报告题目 (Title)：Structure-preserving Discretization for the Poisson-Nernst-Planck Equations（PNP方程的保结构离散化）
报告人 (Speaker)：丁洁（江南大学）
报告时间 (Time)：2024年11月22日 (周五) 14:30-15:30
报告地点 (Place)：校本部 GJ406教室
邀请人(Inviter)：涂一辉
报告摘要：Ion transport, often modeled by the Poisson–Nernst–Planck (PNP) equations, is crucial to many applications of importance. First-order energy dissipative numerical methods in time are available in literature for the PNP equations, but second-order ones are still in lack. This work proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that describe ion transport incorporating effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance.