High-order lattice Boltzmann method for fluid and plasma flows

The lattice Boltzmann method (LBM) is presented as an alternative computational approach for simulating both fluid and plasma systems. Part one introduces the LBM for fluid, utilizing the high-order equilibrium distribution function (HEQ), high-order regularization (HR), and the high degree of precision of quadrature (HPQ) to enhance accuracy and numerical stability. The testing simulations consist of Kolmogorov flow and Taylor-Green vortex flow. Part two focuses on constructing the LBM for simulating plasma systems. This method consists of four distinct species of distribution function: ion, electron, electric field, and magnetic field, which efficiently recover the two-fluid description for plasma. Additionally, the accuracy and stability of this method are increased by using HPQ. Plasma oscillation and Alfvén wave are considered to validate the accuracy of this model. Hartmann flow is demonstrated as a practical application.The results from the part one indicate that HEQ, HR, and HPQ enhance the accuracy when exist the kinetic effect, i.e., Knudsen number (Kn) >0.1, Kn defined as the ratio between the mean free path and the characteristic length scale. Noticeably, the effect of HPQ is dominant because the high number of direction able to handle the peculiar distribution function existing in transition flow. On the other hand, the effect of HEQ is trivial. HR can be used to capture non-equilibrium distribution when the system is immersed with the kinetic effect.The simulation results of plasma oscillation and Alfvén wave from second part imply the accuracy of the addition force term, electric field and magnetic field, which are newly incorporated into LBM for plasma model. Furthermore, the results of plasma oscillation indicate that HPQ enhances the numerical stability, particularly as the plasma frequency is increased. The extended application of Hartmann flow indicate that our LBM can provide the behavior of phenomenon accurately.