Spectral - Lagrangian methods for Collisional Models of Non - Equilibrium Statistical States
| dc.creator | Gamba, Irene M. | |
| dc.creator | Tharkabhushanam, Sri Harsha | |
| dc.date | 2007-10-28 | |
| dc.date | 2008-03-25 | |
| dc.date.accessioned | 2026-07-07T09:27:58Z | |
| dc.date.available | 2026-07-07T09:27:58Z | |
| dc.description | We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann Transport Equation for Variable Hard Potential (VHP) collision kernels with conservative or non-conservative binary interactions. The method is based on symmetries of the Fourier transform of the collision integral, where the complexity in its computing is reduced to a separate integral over the unit sphere $S^2$. In addition, the conservation of moments is enforced by Lagrangian constraints. The resulting scheme, implemented in free space is very versatile and adjusts in a very simple manner, to several cases that involve energy dissipation due to local micro-reversibility (inelastic interactions) or elastic model of slowing down process. Our simulations are benchmarked with the available exact self-similar solutions, exact moment equations and analytical estimates for homogeneous Boltzmann equation for both elastic and inelastic VHP interactions. Benchmarking of the simulations involves the selection of a time self-similar rescaling of the numerical distribution function which is performed using the continuous spectrum of the equation for Maxwell molecules as studied first in \cite{asympGranular} and generalized to a wide range of related models in \cite{BCG}. The method also produces accurate results in the case of inelastic diffusive Boltzmann equations for hard-spheres (inelastic collisions under thermal bath), where overpopulated non-Gaussian exponential tails have been conjectured in computations by stochastic methods in \cite{vanNoi-Ernst, ernst-brito, MSS, GRW04} and rigourously proven in \cite{diffGran} and \cite{highEnergyTails}. | |
| dc.description | 41 pages with 15 figures | |
| dc.identifier | https://arxiv.org/abs/0710.5308 | |
| dc.identifier | http://arxiv.org/abs/0710.5308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157293 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 45K05, 82C40, 82C80 | |
| dc.title | Spectral - Lagrangian methods for Collisional Models of Non - Equilibrium Statistical States | |
| dc.type | text |