Scientific Computing Group Seminars - Detail View

Speaker: I. Gamba

Affiliation: University of Texas, Austin

Talk Title: Analysis and Spectral Solvers for Dissipative Non-linear Boltzmann Equations

Notes: Note --- Special time for seminar

Time: May 07 2007 4 p.m.

Location: 182 George Street, Room 110

Abstract:

We study long time dynamics to solutions of initial value problems to rather general Boltzmann kinetic models may describe qualitatively different processes in applications, but have many features in common. In particular we focus in the existence, uniqueness and asymptotics to dynamical scaling (self-similar) solutions and connections to stable laws for non-Gaussian states. In adition we present a deterministic spectral solver for the non-linear Boltzmann Transport Equation (energy conservative and non-conservative) for rather general collision kernels. The computation of the non-linear Boltzmann Collision integral and the lack of appropriate conservation properties due to spectral methods has been remedied by framing the conservation properties in the form of a constrained minimization problem which is solved easily using a Lagrange multiplier method. We benchmark our code with several examples of models for Maxwell type of interactions, (elastic or inelastic) for which explicit solution formulas are known. The numerical moments are compared with exact moments formulas and the numerical non-equilibrium probability distributions functions are compared to the general asymptotic results. The numerical method also produces accurate results in the case of inelastic hard-sphere interactions.