Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations

TL;DR

This paper introduces a novel discontinuous Galerkin IMEX pressure correction scheme for the coupled Poisson-Nernst-Planck-Navier-Stokes equations, providing optimal error estimates and confirming accuracy through numerical simulations.

Contribution

It develops a fully discrete scheme with proven error bounds and mass conservation for ion concentrations, electrostatic potential, and fluid dynamics.

Findings

Optimal error estimates in $L^2$ and energy norms are derived.

Mass conservation properties for ions are established.

Numerical simulations confirm theoretical error bounds.

Abstract

Based on a discontinuous Galerkin method in the spatial directions and an improved implicit-explicit pressure-correction scheme in the temporal direction, this paper discusses a fully discrete scheme for the Poisson-Nernst-Planck-Navier-Stokes equations. Optimal error estimates are derived in $L^2$ and in the energy norms for the concentrations of positive and negative ions, the electrostatic potential, the fluid velocity, and the $L^2$ norm of the fluid pressure. The discrete mass conservation properties of both ions are established. Finally, numerical simulations are performed, whose results confirm our theoretical findings.