Journal
APPLIED NUMERICAL MATHEMATICS
Volume 99, Issue -, Pages 151-171Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2015.09.002
Keywords
Two-phase flow; Diffuse-interface models; Stable discretization scheme; Cahn-Hilliard Navier-Stokes model; Adaptive meshing
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Funding
- Deutsche Forschungsgemeinschaft [GA695/6-2, HI689/7-1, SPP1506]
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A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time energy inequality. An adaptive spatial discretization is proposed that conserves the energy inequality in the fully discrete setting by applying a suitable post processing step to the adaptive cycle. For the fully discrete scheme a quasi-reliable error estimator is derived which estimates the error both of the flow velocity, and of the phase field. The validity of the energy inequality in the fully discrete setting is numerically investigated. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.
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