Application of the method of parametric differentiation to radiativegasdynamics.

Abstract

The method of parametric differentiation for nonlinear problems is interpreted as a device for introducing a real parameter characteristic into the mathematical description along which one can then integrate the parametrically differentiated equations. The applicability of the method to radiative gasdynamics is illustrated first by the solution of a test problem- — the one-dimensional, hypersonic, radiating shock layer. The technique's utility is further demonstrated in a solution of an inviscid, radiating gas flow in the stagnation region of a blunt body. Use of the shock-layer optical depth as the descriptive parameter permits application of the technique. In both problems, numerical results are obtained over a wide range of conditions which indicate the integrity and utility of the approach. Comparison of the differential approximation with the exact integral formulation for the radiative transfer is given for the blunt body problem in order to ascertain the validity of the former.