Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems

Frank F, Ray N, Knabner P (2011)


Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2011

Journal

Publisher: Springer Verlag

Book Volume: 14

Pages Range: 385-400

Journal Issue: 8

URI: https://www1.am.uni-erlangen.de/research/publications/Jahr_2011/2011_FrankRayKn_NumericalInvestiOfHomogeStokNernPlanPoissSystmes

DOI: 10.1007/s00791-013-0189-0

Abstract

We consider charged transport within a porous medium, which at the pore scale can be described by the non-stationary Stokes-Nernst-Planck-Poisson (SNPP) system. We state three different homogenization results using the method of two-scale convergence. In addition to the averaged macroscopic equations, auxiliary cell problems are solved in order to provide closed-form expressions for effective coefficients. Our aim is to study numerically the convergence of the models for vanishing microstructure, i. e.; the behavior for ε → 0, where is the characteristic ratio between pore diameter and size of the porous medium. To this end, we propose a numerical scheme capable of solving the fully coupled microscopic SNPP system and also the corresponding averaged systems. The discretization is performed fully implicitly in time using mixed finite elements in two space dimensions. The averaged models are evaluated using simulation results and their approximation errors in terms of ε are estimated numerically. © 2013 Springer-Verlag Berlin Heidelberg.

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How to cite

APA:

Frank, F., Ray, N., & Knabner, P. (2011). Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems. Computing and Visualization in Science, 14(8), 385-400. https://dx.doi.org/10.1007/s00791-013-0189-0

MLA:

Frank, Florian, Nadja Ray, and Peter Knabner. "Numerical investigation of homogenized Stokes-Nernst-Planck-Poisson systems." Computing and Visualization in Science 14.8 (2011): 385-400.

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