  The accuracy and stability of implicit CFD codes are frequently impaired by
the decoupling between variables, which can ultimately lead to numerical
divergence. Coupled solvers, which solve all the governing equations
simultaneously, have the potential to fix this problem. In this work, we report
the implementation of coupled solvers for transient and steady-state
electrically-driven flow simulations in the finite-volumes framework. The
numerical method, developed in OpenFOAM, is generic for Newtonian and
viscoelastic fluids and is formulated for the Poisson-Nernst-Planck and
Poisson-Boltzmann models. The resulting coupled systems of equations are solved
efficiently with PETSc library. The performance of the coupled solvers is
assessed in two test cases: induced-charge electroosmosis of a Newtonian fluid
around a cylinder; electroosmotic flow of a PTT viscoelastic fluid in a
contraction/expansion microchannel. The coupled solvers are more accurate in
transient simulations and allow the use of larger time-steps without numerical
divergence. For steady-state simulations, the coupled solvers converge in fewer
iterations than segregated solvers. Although coupled solvers are much slower in
a per time-step basis, the overall speedup factor obtained in this study
reached a maximum value of ~100, where the highest factors have been obtained
with semi-coupled solvers, which drop some coupling terms between equations.
While further research is needed to improve the efficiency of the matrix
solving stage, coupled solvers are already superior to segregated solvers in a
number of cases.
