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We consider in this paper a numerical approximation ofPoisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupledsemi-discrete and fully discrete scheme that enjoys the properties ofpositivity 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 suitableassumptions on the initial data, and carry out a rigorous convergence analysisfor the fully discretized scheme. We also present some numerical results tovalidate the positivity-preserving property and the accuracy of our scheme.

A positivity preserving scheme for Poisson-Nernst-Planck Navier-Stokes equations and its error analysis