THE INITIAL VALUE PROBLEM, SOUND PROPAGATION, AND MODELING IN KINETIC THEORY
Abstract
The one dimensional initial value problem of a monatomic single component gas is considered. Using the linearized Boltzmann equation the dispersion relation is studied. In addition to the usual gas dynamic sound waves one finds an infinity of decaying propagating waves. The phenomenon naturally exhibits itself as a sequence of epochs, the last stage of which is hydrodynamic. With reference to the same problem macroscopic equations such as Euler, NavierStokes, Burnett, Grad's moments equations, etc., are considered. In addition the recently considered kinetic models of Gross (Phys. Fluids 2:432, (1959)) are applied to the problem. These various formulations are critically analyzed and compared with each other and with the Boltzmann analysis. Lastly, several alternate molecular and macroscopic equations are offered whic remedy some of the shortcomings which appear in the above mentioned approximate theories. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 15, 1961
- Accession Number
- AD0264889
Entities
People
- Lawrence Sirovich
Organizations
- New York University