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Numerical methods for the Navier–Stokes equations applied to turbulent flow and to multi-phase flow
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis discusses the numerical approximation of flow problems, in particular the large eddy simulation of turbulent flow and the simulation of laminar immiscible two-phase flow. The computations for both applications are performed with a coupled solution approach of the Navier-Stokes equations discretized with the finite element method.

Firstly, a new implementation strategy for large eddy simulation of turbulent flow is discussed. The approach is based on the variational multiscale method, where scale ranges are separated by variational projection. The method uses a standard Navier-Stokes model for representing the coarser of the resolved scales, and adds a subgrid viscosity model to the smaller of the resolved scales. The scale separation within the space of resolved scales is implemented in a purely algebraic way based on a plain aggregation algebraic multigrid restriction operator. A Fourier analysis underlines the importance of projective scale separations and that the proposed model does not affect consistency of the numerical scheme. Numerical examples show that the method provides better results than other state-of-the-art methods for computations at low resolutions.

Secondly, a method for modeling laminar two-phase flow problems in the vicinity of contact lines is proposed. This formulation combines the advantages of a level set model and of a phase field model: Motion of contact lines and imposition of contact angles are handled like for a phase field method, but the computational costs are similar to the ones of a level set implementation. The model is realized by formulating the Cahn-Hilliard equation as an extension of a level set model. The phase-field specific terms are only active in the vicinity of contact lines. Moreover, various aspects of a conservative level set method discretized with finite elements regarding the accuracy of force balance and prediction in jump of pressure between the inside and outside of a circular bubble are tested systematically. It is observed that the errors in velocity are mostly due to inaccuracies in curvature evaluation, whereas the errors in pressure prediction mainly come from the finite width of the interface. The error in both velocity and pressure decreases with increasing number of mesh points.

Place, publisher, year, edition, pages
Uppsala University, 2009.
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2009-005
National Category
Computational Mathematics
Research subject
Scientific Computing with specialization in Numerical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-110246OAI: oai:DiVA.org:uu-110246DiVA, id: diva2:275573
Supervisors
Available from: 2009-12-16 Created: 2009-11-05 Last updated: 2017-08-31Bibliographically approved
List of papers
1. An algebraic variational multiscale–multigrid method for large eddy simulation of turbulent flow
Open this publication in new window or tab >>An algebraic variational multiscale–multigrid method for large eddy simulation of turbulent flow
2010 (English)In: Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, E-ISSN 1879-2138, Vol. 199, p. 853-864Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-106684 (URN)10.1016/j.cma.2009.05.017 (DOI)000274827400009 ()
Available from: 2009-06-26 Created: 2009-06-26 Last updated: 2018-01-13Bibliographically approved
2. An algebraic variational multiscale–multigrid method for large-eddy simulation: Generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder
Open this publication in new window or tab >>An algebraic variational multiscale–multigrid method for large-eddy simulation: Generalized-α time integration, Fourier analysis and application to turbulent flow past a square-section cylinder
2011 (English)In: Computational Mechanics, ISSN 0178-7675, E-ISSN 1432-0924, Vol. 47, p. 217-233Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-110245 (URN)10.1007/s00466-010-0541-x (DOI)000286614600007 ()
Available from: 2009-11-05 Created: 2009-11-05 Last updated: 2018-01-12Bibliographically approved
3. A hybrid level-set Cahn–Hilliard model for two-phase flow
Open this publication in new window or tab >>A hybrid level-set Cahn–Hilliard model for two-phase flow
2008 (English)In: Proc. 1st European Conference on Microfluidics, La Société Hydrotechnique de France , 2008, p. 59:1-10Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
La Société Hydrotechnique de France, 2008
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-104899 (URN)
Available from: 2009-05-20 Created: 2009-05-30 Last updated: 2018-01-13Bibliographically approved
4. Spurious currents in a finite-element based level set method for two phase flow
Open this publication in new window or tab >>Spurious currents in a finite-element based level set method for two phase flow
2009 (English)Report (Other academic)
Series
Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2009-026
National Category
Computational Mathematics Computer Sciences
Identifiers
urn:nbn:se:uu:diva-110112 (URN)
Available from: 2009-11-04 Created: 2009-11-04 Last updated: 2018-01-12Bibliographically approved

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Kronbichler, Martin

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