Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension.

Braack, Malte and Prohl, A. (2013) Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension. ESAIM: Mathematical Modelling and Numerical Analysis-Modelisation Mathematique Et Analyse Numerique, 47 (2). pp. 404-423. DOI 10.1051/m2an/2012032.

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Abstract

The isothermal Navier–Stokes–Korteweg system is used to model dynamics of a compressible fluid exhibiting phase transitions between a liquid and a vapor phase in the presence of capillarity effects close to phase boundaries. Standard numerical discretizations are known to violate discrete versions of inherent energy inequalities, thus leading to spurious dynamics of computed solutions close to static equilibria (e.g., parasitic currents). In this work, we propose a time-implicit discretization of the problem, and use piecewise linear (or bilinear), globally continuous finite element spaces for both, velocity and density fields, and two regularizing terms where corresponding parameters 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 a discrete energy law to control dynamics are shown. Computational experiments are provided to study interesting regimes of coefficients for viscosity and capillarity.

Document Type: Article
Additional Information: Times Cited: 0 Braack, Malte Prohl, Andreas
Keywords: Diffuse interface model / surface tension / structure preserving discretization / space-time discretization
Research affiliation: OceanRep > The Future Ocean - Cluster of Excellence > FO-R11
Kiel University
Refereed: Yes
Open Access Journal?: No
DOI etc.: 10.1051/m2an/2012032
ISSN: 0764-583X
Projects: Future Ocean
Date Deposited: 08 Jul 2014 08:54
Last Modified: 16 Jul 2019 09:07
URI: http://oceanrep.geomar.de/id/eprint/24845

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