Abstract:
Due to high computational efficiency and implementation simplicity, lattice Boltzmann method (LBM) has been widely used to simulate a variety of complex flows since its invention in the 1990s. Traditional LBM, derived from Taylor expansion of equilibrium distribution function and semi-empirical theory, employing a low Mach-number assumption, was once considered only capable for isothermal weakly compressible flows. In recent years, several models extending LBM to compressible and thermal flow have been proposed, among those the multi-speed model with multiple speed magnitude in each directions, has received widespread attention since its single distribution function is more physically realistic. We described the ideas of several typical multi-speed models, including multi-speed models of early ages, Watari-Tsutahara model, flexible specific-heat ratio and Hermite polynomial model. Since the multi-speed model constructed by Hermite polynomial expansion method is more mathematically self-consistent, and its low-order form is consistent with the traditional isothermal weakly compressible LBM model, we focus on interpretation of the multi-speed models constructed by Hermite polynomial expansion method, including the construction principle, procedure of discrete velocity model solution and time-space discrete method. Several combination of LBM and traditional computational fluid dynamics method, including finite difference LBM, finite volume LBM, and finite element LBM are briefed. The remained issues and future directions of LBM multi-speed models are summarized in the end.