A perturbation expansion of the NavierStokes equations for shock waves
Abstract
A systematic perturbation expansion is developed for the steadystate NavierStokes equations describing shock propagation in an ideal gas. The temperature dependence of the viscosity and thermal conductivity is accounted for, though the specific heat and Prandtl number are assumed constant. It is shown that if the first n1 terms in the expansion are known, the n th term can always be expressed in terms of a quadrature. Explicit calculation of the expansion is carried out to second order in the shock strength, and the results are compared with a specialcase exact calculation. It is shown that the results are in surprisingly good agreement with the exact calculation even for rather strong shock waves. The effect on shock structure of the temperaturedependent transport coefficients is discussed.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 September 1976
 Bibcode:
 1976STIN...7718411P
 Keywords:

 Hydrodynamics;
 NavierStokes Equation;
 Perturbation Theory;
 Shock Waves;
 Gas Dynamics;
 Specific Heat;
 Thermal Conductivity;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer