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The intermediate section or “rarefied” mode can be approached by either using the Navier–Stokes equations with slip conditions at the wall (for flows close to continuous) or using Boltzman equations (valid everywhere else) solved by the direct methods of resolution or by direct Monte Carlo simulation (DSMC) methods. 40 4 Aerodynamics In addition to these modes related to the number of molecules per unit volume, one can further classify the flows with respect to chemical reactions, and reactions of dissociation and their kinetics.
The real gas effects can be taken into account in the computation by using the equation of state of air at thermodynamic equilibrium at the local conditions of temperature and pressure. Inviscid treatment of the subsonic zones (for example, around the stagnation point) requires the resolution the nonstationary Euler equations (time marching method). Treatment of the supersonic zones is generally optimized by using “space marching” methods. “Shock capturing” methods use fixed mesh in which the shock discontinuity is treated as the other points of the flow.
2. At low altitudes, when Kn << 1, we are in “continuous flow” mode, governed by classical fluid mechanics theory (Euler equations for the inviscid flows, or Navier–Stokes equations to include viscous effects). 3. The intermediate section or “rarefied” mode can be approached by either using the Navier–Stokes equations with slip conditions at the wall (for flows close to continuous) or using Boltzman equations (valid everywhere else) solved by the direct methods of resolution or by direct Monte Carlo simulation (DSMC) methods.