Restricted variational principle method for problems of low-density aerodynamics

Rosen's restricted variational principle representation of the Boltzmann equation is applied to the problem of determining the transitional-regime, low-density, hypersonic flow over slender, conical vehicles with diffusely reflecting surfaces. If the trial distribution function is suitably chosen, the Euler-Lagrange equations associated with Rosen's functional result in a semilinear hyperbolic system amenable to solution by classical characteristics methods. Sample calculations are given and compared with the low-density cone flow experiments of Hickman to assess the accuracy of the method presented. It is believed that the present method constitutes the first solution method for boundary value problems in the low-density transitional flow regime.This work was supported by the United States Air Force, Contract No. AF04(695)-1001.