2026-09-22T02:11:16Zhttps://ruor.uottawa.ca/server/oai/request

oai:ruor.uottawa.ca:10393/456572024-02-23T09:18:19Zcom_10393_242col_10393_11105

An Approximation for the Twenty-One-Moment Maximum-Entropy Model of Rarefied Gas Dynamics Giroux, Fabien McDonald, James Gerald Moment Closure Computational Fluid Dynamics Boltzmann Equation Maximum-Entropy 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 balance laws. In particular, the twenty-one moment model of the maximum-entropy hierarchy offers a hyperbolic treatment of viscous flows exhibiting heat transfer. This twenty-one moment model has the ability to provide accurate solutions where the Navier-Stokes equations lose physical validity due to the solution being too far from local equilibrium. Furthermore, its first-order hyperbolic nature offers the potential for improved numerical accuracy as well as a decreased sensitivity to mesh quality. Unfortunately, higher-order maximum-entropy closures cannot be expressed in closed form. The only known affordable option is to propose approximations. Previous approximations to the fourteen-moment maximum-entropy model have been proposed [McDonald and Torrilhon, 2014]. Although this fourteen-moment model also predicts viscous flow with heat transfer, the necessary moments to close the system renders it more difficult to approximate accurately than the twenty-one moment model. The proposed approximation for the fourteen-moment model also has realizable states for which hyperbolicity is lost. Unfortunately, the velocity distribution function associated with the twenty-one moment model is an exponential of a fourth-order polynomial. Such a function cannot be integrated in closed form, resulting in closing fluxes that can only be obtained through complex numerical methods. The goal of this work is to present a new approximation to the closing fluxes that respect the maximum-entropy philosophy as closely as possible. Preliminary results show that a proposed approximation is able to provide shock predictions that are in good agreement with the Boltzmann equation and surpassing the prediction of the Navier-Stokes equations. Furthermore, Couette flow results as well as lid-driven cavity flows are computed using a novel approach to Knudsen layer boundary conditions. A dispersion analysis as well as an investigation of the hyperbolicity of the model is also shown. The Couette flow results are compared against Navier-Stokes and the free-molecular analytical solutions for a varying Knudsen number, for which the twenty-one moment model show good agreement over the domain. The shock-tube problem is also computed for different Knudsen numbers. The results are compared with the one obtained by directly solving the BGK equation. Finally, the lid-driven cavity flow computed with the twenty-one moment model shows good agreement with the direct simulation Monte-Carlo (DSMC) solution. 2023-11-23T14:51:41Z 2023-11-23T14:51:41Z 2023-11-23 Thesis http://hdl.handle.net/10393/45657 http://dx.doi.org/10.20381/ruor-29861 en Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Université d'Ottawa / University of Ottawa