Application of the ghost fluid lattice Boltzmann method to injection-induced electroconvection in a dielectric liquid

In paper, we develop a ghost fluid-lattice Boltzmann method(GF-LBM) to simulate electroconvection problems with complex boundaries. A unified lattice Boltzmann model with two-relaxation-time (TRT) scheme is employed to solve the flow field, the spatial-temporal evolution of charge density, and the electric potential. The ghost fluid method (GFM) enforces Dirichlet and Neumann boundary conditions on curved boundaries with second-order accuracy. Considering unipolar charge injection, we firstly validate the present model by comparing the numerical results for concentric cylindrical electrodes with analytical solutions and previously published data. The good agreement confirms the accuracy of the proposed model and demonstrates that the GF-LBM retains second-order accuracy for electroconvection problems. In addition, the proposed model is applied to investigate electroconvection in elliptical electrode, with systematic comparisons under varying aspect ratios η, electric Rayleigh numbers T, and electrode configurations. The results indicate that variations in geometry and T significantly influence the charge distribution and flow patterns. Distinct subcritical bifurcation curves are observed for different electrode configurations.