A free energy satisfying finite difference method for Poisson--Nernst--Planck equations
arXiv:1308.6632 · doi:10.1016/j.jcp.2014.02.036
Abstract
In this work we design and analyze a free energy satisfying finite difference method for solving Poisson-Nernst-Planck equations in a bounded domain. The algorithm is of second order in space, with numerical solutions satisfying all three desired properties: i) mass conservation, ii) positivity preserving, and iii) free energy satisfying in the sense that these schemes satisfy a discrete free energy dissipation inequality. These ensure that the computed solution is a probability density, and the schemes are energy stable and preserve the equilibrium solutions. Both one and two-dimensional numerical results are provided to demonstrate the good qualities of the algorithm, as well as effects of relative size of the data given.
References in corpus (1)
Cited by in corpus (21)
- A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson--Nernst--Planck systems
- Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
- A Positive and Energy Stable Numerical Scheme for the Poisson-Nernst-Planck-Cahn-Hilliard Equations with Steric Interactions
- An energy preserving finite difference scheme for the Poisson-Nernst-Planck system
- Positivity-preserving third order DG schemes for Poisson--Nernst--Planck equations
- Structure-Preserving and Efficient Numerical Methods for Ion Transport
- A dynamic mass transport method for Poisson-Nernst-Planck equations
- Positive and free energy satisfying schemes for diffusion with interaction potentials
- Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model
- A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
- Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system
- Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems
- Asymptotic behavior of Nernst-Planck equation
- Linear-Scaling Selected Inversion based on Hierarchical Interpolative Factorization for Self Green's Function for Modified Poisson-Boltzmann Equation in Two Dimensions
- Field model for complex ionic fluids: analytical properties and numerical investigation
- Structure-Preserving Numerical Methods for Nonlinear Fokker--Planck Equations with Nonlocal Interactions by an Energetic Variational Approach
- The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach
- Modeling coupled electrochemical and mechanical behavior of soft ionic materials and ionotronic devices
- Local Averaging Type a Posteriori Error Estimates for the Nonlinear Steady-state Poisson-Nernst-Planck Equations
- Modeling Concentration Profiles in Electrolytes by Solving 3-D Poisson-Nernst-Planck Equations via Finite Difference Method
- A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels