Unconditionally energy stable schemes for an electrohydrodynamic model of charge transport in dielectric liquids

In this paper, we develop numerical schemes for an electrohydrodynamic model of charge transport in dielectric liquids. The model consists of the incompressible Navier-Stokes equations for the liquids and two extra equations for the charge transport and the electric potential. Three types of linear time-stepping schemes, namely a fully-implicit linear extrapolated Crank-Nicolson scheme and two projection-type schemes, are constructed which differ in their accuracy and efficiency. All the proposed schemes with spatial discretization by finite difference on staggered grids are proved to be unconditionally energy stable, and the associated linear systems are uniquely solvable. Numerical experiments are presented to demonstrate the convergence rates and the energy stability of the schemes. In addition, the effects of the Coulomb force on the steady state flow structures for the electro-convection phenomena are exhibited to validate the accuracy and robustness of the schemes. (C) 2019 Elsevier B.Y. All rights reserved.