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Nitsche‐XFEM for a transport problem in two‐phase incompressible flows
Author(s) -
Lehrenfeld Christoph
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110296
Subject(s) - discretization , discontinuity (linguistics) , convection–diffusion equation , classification of discontinuities , compressibility , convection , divergence (linguistics) , mechanics , diffusion , phase (matter) , polygon mesh , flow (mathematics) , jump , interface (matter) , incompressible flow , mathematics , mathematical analysis , geometry , physics , thermodynamics , bubble , linguistics , philosophy , quantum mechanics , maximum bubble pressure method
Abstract We consider the transport of a dissolved species in a divergence‐free immiscible incompressible two‐phase flow modeled by a convection diffusion equation. The so‐called Henry interface condition leads to a jump condition for the concentration at the interface between the two phases. This discontinuity of the solution render the numerical solution on unfitted meshes difficult. Furthermore time discretization on moving interfaces and handling typically convection dominant situations makes the overall problem delicate. We propose a numerical method using extended finite elements and a Nitsche‐type technique combined with streamline diffusion stabilization. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)