Comparison of the Lbm With the Modified Local Crank-Nicolson Method Solution of Transient Two-Dimensional Non-Linear Burgers EˆQuation

Burgers equation is a simplified form of the navier-stokes equation that represents the non-linear fea- tures of it. in this paper, the transient two-dimensional non-linear burgers equation is solved using the lattice boltzmann method (lbm). the results are compared with the modified local crank-nicolson method (mlcn) and exact solutions. the lbm has been emerged as a new numerical method for solving various physical problems. compared with the traditional computational approaches, the lbm has many outstanding advantages, such as its algorithmic simplicity, parallel computation and easy handling of complicated boundary conditions. two examples, distinguished by different initial conditions, are solved using the lbm and the mlcn method and the accuracy of these two methods at various reynolds numbers are analyzed. also, the effects of different numbers of particle velocities on the accuracy of the lbm are evaluated. the results show that at higher reynolds numbers the accuracy of the lbm is higher than the mlcn method.