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.