Implementation of a Spectral Decomposition of the Boltzmann Equation with the Streaming in the Lattice-Boltzmann Method*

Recent developments in mathematics have allowed for the collision process of the Boltzmann equation to be discretized using spectral methods. This new method has the potential for replacing the Bhatnagar-Gross-Krook (BGK) approximation used in approaches such as the lattice-Boltzmann method (LBM). This would end the need for a low Mach approximation to the linearized Boltzmann equation in LBM. This allows solving the full Boltzmann equation and should therefore avoid many of the limitations of current approxima- tions. This paper shows a derivation for the spectral method as well as an implementation for a 2-D and 3-D test cases with results. A simulation of decaying isotropic turbulence is also presented.