NDLI: Analysis of an extended pressure finite element space for two-phase incompressible flows

Content Provider	Springer Nature Link
Author	Reusken, Arld
Copyright Year	2008
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 [6] it is shown that an extended finite element space (XFEM) is much better suited for the discretization of the pressure variable. In this paper we derive important properties of the XFEM space. We present (optimal) approximation error bounds and prove that the diagonally scaled mass matrix has a uniformly bounded spectral condition number. Results of numerical experiments are presented that illustrate properties of the XFEM space.
Ending Page	305
Page Count	13
Starting Page	293
File Format	PDF
ISSN	14329360
e-ISSN	14330369
Journal	Computing and Visualization in Science
Issue Number	4-6
Volume Number	11
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-04-01
Publisher Place	Berlin, Heidelberg
Access Restriction	Subscribed
Subject Keyword	Visualization Computational Mathematics and Numerical Analysis Extended finite element space Spurious velocities Algorithms Two-phase flow Calculus of Variations and Optimal Control; Optimization Numerical Analysis Error bounds Capillarity (surface tension) Surface tension Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Computer Applications in Chemistry
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Engineering Computational Theory and Mathematics Computer Vision and Pattern Recognition Modeling and Simulation Software

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