title: An Unfitted Higher-Order Discontinuous Galerkin Method for Incompressible Two-Phase Flow with Moving Contact Lines
creator: Heimann, Felix
subject: 004
subject: 004 Data processing Computer science
subject: 500
subject: 500 Natural sciences and mathematics
subject: 510
subject: 510 Mathematics
subject: 530
subject: 530 Physics
description: The author presents an unfitted discontinuous Galerkin method for incompressible two-phase flow applicable to dynamic regimes with significant surface tension. The method is suitable for simulations in complex geometries and a recursive algorithm is proposed, which allows the generation of piecewise linear sub-triangulations re- solving both the domain boundaries and the interface between the two immiscible phases. Hence, discontinuous finite element spaces can be employed to capture the irregularities in the solution along the interface, i.e. the jump in the pressure field and in the velocity derivatives.  While the sub-triangulation is based on a linear Cartesian cut-cell approach, its resolution is decoupled from the resolution of the finite element mesh thus enabling the application of higher-order finite element spaces. The time development of the two subdomains is realized by level set methods and an unfitted discretization for the solution of the corresponding equations is described. Multiple approaches for the numerical treatment of surface tension in the context of unfitted discretizations are discussed and compared. Furthermore, these methods are extended to allow simulations with contact lines taking into account the occurrence of microscopic deformations of the contact angle. All proposed methods are verified by numerical test simulations in two and three dimensions.
date: 2013
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/15271/1/publication_210713.pdf
identifier: DOI:10.11588/heidok.00015271
identifier: urn:nbn:de:bsz:16-heidok-152715
identifier:   Heimann, Felix  (2013) An Unfitted Higher-Order Discontinuous Galerkin Method for Incompressible Two-Phase Flow with Moving Contact Lines.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/15271/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng