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Numerical solution of nonstationary problems for a system of nernst-planck equations

: Vabishchevich, P.N.; Iliev, O.P.


Mathematical models and computer simulations 5 (2013), No.3, pp.229-243
ISSN: 2070-0490 (online)
ISSN: 2070-0482 (print)
Journal Article
Fraunhofer ITWM ()

The mathematical model of electricity and mass transfer is based on the equations for charged particles (ions and cations) in the electrolyte, i.e., the Nernst-Planck equations. These equations are supplemented by the equation for the electric field and the motion equations for the electrolyte as a continuum. The paper mostly focuses on the construction of the time approximation for the approximate solution of nonstationary problems. The system of Nernst-Planck equations is characterized by a quadratic nonlinearity. Special linearization schemes are proposed for taking this into account. Computational algorithms are studied on a model problem for the binary electrolyte (two kinds of charged particles).