Shockwave structure at the thirteenmoment level based on a spatially varying weight function
Abstract
The distribution function is expanded in a polynomial series with Maxwellian weight function to which two simple transformations are applied. The first is to replace the local temperature appearing in the weight function by a characteristic temperature related to the local stagnation temperature, so that Bessel's inequality guarantees convergence of the expansion; convergence is demonstrated by carrying out the singularpoint analysis to high order. The second is to displace the mean of the weight function from its usual position at the fluid velocity, so that the outer regions of f are more faithfully represented and convergence is accelerated, as is demonstrated by comparing the thirteenmoment singularpoint solution with the highorder results obtained previously. Using the proposed thirteenmoment closure relations, Maxwell's moment equations are numerically integrated to obtain shock wave density profiles for two molecular models. Results for Maxwell molecules are in agreement with numerical solutions of Yen and Bird, while those for a realistic molecular model agree quite well with Alsmeyer's experimental results for argon.
 Publication:

Shock Tube and Shock Wave Research
 Pub Date:
 1978
 Bibcode:
 1978stsw.proc..172E
 Keywords:

 Distribution Functions;
 Series Expansion;
 Shock Wave Profiles;
 Weighting Functions;
 Bessel Functions;
 Convergence;
 MaxwellBoltzmann Density Function;
 Stagnation Temperature;
 Atomic and Molecular Physics