Accuracy of the lattice Boltzmann method based on analytical solutions

Abstract

In this paper, a simple method is proposed to obtain steady analytical solutions for the lattice Boltzmann method. Based on such analytical results, it is demonstrated how the accuracy of the lattice Boltzmann method can depend on the relative orientation of the lattice and the flow field. It is also demonstrated that the method can be useful to obtain a general class of analytical solutions for the lattice Boltzmann method. Finally, a simple relation is given between the compressibility error and the velocity field.