Predicting Breakdown of the Continuum Equations Under Rarefied Flow Conditions

The breakdown of the continuum equations of gas dynamics under conditions of rarefied flow is considered. The conditions of breakdown are of interest in assessing the physical accuracy of continuum solutions, in understanding the mathematical relations between different sets of continuum transport equations, and play a significant role in the development of hybrid methods that use both continuum and kinetic simulation techniques. A number of previous breakdown parameters are reviewed. A new method, based on kinetic theory analysis, is introduced for detecting conditions where the continuum approach is valid. Continuum breakdown is discussed in detail for gas expansions and shock waves by considering the basic physical phenomena involved in each case. Success of the breakdown parameters for these flows is assessed. It is shown that continuum breakdown in gas expansions and shock waves proceeds through different physical mechanisms that are best predicted by different types of breakdown parameters. The new method for detecting continuum onset is applied to shock waves and shown to offer promising results. © 2003 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87928/2/899_1.pd