Exploring the accuracy of the Lattice Boltzmann method

Lattice Boltzmann method is a mesoscopic used for solving hydrodynamics problems of both incompressible and compressible fluids. Although the widely used, reliability results unclear. Therefore, we use to solve fundamental problem with known analytical solution, Couette flow. We estimate accuracy simulation obtained by setting different types spatial grids, boundary conditions, equilibrium distribution functions. However, imposes restrictions on large number parameters such as Reynolds Mach numbers. During discovered an unexpected behavior solution using classical lattice method. In these simulations find that conservation law violated due inflow in upper corners computational domain.