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A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics, ,
Gonca Aki1 ; Johannes Daube2 ; Wolfgang Dreyer1 ; Jan Giesselmann3 ; Mirko Kränkel2 ; Christiane Kraus1
1Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
2Department of Mathematics, University of Freiburg, Germany
3ACMAC, University of Crete, Greece
ESAIM. Proceedings, Tome 38 (2012), pp. 54-77
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In this contribution, we investigate a diffuse interface model for quasi–incompressible flows. We determine corresponding sharp interface limits of two different scalings. The sharp interface limit is deduced by matched asymptotic expansions of the fields in powers of the interface. In particular, we study solutions of the derived system of inner equations and discuss the results within the general setting of jump conditions for sharp interface models. Furthermore, we treat, as a subproblem, the convective Cahn–Hilliard equation numerically by a Local Discontinuous Galerkin scheme.
DOI : 10.1051/proc/201238004

Gonca Aki  1   ; Johannes Daube  2   ; Wolfgang Dreyer  1   ; Jan Giesselmann  3   ; Mirko Kränkel  2   ; Christiane Kraus  1

1 Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
2 Department of Mathematics, University of Freiburg, Germany
3 ACMAC, University of Crete, Greece 
@article{EP_2012_38_a3,
     author = {Gonca Aki and Johannes Daube and Wolfgang Dreyer and Jan Giesselmann and Mirko Kr\"ankel and Christiane Kraus},
     title = {A diffuse interface model for quasi{\textendash}incompressible flows : {Sharp} interface limits and numerics, ,},
     journal = {ESAIM. Proceedings},
     pages = {54--77},
     year = {2012},
     volume = {38},
     doi = {10.1051/proc/201238004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201238004/}
}
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%A Johannes Daube
%A Wolfgang Dreyer
%A Jan Giesselmann
%A Mirko Kränkel
%A Christiane Kraus
%T A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics, ,
%J ESAIM. Proceedings
%D 2012
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Gonca Aki; Johannes Daube; Wolfgang Dreyer; Jan Giesselmann; Mirko Kränkel; Christiane Kraus. A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics, ,. ESAIM. Proceedings, Tome 38 (2012), pp. 54-77. doi: 10.1051/proc/201238004

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