A Structure-Preserving JKO Scheme for the SizeModified Poisson-Nernst-Planck-Cahn-Hilliard Equations  

作　　者：Jie Ding Xiang Ji 

机构地区：[1]School of Science,Jiangnan University,Wuxi,Jiangsu,214122,China [2]Department of Mathematics and Mathematical Center for Interdiscipline Research,Soochow University,1 Shizi Street,Suzhou 215006,Jiangsu,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2023年第1期204-229,共26页高等学校计算数学学报（英文版）

基　　金：J.Ding was supported by the Natural Science Foundation of Jiangsu Province(Grant BK20210443);by the National Natural Science Foundation of China(Grant 12101264);by the Shuangchuang program of Jiangsu Province(Grant 1142024031211190)。

摘　　要：In this paper,we propose a structure-preserving numerical scheme for the size-modified Poisson-Nernst-Planck-Cahn-Hilliard(SPNPCH)equations derived from the free energy including electrostatic energies,entropies,steric energies,and Cahn-Hilliard mixtures.Based on the Jordan-Kinderlehrer-Otto(JKO)framework and the Benamou-Brenier formula of quadratic Wasserstein distance,the SPNPCH equations are transformed into a constrained optimization problem.By exploiting the convexity of the objective function,we can prove the existence and uniqueness of the numerical solution to the optimization problem.Mass conservation and unconditional energy-dissipation are preserved automatically by this scheme.Furthermore,by making use of the singularity of the entropy term which keeps the concentration from approaching zero,we can ensure the positivity of concentration.To solve the optimization problem,we apply the quasi-Newton method,which can ensure the positivity of concentration in the iterative process.Numerical tests are performed to confirm the anticipated accuracy and the desired physical properties of the developed scheme.Finally,the proposed scheme can also be applied to study the influence of ionic sizes and gradient energy coefficients on ion distribution.

关 键 词：Structure-preserving size-modified Poisson-Nernst-Planck-Cahn-Hilliard equations JKO framework POSITIVITY 

分 类 号：O175[理学—数学]