A decoupled structure preserving scheme for the Poisson-Nernst-Planck Navier-Stokes equations and its error analysis

作者：Ziyao Yu, Qing Cheng, Jie Shen, Changyou Wang · 发表于：arXiv (Cornell University) · 年份：2023 · DOI：10.48550/arxiv.2311.17349 · 研究领域：Stochastic processes and financial applications、Navier-Stokes equation solutions、Computational Fluid Dynamics and Aerodynamics

We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that enjoys the properties of positivity preserving, mass conserving, and unconditionally energy stability. Then, we establish the well-posedness and regularity of the initial and (periodic) boundary value problem of the PNP-NS system under suitable assumptions on the initial data, and carry out a rigorous convergence analysis for the fully discretized scheme. We also present some numerical results to validate the positivity-preserving property and the accuracy of our scheme.