Extending Navier-Stokes to Smaller Length Scales and Nonlinear Acoustics

Research Area: Theoretical and computational mechanics
Project Members:
Söderholm,  L. H. S.

Project Description

The Navier-Stokes equations apply for length scales larger than 20 times the mean free path in a gas. They are to first order in the mean free path. For smaller length scales, second order terms have to be included. The resulting Burnett equations have however an unphysical instability. Two different methods of stabilizing the Burnett equations are proposed. The first one is a set of thirteen first order equations for the 5 fluid dynamic variables and 8 kinetic variables. These equations have been applied to the evolution of a very high frequence nonlinear sound wave. In the second method, a set of 5 equations for only the fluid dynamic variables is derived.

Publications related to the project

2007Hybrid Burnett Equations. A New Method of Stabilizing
Transport Theory and Statistical Physics 36 495-512 (Published)
2005Nonlinear Acoustics to Second Order in Knudsen Number Without Unphysical Instabilities
Rarefied Gas Dynamics 24 54-59 (Published)
1993Nonliear propagation through a fluid of waves originating from a biharmonic sound source.
J. of the acoustical society of America  29 (Published)

Internal Reports related to the project

YearTitleDocument Type