2012/11/01 by Irene M. Gamba, Gamba, Irene M., J. Haack +1
Mathematics · Engineering · Materials Science · #Gas Dynamics and Kinetic Theory #Radiative Heat Transfer Studies #Thermal properties of materials
paper · pdf · doi:10.48550/arxiv.1211.0327
We present new results building on the conservative deterministic spectral\nmethod for the space homogeneous Boltzmann equation developed by Gamba and\nTharkabhushaman. This approach is a two-step process that acts on the weak form\nof the Boltzmann equation, and uses the machinery of the Fourier transform to\nreformulate the collisional integral into a weighted convolution in Fourier\nspace. A constrained optimization problem is solved to preserve the mass,\nmomentum, and energy of the resulting distribution.\n Within this framework we have extended the formulation to the case of more\ngeneral case of collision operators with anisotropic scattering mechanisms,\nwhich requires a new formulation of the convolution weights. We also derive the\ngrazing collisions limit for the method, and show that it is consistent with\nthe Fokker-Planck-Landau equations as the grazing collisions parameter goes to\nzero.\n