Fourth compact finite difference (FD) method for solving two dimensional Discrete Boltzmann Equation (DBE) for simulation of fluid flows is proposed in this paper. The solution procedure is carried out in Eulerian framework. BGK (Bhatnagar–Gross–Krook) scheme is adopted to approximate the collison term. The convective terms are discretized using 4th compact finite difference method to improve the accuracy and stability. Te semidiscrete equations are updated using 4th order explicit Runge-Kutta method. Preliminary results of the method applied on the Taylor-Green vortex flows benchmark are presented. We compared the numerical results
with other numerical results, i.e. explicit 2nd and 4th
FD, and exact solutions. The comparisons showed excellent agreement.