Computer simulation of some types of flows arising at interactions between a supersonic flow and a boundary layer

Abstract

As it is known the gas dynamics Euler and Navier-Stokes equations are obtained by a usual averaging procedure from the integro-differential Boltzmann equation for description of aone-frequancy distribution function. At the difference approximation of the gas dynamics equations we do not use the fact that these equations follow from a more complex transport equation, and macroscopic gasdynamic parameters the density, the velocity, the temperature may be obtained as momenta of the distribution function *) . Employment of the Boltzmann equation or its simplified kinetic models for describing the behaviour of dense gases appears~ first sight to be inexpedient because an amount of computations is considerably larger in this case than for solving the gas dynamics equations. By basing on kinetic models the authors managed to construct the difference system of equations for determining macroscopic gas parameters (the density, the velocity, the temperature), which depends only on spatial variables and time L I~. Constructing the difference schemes may be treated in the following way: first the difference scheme is written down for the Boltzmann equation and then it is averaged by using the notion about the local Maxwell or local Navier-Stokes form of the distribution function to close the system of macroscopic equations. To a considerable extent this procedure is similar to that which is applied to obtain the Euler or Navier-Stokes equations from the Boltzmann equation. Et is natural to call these schemes the kinetic-consistent difference schemes because their form is consistent with a choice of difference approximation for the Boltzman equation. Thus the kinetic