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

IF 1.9 4区 数学 Q1 MATHEMATICS
Jie Ding null, Xiang Ji
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引用次数: 0

Abstract

. 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.
尺寸修正Poisson-Nernst-Planck-Cahn-Hilliard方程的保结构JKO格式
.在本文中,我们提出了一种保结构的数值格式,用于从自由能(包括静电能、熵、空间能和Cahn-Hilliard混合物)导出的尺寸修正的Poisson-Nernst-Planck-Cahn-Hilliand(SPNPCH)方程。基于Jordan Kinderlehrer-Otto(JKO)框架和二次Wasserstein距离的Benamou-Brenier公式,将SPNPCH方程转化为一个约束优化问题。通过利用目标函数的凸性,我们可以证明优化问题数值解的存在性和唯一性。该方案自动地保持了质量守恒和无条件的能量耗散。此外,通过利用熵项的奇异性来防止浓度接近零,我们可以确保浓度的正性。为了解决优化问题,我们应用了拟牛顿方法,该方法可以确保迭代过程中浓度的正性。进行数值测试以确定所开发方案的预期精度和所需物理特性。最后,所提出的方案也可用于研究离子尺寸和梯度能量系数对离子分布的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.80
自引率
7.70%
发文量
33
审稿时长
>12 weeks
期刊介绍: Numerical Mathematics: Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction, analysis and application of numerical methods for solving scientific and engineering problems. Important research and expository papers devoted to the numerical solution of mathematical equations arising in all areas of science and technology are expected. The journal originates from the journal Numerical Mathematics: A Journal of Chinese Universities (English Edition). NM-TMA is a refereed international journal sponsored by Nanjing University and the Ministry of Education of China. As an international journal, NM-TMA is published in a timely fashion in printed and electronic forms.
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