Application of the Method of Parametric Differentiation to Radiation Gasdynamics

摘要

It is shown that the method of parametric differentiation, used in solving nonlinear systems of equations, can be interpreted as a device for introducing a real 'parameter' characteristic into the mathematical description of the problem along which one can integrate the parametrically differentiated system of equations. In this way, the method of parametric differentiation yields a characteristic initial value problem where the necessary data along distinct families of characteristics are the parametrically differentiated boundary conditions of the original problem and a solution of the original system for a particular value of the descriptive parameter. The applicability of the method of parametric differentiation to problems in radiation gasdynamics is first indicated by the solution of a simple test problem - the one-dimensional, hypersonic, radiating shock layer. Treating the total optical depth of the shock layer as the descriptive parameter, solutions were obtained for a large range of values of this parameter which appeared to be consistent with existing approximate solutions. The utility of this technique in radiation gasdynamics is further demonstrated in a solution of the problem of an inviscid, radiating gas flow in the stagnation region of a blunt body. (Author)