کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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521824 | 867789 | 2012 | 25 صفحه PDF | دانلود رایگان |
We propose a new spectral Lagrangian based deterministic solver for the non-linear Boltzmann transport equation (BTE) in d -dimensions for variable hard sphere (VHS) 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 computation is reduced to a separate integral over the unit sphere Sd-1Sd-1. 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 models of slowing down process. Our simulations are benchmarked with available exact self-similar solutions, exact moment equations and analytical estimates for the homogeneous Boltzmann equation, both for elastic and inelastic VHS 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 Bobylev et al. [A.V. Bobylev, C. Cercignani, G. Toscani, Proof of an asymptotic property of self-similar solutions of the Boltzmann equation for granular materials, Journal of Statistical Physics 111 (2003) 403–417] and generalized to a wide range of related models in Bobylev et al. [A.V. Bobylev, C. Cercignani, I.M. Gamba, On the self-similar asymptotics for generalized non-linear kinetic Maxwell models, Communication in Mathematical Physics, in press. URL:
Journal: Journal of Computational Physics - Volume 228, Issue 6, 1 April 2009, Pages 2012–2036