems. In this work a high-order multi-phase flow solver on the basis of the extended Discontinuous Galerkin (extended DG/XDG) method is developed. This allows the direct numerical simulation of the transient incompressible two-phase Navier-Stokes equations in their sharp interface formulation. The approximation space of the local ansatz-functions is adapted to be conform to the position of the interface. The interface, described as a level-set function, is discretized by a standard DG method that enables a sub-cell accurate representation of sharp jumps in the pressure field and kinks in the velocity field. For the numerical treatment of the surface tension force the Laplace-Beltrami formulation without regularization is implemented. Stability issues regarding the energy conservation of the solver are addressed. The developed solver is validated against a wide range of typical two-phase surface tension driven flow phenomena including capillary waves, an oscillating droplet and a rising bubble. Allowing the simulation of dynamic contact line problems, the generalized Navier boundary condition is adapted for the XDG discretization. The results regarding the rise of liquid in a capillary build the basis of a new benchmark setup for capillarity driven flow problems. Another extension of the solver is the implementation of the coupled two-phase heat equation in context of the XDG method. Furthermore, the discretization for both the Navier-Stokes equations and the heat equation is extended to allow a mass and energy flow across the interface. This way the velocity field exhibits a sharp jump and the temperature field shows a kink at the interface. A first basic validation is provided against analytical solutions. This work presents a multi-purpose flow solver for the direct simulation of multi-phase flows involving dynamic contact lines and phase changes due to evaporation. It is based on the XDG method to allow a sub-cell accurate approximation in context of the sharp interface formulation. |
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Place of Publication: | Darmstadt | ||||
Collation: | xxv, 125 Seiten | ||||
Classification DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
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Divisions: | 16 Department of Mechanical Engineering > Fluid Dynamics (fdy) > Mehrphasenströmung 16 Department of Mechanical Engineering > Fluid Dynamics (fdy) > Numerische Strömungssimulation DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 1194: Interaction between Transport and Wetting Processes > Research Area B: Modeling and Simulation > B06: Higher Order Schemes for Direct Numerical Simulation for Wetting and De-Wetting Problems based on Discontinuous Galerkin Methods Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE) |
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Date Deposited: | 12 Mar 2021 09:29 | ||||
Last Modified: | 12 Mar 2021 09:29 | ||||
DOI: | 10.26083/tuprints-00017376 | ||||
URN: | urn:nbn:de:tuda-tuprints-173763 | ||||
Referees: | Oberlack, Prof. Dr. Martin ; Bothe, Prof. Dr. Dieter | ||||
Date of oral examination: | 20 October 2020 | ||||
URI: | https://tuprints.ulb.tu-darmstadt.de/id/eprint/17376 | ||||
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