A Fast Fourier Spectral Method for the Linearized Boltzmann Collision Operator
Abstract
Abstract. We introduce a fast Fourier spectral method to compute linearized collision operators of the Boltzmann equation for variable hard-sphere gases. While the state-of-the-art method provides a computational cost [Formula: see text], with [Formula: see text] being the number of modes in each direction and [Formula: see text] being the number of quadrature points on a hemisphere, our method reduces the cost to [Formula: see text], removing the factor [Formula: see text], which could be large in our numerical tests. The method is applied in a numerical solver for the steady-state Boltzmann equation with quadratic collision operators. Numerical experiments for both spatially homogeneous and inhomogeneous Boltzmann equations have been carried out to test the accuracy and efficiency of our method.
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Lattice Boltzmann Simulation Studies
Advanced Thermodynamics and Statistical Mechanics
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 48
- Issue
- 1
- Pages
- B83–B111
- Publication date
- 9 February 2026
- Language
- EN