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Generalized Gas Dynamic Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Guo, Zhaoli |
| Copyright Year | 2009 |
| Abstract | In an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids 19, 016101 (2007)] to simulate nonequilibrium flows. In this paper, instead of using three temperatures in the x−, y−, and z-directions, we further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives the 10 moment closure equations of Levermore [C.D. Levermore, J. Stat. Phys 83, pp.1021 (1996)]. The derived gas dynamic equations can be considered as a regularization of Levermore’s 10 moments equations in the first-order expansion. Our new gas dynamic equations have the same structure as the Navier-Stokes equations, but the stress-strain relationship in the Navier-Stokes equations is replaced by an algebraic equation with temperature differences. At the same time, the heat flux, which is absent in Levermore’s 10 moment closure, is recovered. As a result, both the viscous and the heat conduction terms are unified under a single anisotropic temperature concept. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier-Stokes equations. Our gas dynamic equations are natural extensions of the Navier-Stokes equations to the near continuum flow regime and can be used for microflow computations. Two examples, the force-driven Poiseuille flow and the Couette flow in the transition flow regime, are used to validate the model. Both analytical and numerical results are encouraging. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.ust.hk/~makxu/PAPER/AIAA-2009-672-336-xu.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algebraic equation Bhatnagar–Gross–Krook operator Closure Computation First-order reduction Flow Genetic Translation Process Kinetics Laminar-turbulent transition Liquid substance Navier–Stokes equations Numerical analysis Simulation Time-scale calculus Triune continuum paradigm collision |
| Content Type | Text |
| Resource Type | Article |
