摘要
研究了Nernst-Planck-Poisson(NPP)方程的数值计算方法.推导了弱解的稳定性,提出了一系列时间离散格式,分析了半离散问题的若干性质,如离散浓度解的非负性(非负浓度是NPP系统的重要性质),格式的条件/无条件稳定性.结合谱方法进行空间离散,得到全离散数值格式,通过数值实验验证了算法的时间一阶、二阶收敛性,空间谱收敛性,以及离子浓度数值解的非负性.
Numerical methods for Nernst-Planck-Poisson equation are investigated. Stability of weak solution is derived. Several time-discretizations are proposed, and certain of their different properties are demonstrated, such as non-negativity of discrete concentrations, stability condition, and unconditional stability. With application to spectral discretization in space, full discrete numerical schemes are given. Numerical tests carried out show first/second order convergence in time, spectral convergence in space, nonnegativity of numerical solution of concentration.
出处
《北京师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2017年第6期643-649,共7页
Journal of Beijing Normal University(Natural Science)
基金
国家自然科学基金资助项目(11471274
71671017)
北京师范大学学科建设经费教师自主项目
