# Accession Number:

## AD0676671

# Title:

## APPLICATION OF THE METHOD OF PARAMETRIC DIFFERENTIATION TO RADIATION GASDYNAMICS.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## MASSACHUSETTS INST OF TECH CAMBRIDGE AEROPHYSICS LAB

# Personal Author(s):

# Report Date:

## 1968-07-01

# Pagination or Media Count:

## 298.0

# Abstract:

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

# Descriptors:

- (*BOUNDARY VALUE PROBLEMS
- *NONLINEAR DIFFERENTIAL EQUATIONS)
- (*REENTRY VEHICLES
- AERODYNAMIC HEATING)
- (*ATMOSPHERE ENTRY
- HYPERSONIC CHARACTERISTICS)
- PROBLEM SOLVING
- HEAT TRANSFER
- BOUNDARY VALUE PROBLEMS
- BLUNT BODIES
- SHOCK WAVES
- STAGNATION POINT
- THERMAL RADIATION
- ONE DIMENSIONAL FLOW
- PERTURBATION THEORY
- COMPUTER PROGRAMS
- DIFFERENCE EQUATIONS

# Subject Categories:

- Numerical Mathematics
- Guided Missiles
- Fluid Mechanics
- Thermodynamics