Published online by Cambridge University Press: 12 August 2004
Recently a new system of field equations for the accurate description of flows in rarefied gases, called regularized 13-moment equations, was obtained by means of a hybrid gas kinetic approach. The first part of this paper discusses the relationship of the new system to classical high-order theories like the Burnett and super-Burnett equations as well as to modified models like the augmented and regularized Burnett equations. In the second part, shock structure calculations with the new theory are presented and compared to direct-simulation Monte Carlo (DSMC) solutions and to solutions of the Burnett models. Owing to additional higher-order dissipation in the system, the profiles are smooth for any Mach number, in contrast to the results of Grad's 13-moment case. The results show reliable quantitative agreement with DSMC simulations for Mach numbers up to $M_{0}\approx 3.0$. The agreement is better for Maxwell molecules than for hard spheres. The results of the augmented Burnett equations are comparable, but these equations are shown to be spatially unstable. Additionally, a validiation procedure for the new equations is presented by investigating the positivity of Grad's distribution function.
To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.
To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.