Application of the Moment Equations to the Rarefied Supersonic Flow

摘要

Moment equations derived from the Boltzmann equation were applyed to the leading edge problem in the supersonic flow. Boundary conditions for the flow properties and higher order moments were derived by applying a generalized Grad's slip conditions. The moment equations were solved using MaCcormack's central difference scheme. Two-dimensional flow field on the flat plate was obtained in the scale of one mean free path. Numerical simulation with the mesh size of sub-mean free path yielded undesirable numerical oscillation in vicinity of the leading edge and in the vicinity of the flat plate. On the other hand, numerical simulation with the mesh size of several mean free pahts suggested that the moment equations were applicable to the hypersonic flow. The results with the mesh size of one mean free path showed a good agreement with the results of DSMC method. Present results showed a good agreement with the results of DSMC. We then assured that moment equations with generalized slip boundary conditions were valid for the analysis of rarefied supersonic flows. It was expected that introduction of certain new types of artificial viscosity like the TVD schemefor further extend the applicable range of the moment equations.