Advanced Diagnosis Techniques in Medical Imaging

Abstract

The Boltzmann distribution was derived in this chapter. The Boltzmann equation was explained next to the main difficulty of this equation, the integral of the collision operator, which was solved by the BGK-approximation where a long-term substitute is essential. The discretization of the Boltzmann comparison with the BGK-approximation was introduced along with the lattice and the different lattice configurations to define the lattice framework where the method is applied. Also, in this framework, the algorithm of the process was described. The boundary conditions were summarised, where one can see that they represent macroscopic conditions acting locally in every node.