A numerical model of the Boltzmann equation related to the discontinuous Galerkinmethod

Armando Majorana

doi:10.3934/krm.2011.4.139

Article Contents

2011, Volume 4, Issue 1: 139-151. Doi: 10.3934/krm.2011.4.139

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A numerical model of the Boltzmann equation related to the discontinuous Galerkin method

Armando Majorana^1,

1.
Dipartimento di Matematica e Informatica, Viale A. Doria 6, 95125 Catania

Received: August 31, 2010

Revised: November 30, 2010

Published: February 2011

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Abstract

We propose a new deterministic numerical model, based on the discontinuous Galerkin method, for solving the nonlinear Boltzmann equation for rarefied gases. A set of partial differential equations is derived and analyzed. The new model guarantees the conservation of the mass, momentum and energy for homogeneous solutions. We avoid any stochastic procedures in the treatment of the collision operator of the Boltzmamn equation.

Keywords:

Boltzmann equation,
discontinuous Galerkin finite elements.

Mathematics Subject Classification: Primary: 76P, 82C40; Secondary: 65M60.

Citation:

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References

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