Two-relaxation time lattice Boltzmann models for the ion transport equation in electrohydrodynamic flow: D2Q5 vs D2Q9 and D3Q7 vs D3Q27

Two commonly used discrete velocity models (the linear discrete velocity model (LDVM) and the full discrete velocity model (FDVM)) are investigated using the two-relaxation time lattice Boltzmann method coupled to a fast Poisson solver in an electroconvection system. We derived analytically the LDVM, i.e., D2Q5 and D3Q7 and FDVM, i.e., D2Q9 and D3Q27, for the ion transport equation (convection–diffusion–drift equation) in both two- and three-dimensional systems. The analytical results indicate that the error terms in LDVM are higher orders and can be neglected in practical simulations. The numerical results of LDVM and FDVM are quantitatively compared, showing the differences between the models’ prediction in charge density, velocity, and stability hysteresis loops. The numerical results are consistent with the theoretical analysis. We perform all the simulations using graphics processing units, and the computational efficiency is measured via the wall clock time. We find that the LDVM can substitute FDVM in certain conditions with a substantial saving in computational costs and a small sacrifice in accuracy.

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Recommended citation: Baojie Zhu, Yifei Guan, and Jian Wu. “Two-relaxation time lattice Boltzmann models for the ion transport equation in electrohydrodynamic flow: D2Q5 vs D2Q9 and D3Q7 vs D3Q27.” Physics of Fluids 33, no. 4 (2021): 044108.