Abstract:
The Fourier transform of both, the non-linear Boltzmann
collisional integral and the Landau operator, derived from the weak
formulation of their respective equations, can be represent as weighted
convolutions in Fourier space.
We will present an overview of analytical issues and novel numerical
methods consisting on spectral-conservative schemes for these equations
that preserve the expected conserved properties of the described
phenomena, while enabling rigorous stability, convergence and error
analysis.
Within this framework, we study the rate of convergence of the Fourier
transforms of the difference of the Boltzmann grazing collision and Landau
operators, for a large family of power law Boltzmann angular scattering
cross sections that include the Rutherford potential as the critical limit
for grazing conditions. We analytically show that the decay rate to
equilibrium depends on the parameters associated to these collision cross
section.
This is work in collaboration with Ricardo Alonso, Jeff Haack and S.
Harsha Tharkabhushanam. |