Spectral-Lagrangian methods for collisional models of non-equilibrium statistical states
Journal of Computational Physics
Journal of Computational Physics
An Asymptotic Preserving Scheme for the ES-BGK Model of the Boltzmann Equation
Journal of Scientific Computing
Journal of Computational Physics
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method
Journal of Computational Physics
A direct method for the Boltzmann equation based on a pseudo-spectral velocity space discretization
Journal of Computational Physics
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In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on spectral methods were derived for the Boltzmann collision operator for a class of interactions including the hard spheres model in three dimensions. These algorithms are implemented for the solution of the Boltzmann equation in two and three dimensions, first for homogeneous solutions, then for general nonhomogeneous solutions. The results are compared to explicit solutions, when available, and to Monte Carlo methods. In particular, the computational cost and accuracy are compared to those of Monte Carlo methods as well as to those of previous spectral methods. Finally, for inhomogeneous solutions, we take advantage of the great computational efficiency of the method to show an oscillation phenomenon of the entropy functional in the trend to equilibrium, which was suggested in the work [L. Desvillettes and C. Villani, Invent. Math., 159 (2005), pp. 245-316].