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<p>We present a three-dimensional lattice Boltzmann framework for electrohydrodynamic flows driven by unipolar charge injection. Flow momentum and charge transport are predicted by a multiple-relaxation-time, central-moments-based collision operator, while the electric potential is evolved with a single-relaxation-time scheme. We discuss the merits of a fully LBM formulation versus a hybrid approach in which the potential is obtained from a finite-difference Poisson solver. Although the electric field can be evaluated locally within LBM, we recommend finite-difference reconstruction, which we demonstrate to be more accurate. For charge carriers, as for the flow, we adopt a fourth-order Hermite equilibrium on the D3Q19 discretisation; using the highest order supported by the lattice markedly improves stability and fidelity in strongly forced regimes. Validation against the hydrostatic analytical solution and canonical electroconvection benchmarks reproduces reference bifurcations and quantitative metrics at moderate cost. Our direct numerical simulations capture the transition from steady cellular patterns to chaotic electroconvection as the electric Rayleigh number increases; the electric Nusselt number displays a conduction plateau, a convection-dominated growth window, and a high-forcing roll-off consistent with space-charge depletion and intermittent dynamics. Compared with single-relaxation-time LBM, the present formulation achieves a substantially larger stability envelope with comparable throughput in our bandwidth-bound implementation; relative to finite-volume projection methods it eliminates the pressure-Poisson bottleneck and scales efficiently on accelerators. Finally, genuinely three-dimensional simulations reveal complex plume topology and vortex stretching, underscoring the robustness and generality of the proposed scheme for electrohydrodynamics.</p>

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

  • 期刊论文

  • 发表日期：

    2025年12月2日

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  • Shiladitya Patnaik,
  • Alex Skillen,
  • Alessandro De Rosis

摘要

We present a three-dimensional lattice Boltzmann framework for electrohydrodynamic flows driven by unipolar charge injection. Flow momentum and charge transport are predicted by a multiple-relaxation-time, central-moments-based collision operator, while the electric potential is evolved with a single-relaxation-time scheme. We discuss the merits of a fully LBM formulation versus a hybrid approach in which the potential is obtained from a finite-difference Poisson solver. Although the electric field can be evaluated locally within LBM, we recommend finite-difference reconstruction, which we demonstrate to be more accurate. For charge carriers, as for the flow, we adopt a fourth-order Hermite equilibrium on the D3Q19 discretisation; using the highest order supported by the lattice markedly improves stability and fidelity in strongly forced regimes. Validation against the hydrostatic analytical solution and canonical electroconvection benchmarks reproduces reference bifurcations and quantitative metrics at moderate cost. Our direct numerical simulations capture the transition from steady cellular patterns to chaotic electroconvection as the electric Rayleigh number increases; the electric Nusselt number displays a conduction plateau, a convection-dominated growth window, and a high-forcing roll-off consistent with space-charge depletion and intermittent dynamics. Compared with single-relaxation-time LBM, the present formulation achieves a substantially larger stability envelope with comparable throughput in our bandwidth-bound implementation; relative to finite-volume projection methods it eliminates the pressure-Poisson bottleneck and scales efficiently on accelerators. Finally, genuinely three-dimensional simulations reveal complex plume topology and vortex stretching, underscoring the robustness and generality of the proposed scheme for electrohydrodynamics.