Stability and error analysis of pressure-correction scheme for the Navier–Stokes–Planck–Nernst–Poisson equations

In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier–Stokes–Planck–Nernst–Poisson (NSPNP) equations. By introducing a governing equation for the auxiliary variable through the convective PNP parts, we reconstruct the original equations into an equivalent system and develop a first-order decoupled and linearized scheme. This scheme preserves non-negativity and mass conservation of the concentration components and is unconditionally energy stable. We derive the rigorous error estimates in the two dimensional case for the ionic concentrations, electric potential, velocity and pressure in the L2- and H1-norms. Numerical examples are presented to validate the proposed scheme.