Variational Estimates of the Spectral Gap and Eigenvalue Spectra of the Linearized and Linear Boltzmann Hard Sphere Collision Operators

Abstract

The eigenvalue spectra of the linearized Boltzmann collision operator and the mass ratio–dependent linear Boltzmann collision operator for binary systems are reported. A variational method is used with either the Sonine polynomial basis set or the basis set of nonclassical Maxwell polynomials orthogonal with respect to the weight function , x ∈ [0, ∞). In the latter case, a pseudospectral method is used based on the Maxwell quadrature weights and points. A multidomain pseudospectral method is also used to accurately calculate the eigenvalues close to the continuum boundary so as to compare with the asymptotic Wentzel-Kramers-Brillouin results.