Metzger S (2015)
Publication Type: Journal article
Publication year: 2015
Book Volume: 15
Pages Range: 715-718
Issue: 1
We present an energy‐stable, decoupled discrete scheme for a recent model (see [1]) supposed to describe electrokinetic phenomena in two‐phase flow with general mass densities. This model couples momentum and Cahn–Hilliard type phase‐field equations with Nernst–Planck equations for ion density evolution and an elliptic transmission problem for the electrostatic potential.
The transport velocities in our scheme are based on the old velocity field updated via a discrete time integration of the force densities. This allows to split the equations into three blocks which can be treated sequentially: The phase‐field equation, the equations for ion transport and electrostatic potential, and the Navier–Stokes type equations. By establishing a discrete counterpart of the continuous energy estimate, we are able to prove the stability of the scheme.
APA:
Metzger, S. (2015). On numerical schemes for phase-field models for electrowetting with electrolyte solutions. Proceedings in Applied Mathematics and Mechanics, 15, 715-718. https://dx.doi.org/10.1002/pamm.201510346
MLA:
Metzger, Stefan. "On numerical schemes for phase-field models for electrowetting with electrolyte solutions." Proceedings in Applied Mathematics and Mechanics 15 (2015): 715-718.
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