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

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Abstract

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).

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Authors and Affiliations

  1. Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia

    P. N. Vabishchevich & O. P. Iliev

Authors
  1. P. N. Vabishchevich
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  2. O. P. Iliev
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Correspondence to P. N. Vabishchevich.

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Original Russian Text © P.N. Vabishchevich, O.P. Iliev, 2012, published in Matematicheskoe Modelirovanie, 2012, Vol. 24, No. 10, pp. 133–148.

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Vabishchevich, P.N., Iliev, O.P. Numerical solution of nonstationary problems for a system of nernst-planck equations. Math Models Comput Simul 5, 229–243 (2013). https://doi.org/10.1134/S2070048213030125

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