  In this paper, we develop a general rectangular multiple-relaxation-time
lattice Boltzmann (RMRT-LB) method for the Navier-Stokes equations (NSEs) and
nonlinear convection-diffusion equation (NCDE) by extending our recent unified
framework of MRT-LB method [Z.H. Chai and B.C. Shi, Phys. Rev. E 102, 023306
(2020)], where a rectangular equilibrium distribution function (REDF) [J.H. Lu
et al, Phil. Trans. R. Soc. A 369, 2311-2319 (2011)] on a rectangular lattice
is utilized. Due to the anisotropy of discrete velocities on a rectangular
lattice, the third-order moment of REDF is inconsistent with that of popular LB
method, and thus the previous unified framework of MRT-LB method cannot be
directly applied to the NSEs using the REDF on the rectangular rDdQq lattice.
The macroscopic NSEs can be recovered from the RMRT-LB method through the
direct Taylor expansion method by properly selecting the relaxation sub-matrix
$\mathbf{S}_2$ which is related to kinetic viscosity and bulk viscosity. While
the rectangular lattice does not lead to the change of the zero-th, first and
second-order moments of REDF, thus the unified framework of MRT-LB method can
be directly applied to the NCDE. It should be noted that the RMRT-LB model for
NSEs can be derived on the rDdQq lattice, including rD2Q9, rD3Q19, and rD3Q27
lattices, and the RMRT-LB versions (if existed) of the previous MRT-LB models
can be obtained, including those based on raw (natural)-moment, central-moment,
Hermite-moment, and central Hermite-moment, respectively.
