Stable Equations to Second Order in the Knudsen number for the Fluid Dynamics Variables

Authors: Söderholm,  L. H. S.
Document Type: Article
Pubstate: Published
Journal: Rarefied Gas Dynamics
Volume: 25   137-42
Year: 2007


Two methods to formulate well posed equations which are consistent approximations of the Burnett equations are given. In the first method, attention is drawn to the Chapman-Enskog replacement of time derivatives by the approximate conservation laws. It is shown that partly restoring the time derivatives in the Burnett equations results in well posed equations. In the second method the linearized Burnett equations are studied by a multiple time analysis. All resulting equations are well posed. It is also shown that the full set of perturbation equations can to within third order terms be summarized as well posed equations for transformed fields.