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Rayleigh-Bénard convection in a dielectric fluid under an external electric field with a melting boundary

Rayleigh-B\'enard convection during a solid-liquid phase change in the presence of an electric field is studied via a lattice Boltzmann method. We investigate both the onset of flow motion and pattern formation in the presence of an electric field and a melting boundary. The critical Rayleigh number decreases monotonically with the timescale separation. We predict the robust locked-in behavior of topography, which is broken when a strong enough electric field is considered.