2012 Young Researchers Workshop:
Kinetic Description of Multiscale Phenomena

Conservative Spectral Methods for the Inhomogeneous Boltzmann equation

Jeff Haack

University of Texas at Austin

In this talk we will discuss extensions to the deterministic conservative spectral method for the Boltzmann equation developed by Gamba and Tharkabhushanam. This method uses the weak form and the Fourier structure of the collision operator to recast the collisional term as a weighted convolution with precomputed weights, which contain all of the collision mechanism information, and a constrained optimization problem is solved to ensure preservation of the macroscopic moments. This formulation has been extended to the more general case of anisotropic scattering kernels, and we investigate the performance of the method in the singular grazing collisions limit. We also investigate the scaling of the method to massively parallel systems using openMP and MPI. Finally, we discuss extension of the scheme for multiple species and for gases with internal energy, which results in inelastic collisions due to internal energy excitation and relaxation. This is joint work with Irene Gamba (Texas) and Thierry Magin and Alessandro Munafo (Von Karman Institute).