Eu's Generalized Hydrodynamics as the Basis of a New Computational Model for Rarefied and Microscale Gasdynamics.

摘要

A new computational model based on Eu's generalized hydrodynamics, which has been recently proposed for describing the motion of gases in non- equilibrium state and is shown to be consistent with the second law of thermodynamics, is presented. The general understanding of Eu's generalized hydrodynamics, which employs the cumulant expansion for the Boltzmann collision integral instead of the BGK approximation, is also obtained by considering three fundamental flows; compressed gas in shock waves, expanding gas, and velocity shear flow. The study on these problems reveals that Grad's equations are similar to Eu's equations in the slip flow, but become drastically different from Eu's equations in shock structure problem. A plausible explanation is that the relaxation time approximation may be insufficient in modeling the extreme nonlinearity of shock structure since the Boltzmann collision integral plays a critical role in this case. Finally, by considering the microscale channel flow, a new slip boundary condition based on Langmuir's theory is presented that predicts a trend of increasing pressure curve nonlinearity with increasing rarefaction and a minimum in mass flow rate, which are not the case with the results predicted by the first-order Maxwell slip condition.