Positive-preserving, mass conservative linear schemes for the Possion-Nernst-Planck equations

2025/06/16 by Li, Jiayin, Li, Jingwei
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.13054

Abstract

The first-order linear positivity preserving schemes in time are available for the time dependent Poisson-Nernst-Planck (PNP) equations, second-order linear ones are still challenging. In this paper, we propose the first- and second-order exponential time differencing schemes with the finite difference spatial discretization for PNP equations, based on the Slotboom transformation of the Nernst-Planck equation. The proposed schemes are linear and preserve the mass conservation and positivity preservation of ion concentration at full discrete level without any constraints on the time step size. The corresponding energy stability analysis is also presented, demonstrating that the second-order scheme can dissipate the modified energy. Extensive numerical results are carried out to support the theoretical findings and showcase the performance of the proposed schemes.

Citations

• Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation
• Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson-Nernst-Planck Equations
• Stabilized exponential time differencing schemes for the convective Allen-Cahn equation
• Convergence Analysis of Structure-Preserving Numerical Methods Based on Slotboom Transformation for the Poisson--Nernst--Planck Equations
• A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving
• A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving
• Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
• Arbitrarily High-order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen-Cahn Equations
• A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
• Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
• Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems
• Arbitrarily high-order exponential cut-off methods for preserving maximum principle of parabolic equations
• Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
• A Wasserstein gradient flow approach to Poisson-Nernst-Planck equations

Related

• A Conservative Finite Difference Scheme for Poisson-Nernst-Planck Equations
• Second-order, Positive, and Unconditional Energy Dissipative Scheme for Modified Poisson-Nernst-Planck Equations
• Positivity preserving and mass conservative projection method for the Poisson-Nernst-Planck equation
• A class of positive-preserving,energy stable and high order numerical schemes for the Poission-Nernst-Planck system
• Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems