A positivity-preserving and free energy dissipative hybrid scheme for the Poisson-Nernst-Planck equations on polygonal and polyhedral meshes. (15th February 2022)

• Record Type: Journal Article
• Authors: Su, Shuai; Tang, Huazhong
• Is Part Of: Computers & mathematics with applications. Volume 108(2022)
• Page Start: 33
• Page End: 48
• Publication Date: 2022-02-15
• Subjects: Poisson-Nernst-Planck equations -- Positivity-preserving -- Free energy dissipation -- Mass conservation -- Finite volume scheme -- Virtual element method; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.12.019
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper develops a positivity-preserving and free energy dissipative hybrid scheme for the multi-dimensional Poisson-Nernst-Planck equations with multiple ions on unstructured polygonal and polyhedral meshes. It is built on the linear virtual element method for the Poisson-type equation for the electrostatic potential and a cell-centered finite volume scheme for the Nernst-Planck equations for the ion concentrations, and preserves the positivity of the ion concentrations, the mass conservation, the free energy dissipation and steady-state properties. The existence of the numerical solutions is also discussed. Numerical results demonstrate the effectiveness of the proposed two- and three-dimensional schemes.