A lattice Boltzmann model based on Cole-Hopf transformation for N-dimensional coupled Burgers' equations. (15th March 2023) - Rong, Fumei; Li, Qianhuan; Shi, Baochang; Chai, Zhenhua
Abstract: In this paper, a lattice Boltzmann(LB) model based on the Cole-Hopf transformation is developed for the n -dimensional coupled Burgers' equations. Compared with the traditional LB model, the Cole-Hopf transformation is used to eliminate the nonlinear convection term in the Burgers' equations, such that simple diffusion equation can be obtained, then the LB model is proposed for the diffusion equation. Based on the Chapman-Enskog analysis, we can accurately recover the linear diffusion equation from this LB model, in which the variable θ in the linear diffusion equation and the gradient of the variable ∇ θ can be calculated conveniently by non-equilibrium distribution function without needing the finite-difference schemes. Then, the variables u in n -dimensional coupled Burgers' equations can be solved conveniently by θ and ∇ θ . Theoretically, this LB model can be used to solve any n -dimensional coupled Burgers' equations. Finally, some numerical experiments are conducted to test the present LB model, and the numerical results show that the model has the advantages in terms of computation, accuracy, stability.