Discontinuous Galerkin IMEX Pressure Correction Scheme for the Poisson-Nernst-Planck-Navier-Stokes Equations
Provides a rigorous numerical analysis for a complex multiphysics system, but the method is an incremental extension of existing techniques to a specific set of equations.
The paper develops a fully discrete discontinuous Galerkin IMEX pressure correction scheme for the Poisson-Nernst-Planck-Navier-Stokes equations, proving optimal error estimates and mass conservation, with numerical validation.
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.