Numerical simulation of EHD flows using Discontinuous Galerkin Finite Element methods

• Validation of the capability of DG-FEM to deal with electrohydrodynamic flows.
• Comparison with analytical predictions for strong and weak injection.
• Comparison with results computed with other numerical methods.

The aim of this paper is to explore the capability of Discontinuous Galerkin Finite Element methods to solve numerically the charge transport equation in EHD convective flows, in both strong and weak injection regimes. These methods are especially suited to treat purely hyperbolic problems, as it is the charge transport equation in most EHD problems. We consider the 2D electroconvective flow between two parallel plates. We compare our computations with the analytical results in the hydrostatic regime, the linear and non-linear stability analysis, computing both the electric and velocity fields. The stability of the finite amplitude electroconvection is also analysed. Comparisons are made with computations in the literature obtained with other numerical techniques. The results show that DG-FEM are a very good alternative to simulate numerically EHD convective flows.