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Numerical Algorithms

, Volume 80, Issue 4, pp 1361–1390 | Cite as

On stable, dissipation reducing splitting schemes for two-phase flow of electrolyte solutions

  • Stefan MetzgerEmail author
Original Paper
  • 62 Downloads

Abstract

In this paper, we are concerned with the numerical treatment of a recent diffuse interface model for two-phase flow of electrolyte solutions (Campillo-Funollet et al., SIAM J. Appl. Math. 72(6), 1899–1925, 2012) . This model consists of a Nernst–Planck-system describing the evolution of the ion densities and the electrostatic potential which is coupled to a Cahn–Hilliard–Navier–Stokes-system describing the evolution of phase-field, velocity field, and pressure. In the first part, we present a stable, fully discrete splitting scheme, which allows to split the governing equations into different blocks, which may be treated sequentially and thereby reduces the computational costs significantly. This scheme comprises different mechanisms to reduce the induced numerical dissipation. In the second part, we investigate the impact of these mechanisms on the scheme’s sensitivity to the size of the time increment using the example of a falling droplet. Finally, we shall present simulations showing ion induced changes in the topology of charged droplets serving as a qualitative validation for our discretization and the underlying model.

Keywords

Electrolyte solutions Phase-field model Navier–Stokes equations Cahn–Hilliard equation Nernst–Planck equations Finite element scheme Splitting scheme 

Mathematics Subject Classification (2010)

35Q35 65M60 65M12 76D05 76T99 76W05 

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Notes

Funding information

This research has been supported by Deutsche Forschungsgemeinschaft (German Science Foundation) through the Priority Programme 1506 “Transport processes at fluidic interfaces”.

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Authors and Affiliations

  1. 1.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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