The lattice Boltzmann method (LBM) based on single-relaxation-time
(SRT) and multiple-relaxation-time (MRT) collision operators has been widely
used in simulating flow and transport phenomena. However, it is well known
that the SRT LBM is prone to numerical instability for small relaxation rate
while the selection of relaxation parameters in the MRT LBM is challenging.
By contrast, the LBM based on two-relaxation-time (TRT) collision operators
embodies advantages of the SRT LBM for simple implementation and of
the MRT LBM for good numerical stability. However, the TRT LBM has not
been widely used. One reason is that the tedious mathematical derivations and presentations of the TRT LBM impede its understanding and implementation. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in the subsurface environments, including advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform
flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability for these transport phenomena in both simple and complicated geometries. Therefore, the TRT LBM provides powerful potential to simulate various geophysical and
biochemical behaviors in the subsurface environments.