An Approximation for the Twenty-One-Moment Maximum-Entropy Model of Rarefied Gas Dynamics. Issue 8 (14th September 2021)

• Record Type: Journal Article
• Authors: Giroux, Fabien; McDonald, James G.
• Is Part Of: International journal of computational fluid dynamics. Volume 35:Issue 8(2021)
• Page Start: 632
• Page End: 652
• Publication Date: 2021-09-14
• Subjects: Boltzmann equation -- maximum-entropy -- moment closure -- rarefied gas-dynamic -- kinetic theory; Primary: 82C40 -- 35Q20 -- 35Q35 -- 78M05 -- Secondary: 35L40; Fluid dynamics -- Data processing -- Periodicals; 532.05
• DOI: 10.1080/10618562.2022.2047666
• Languages: English
• ISSNs: 1061-8562

Abstract

Abstract : The use of moment-closure methods to predict continuum and moderately rarefied flow offers many modelling and numerical advantages over traditional methods. The maximum-entropy family of moment closures offers models described by hyperbolic systems of equations. In particular, the twenty-one moment model of the maximum-entropy hierarchy offers a hyperbolic treatment of viscous flows exhibiting heat transfer. This model has the ability to provide accurate solutions where the Navier–Stokes equations lose physical validity. Furthermore, its first-order hyperbolic nature offers the potential for improved numerical accuracy as well as a decreased sensitivity to mesh quality. Unfortunately, the distribution function associated with the 21 moment model is an exponential of a fourth-order polynomial. Such a function cannot be integrated in closed form, resulting in unobtainable closing fluxes. This work presents an approximation to the closing fluxes that respects the maximum-entropy philosophy as closely as possible. The proposed approximation is able to provide shock predictions in good agreement with the Boltzmann equation and surpassing the prediction of the Navier–Stokes equations. A dispersion analysis as well as an investigation of the hyperbolicity of the model is also shown.