Ion flow field modelling based on lattice Boltzmann method and its mesh refinement

Ion flow is a phenomenon that exists in the normal operation of high-voltage direct current (HVDC) transmission lines. It will increase the electric field below the wire and poses a threat to the life and health of humans. Hence ion flow is considered in the HVDC transmission line laying design as a significant factor. However, the control equation of this phenomenon is a form of convective dominance, and it is easy to cause oscillation for its solution. In this study, a mesoscopic approach, the lattice Boltzmann method (LBM), is first proposed to solve the ion flow field. Firstly, the control equation of the ion flow field is rewritten in the form of the lattice Boltzmann equation. Secondly, reducing the computation load of the model by using local mesh refinement. Then a new mesh refinement method based on distribution function is proposed and compared with several other methods. Thirdly, the analytical solutions of the coaxial cylinder model are compared with LBM results, and a measuring platform is set up also for verification. Finally, the three-layer grid is successfully applied in an 800 kV unipolar full-scale transmission line.