Paper Info
Title
An extended pressure finite element space for two-phase incompressible flows with surface tension
Abstract
We consider a standard model for incompressible two-phase flows in which a localized force at the interface describes the effect of surface tension. If a level set (or VOF) method is applied then the interface, which is implicitly given by the zero level of the level set function, is in general not aligned with the triangulation that is used in the discretization of the flow problem. This non-alignment causes severe difficulties w.r.t. the discretization of the localized surface tension force and the discretization of the flow variables. In cases with large surface tension forces the pressure has a large jump across the interface. In standard finite element spaces, due to the non-alignment, the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure. In many simulations these effects cause large oscillations of the velocity close to the interface, so-called spurious velocities. In this paper, for a simplified model problem, we give an analysis that explains why known (standard) methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities. In the paper [S. Grosz, A. Reusken, Finite element discretization error analysis of a surface tension force in two-phase incompressible flows, Preprint 262, IGPM, RWTH Aachen, SIAM J. Numer. Anal. (accepted for publication)], we introduce a new and accurate method for approximation of the surface tension force. In the present paper, we use the extended finite element space (XFEM), presented in [N. Moes, J. Dolbow, T. Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Meth. Eng. 46 (1999) 131-150; T. Belytschko, N. Moes, S. Usui, C. Parimi, Arbitrary discontinuities in finite elements, Int. J. Numer. Meth. Eng. 50 (2001) 993-1013], for the discretization of the pressure. We show that the size of spurious velocities is reduced substantially, provided we use both the new treatment of the surface tension force and the extended pressure finite element space.
Year
DOI
Venue
2007
10.1016/j.jcp.2006.12.021
J. Comput. Physics
Keywords
Field
DocType
spurious velocities,pressure finite element space,finite element method,76t99,surface tension force,finite element space,finite element,two-phase flow,j. numer,n. moes,extended pressure,65n30,two-phase incompressible flow,65n15,surface tension,t. belytschko,large surface tension,finite element discretization error,65m60,76d45,extended finite element space,level set,incompressible flow,two phase flow,standard model,oscillations
Discretization,Surface tension,Classification of discontinuities,Mathematical analysis,Discontinuity (linguistics),Extended finite element method,Finite element method,Incompressible flow,Mathematics,Mixed finite element method
Journal
Volume
Issue
ISSN
224
1
Journal of Computational Physics
Citations 
PageRank 
References 
29
2.79
6
Authors
2
Name
Order
Citations
PageRank
Sven Groí1292.79
Arnold Reusken230544.91