Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4967934 | Journal of Computational Physics | 2017 | 30 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Hailiang Liu, Zhongming Wang,