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

TL;DR

This paper introduces a first-order, unconditionally energy-stable pressure-correction scheme for the Navier-Stokes-Planck-Nernst-Poisson equations, with rigorous error analysis and numerical validation.

Contribution

It develops a novel decoupled, linearized scheme that preserves key physical properties and provides comprehensive error estimates for ionic concentrations, electric potential, velocity, and pressure.

Findings

Scheme is unconditionally energy stable.

Error estimates are rigorously derived in 2D.

Numerical examples confirm theoretical results.

Abstract

In this paper, we propose and analyze first-order time-stepping pressure-correction projection scheme for the Navier-Stokes-Planck-Nernst-Poisson equations. By introducing a governing equation for the auxiliary variable through the ionic concentration equations, 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 $L^2$- and $H^1$-norms. Numerical examples are presented to validate the proposed scheme.