Two-phase electrohydrodynamic simulations using a volume-of-fluid approach: A comment

This comment refers to the article of Tomar et al. [1], which presents a numerical methodology of a continuum surface force formulation for simulating two-phase electrohydrodynamic flows. The present work shows, that due to the diffusive character of the Laplacian equation (∇ · (ϵϵ0E) = 0) with discontinuous physical properties (ϵ(x, y, z)), different averaging methods (arithmetic and harmonic) for the fluid property in the transition region have to be applied. The correct choice of the averaging method depends on the orientation of the flux to the interface.An additional improvement is made by calculating the electric displacement D at the cell faces. This leads to a numerical solution independent of the spatial resolution as well as of the interfacial smearing. Simulation results of two different test cases show that the error of the numerical solution is in the order of machine precision.