A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:328

Article

Liu, Hailiang¹  Wang, Zhongming² 

[1] Iowa State Univ, Dept Math, Ames, IA 50011 USA

[2] Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA

关键词: Poisson-Nernst-Planck equation;    Free energy;    Discontinuous Galerkin methods;   

DOI  :  10.1016/j.jcp.2016.10.008

来源: Elsevier

【 摘 要 】

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free