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Stable discretization of a diffuse interface model forliquid-vapor flows with surface tension

Published online by Cambridge University Press:  11 January 2013

Malte Braack  and
Andreas Prohl
Malte Braack
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Westring 393, 24098 Kiel, Germany.. braack@math.uni-kiel.de
Andreas Prohl
Affiliation:
Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany.; prohl@na.uni-tuebingen.de
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Abstract

The isothermal Navier–Stokes–Korteweg system is used to model dynamics of a compressiblefluid exhibiting phase transitions between a liquid and a vapor phase in the presence ofcapillarity effects close to phase boundaries. Standard numerical discretizations areknown to violate discrete versions of inherent energy inequalities, thus leading tospurious dynamics of computed solutions close to static equilibria (e.g.,parasitic currents). In this work, we propose a time-implicit discretization of theproblem, and use piecewise linear (or bilinear), globally continuous finite element spacesfor both, velocity and density fields, and two regularizing terms where correspondingparameters tend to zero as the mesh-size h > 0 tends to zero.Solvability, non-negativity of computed densities, as well as conservation of mass, and adiscrete energy law to control dynamics are shown. Computational experiments are providedto study interesting regimes of coefficients for viscosity and capillarity.

Keywords

Diffuse interface modelsurface tensionstructure preserving discretizationspace-time discretization
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 2 , March 2013 , pp. 401 - 420
Copyright
© EDP Sciences, SMAI, 2013

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References

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