  The study of heat transport in low-dimensional oscillator lattices presents a
formidable challenge. Theoretical efforts have been made trying to reveal the
underlying mechanism of diversified heat transport behaviors. In lack of a
unified rigorous treatment, approximate theories often may embody controversial
predictions. It is therefore of ultimate importance that one can rely on
numerical simulations in the investigation of heat transfer processes in
low-dimensional lattices. The simulation of heat transport using the
non-equilibrium heat bath method and the Green-Kubo method will be introduced.
It is found that one-dimensional (1D), two-dimensional (2D) and
three-dimensional (3D) momentum-conserving nonlinear lattices display power-law
divergent, logarithmic divergent and constant thermal conductivities,
respectively. Next, a novel diffusion method is also introduced. The heat
diffusion theory connects the energy diffusion and heat conduction in a
straightforward manner. This enables one to use the diffusion method to
investigate the objective of heat transport. In addition, it contains
fundamental information about the heat transport process which cannot readily
be gathered otherwise.
