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In this work, a Cole-Hopf transformation based fourth-ordermultiple-relaxation-time lattice Boltzmann (MRT-LB) model for d-dimensionalcoupled Burgers' equations is developed. We first adopt the Cole-Hopftransformation where an intermediate variable \theta is introduced to eliminatethe nonlinear convection terms in the Burgers' equations on the velocityu=(u_1,u_2,...,u_d). In this case, a diffusion equation on the variable \thetacan be obtained, and particularly, the velocity u in the coupled Burgers'equations is determined by the variable \theta and its gradient term\nabla\theta. Then we develop a general MRT-LB model with the natural momentsfor the d-dimensional transformed diffusion equation and present thecorresponding macroscopic finite-difference scheme. At the diffusive scaling,the fourth-order modified equation of the developed MRT-LB model is derivedthrough the Maxwell iteration method. With the aid of the free parameters inthe MRT-LB model, we find that not only the consistent fourth-order modifiedequation can be obtained, but also the gradient term $\nabla\theta$ can becalculated locally by the non-equilibrium distribution function with afourth-order accuracy, this indicates that theoretically, the MRT-LB model for$d$-dimensional coupled Burgers' equations can achieve a fourth-order accuracyin space. Finally, some simulations are conducted to test the MRT-LB model, andthe numerical results show that the proposed MRT-LB model has a fourth-orderconvergence rate, which is consistent with our theoretical analysis.

A Cole-Hopf transformation based fourth-order multiple-relaxation-time lattice Boltzmann model for the coupled Burgers' equations