Boltzmann equation and hydrodynamics at the Burnett level
Alexander Bobylev - Department of Mathematics, Karlstad University, SE-651 88 Karlstad, Sweden (email)
Abstract: The hydrodynamics at the Burnett level is discussed in detail. First we explain the shortest way to derive the classical Burnett equations from the Boltzmann equation. Then we sketch all the computations needed for details of these equations. It is well known that the classical Burnett equations are ill-posed. We therefore explain how to make a regularization of these equations and derive the well-posed generalized Burnett equations (GBEs). We discuss briefly an optimal choice of free parameters in GBEs and consider a specific version of these equations. It is remarkable that this version of GBEs is even simpler than the original Burnett equations, it contains only third derivatives of density. Finally we prove a linear stability for GBEs. We also present some numerical results on the sound propagation based on GBEs and compare them with the Navier-Stokes results and experimental data.
Keywords: Hydrodynamics, regularized Burnett equations, Stability, sound
Received: October 2011; Revised: November 2011; Published: April 2012.
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