Abstract
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of a GaussHermite quadrature. This is defined by means of half and/or fullrange Hermite polynomials depending whether or not the distribution function presents a discontinuity in the velocity space. The resulting semidiscrete Boltzmann equation is in the form of a system of hyperbolic partial differential equations whose solution can be obtained by standard numerical approaches. The spectral rate of convergence of the results in the velocity space is shown by solving the spatially uniform homogeneous relaxation to equilibrium of Maxwell molecules. As an application, the twodimensional cavity flow of a gas composed of hardsphere molecules is studied for different Knudsen and Mach numbers. Although computationally demanding, the proposed method turns out to be an effective tool for studying subsonic slightly rarefied gas flows.
Original language  English 

Pages (fromto)  568584 
Number of pages  17 
Journal  Journal of Computational Physics 
Volume  258 
DOIs  
Publication status  Published  1 Feb 2014 
Keywords
 Boltzmann equation
 Deterministic solution
 Galerkin method
 Gaussian quadrature
 Half and fullrange Hermite polynomials
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Profiles

Livio Gibelli
 School of Engineering  Lecturer in Mechanical Engineering (Multiscale Thermofluids)
Person: Academic: Research Active