| Issue |
ESAIM: Proc.
Volume 38, December 2012
CEMRACS’11: Multiscale Coupling of Complex Models in Scientific Computing
|
|
|---|---|---|
| Page(s) | 54 - 77 | |
| DOI | https://doi.org/10.1051/proc/201238004 | |
| Published online | 03 January 2013 | |
A diffuse interface model for quasi–incompressible flows : Sharp interface limits and numerics*,, **,, ***
1 Weierstrass Institute for Applied
Analysis and Stochastics, Berlin, Germany ;
e-mail: gonca.aki@wias-berlin.de & dreyer@wias-berlin.de &
kraus@wias-berlin.de
2 Department of Mathematics, University
of Freiburg, Germany ;
e-mail: hannes@mathematik.uni-freiburg.de &
kraenkel@mathematik.uni-freiburg.de
3 ACMAC, University of
Crete, Greece ;
e-mail: jan.giesselmann@acmac.uoc.gr
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.
GA, WD and CK would like to thank the German Research Foundation (DFG) for financial support of the project ”Modeling and sharp interface limits of local and non-local generalized Navier–Stokes–Korteweg Systems”.
© EDP Sciences, SMAI 2012
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