In this work, a Cole–Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensional coupled Burgers’ equations is developed. We first adopt the Cole–Hopf transformation where an intermediate variable \(\theta \) is introduced to eliminate the nonlinear convection terms in the Burgers’ equations on the velocity \(\textbf{u}=(u_1,u_2,\cdots ,u_d)\) . In this case, a diffusion equation on the variable \(\theta \) can be obtained, and particularly, the velocity \(\textbf{u}\) in the coupled Burgers’ equations is determined by the variable \(\theta \) and its gradient term \(\nabla \theta \) . Then we develop a MRT-LB model for the d-dimensional transformed diffusion equation, and present the corresponding macroscopic finite-difference scheme. At the diffusive scaling, the macroscopic modified equation of the developed MRT-LB model is derived through the Maxwell iteration method. With the aid of the free parameters in the MRT-LB model, we find that not only the modified equation at fourth order can be obtained, but also the gradient term \(\nabla \theta \) can be calculated locally by the non-equilibrium distribution function with a fourth-order accuracy, this indicates that theoretically, the MRT-LB model for d-dimensional coupled Burgers’ equations can achieve a fourth-order accuracy in space. Finally, some simulations are conducted to test the MRT-LB model, and the numerical results show that the proposed MRT-LB model has a fourth-order convergence rate, which is consistent with our theoretical analysis.
