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.

翻译：本文研究泊松-能斯特-普朗克-纳维-斯托克斯（PNP-NS）系统的数值逼近方法。我们构造了一种解耦的半离散与全离散格式，该格式具备正性保持、质量守恒以及无条件能量稳定性等特性。随后，在初始数据的适当假设下，建立了PNP-NS系统初边值（周期边界）问题的适定性与正则性，并对全离散格式进行了严格的收敛性分析。我们同时给出了若干数值结果，以验证所提出格式的正性保持性质及其精度。