Three-dimensional electrohydrodynamic flows by a central-moments-based lattice Boltzmann method

We present a three-dimensional lattice Boltzmann method (LBM) tailored for simulating electrohydrodynamic (EHD) flows driven by unipolar charge injection in dielectric liquids. The proposed scheme is built upon a central-moments-based collision operator for both the fluid and charge transport equations, offering enhanced numerical stability and accuracy compared to traditional BGK or MRT approaches. Notably, we construct the equilibrium state for the charge carriers using a fourth-order Hermite expansion, that is the maximum order supported by the D3Q19 lattice, allowing the model to capture nonlinear and turbulent electroconvection with high fidelity. The electric potential is handled via a hybrid strategy that combines LBM and second-order finite differences, the latter shown to yield superior accuracy in evaluating the electric field. Benchmark tests confirm the model’s ability to recover analytical hydrostatic solutions and reproduce known bifurcation phenomena in canonical EHD setups. In closed cavity configurations, the model captures the transition from steady to chaotic electroconvection, with the electric Nusselt number exhibiting a clear nonlinear growth as a function of the electric Rayleigh number. Moreover, our formulation exhibits enhanced numerical stability compared to existing LBM-based approaches. The present work introduces a compact, Galilean-invariant formulation for three-dimensional EHD simulation, offering a general and scalable framework for complex electrokinetic applications.