(untitled) (Advances in Applied Mathematics and Mechanics, 2021)
Over the past two decades, there have been enormous advances in lattice Boltzmann (LB) numerical simulation and modelling. The lattice Boltzmann method has become a practical and promising tool for many fluid problems. A majority of recent studies have relied on numerical computations of isothermal flows. However, much less efforts have been devoted to complex thermal flows, such as flows in porous media subjected to external magnetic force, flows with temperature-dependent properties. In this paper, an overview is made based on some accomplishments in these numerical endeavours. Along with the paper's sections, the state-of-the-art trend and the LBM advances in modelling and in computational aspects for specific classes of problems of major interest will be fully touched on. Concluding remarks are given and the axis of our future studies will be traced.