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Numerical Simulations of Unsteady Flows From Rarefied Transition to Continuum Using Gas-Kinetic Unified Algorithm

Published online by Cambridge University Press:  21 July 2015

Junlin Wu ,
Zhihui Li ,
Aoping Peng  and
Xinyu Jiang
Junlin Wu
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
Zhihui Li*
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China National Laboratory for Computational Fluid Dynamics, Beijing 100191, China
Aoping Peng
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
Xinyu Jiang
Affiliation:
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
*
*Corresponding author. Email: zhli0097@x263.net (Z. H. Li)
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Abstract

Numerical simulations of unsteady gas flows are studied on the basis of Gas-Kinetic Unified Algorithm (GKUA) from rarefied transition to continuum flow regimes. Several typical examples are adopted. An unsteady flow solver is developed by solving the Boltzmann model equations, including the Shakhov model and the Rykov model etc. The Rykov kinetic equation involving the effect of rotational energy can be transformed into two kinetic governing equations with inelastic and elastic collisions by integrating the molecular velocity distribution function with the weight factor on the energy of rotational motion. Then, the reduced velocity distribution functions are devised to further simplify the governing equation for one- and two-dimensional flows. The simultaneous equations are numerically solved by the discrete velocity ordinate (DVO) method in velocity space and the finite-difference schemes in physical space. The time-explicit operator-splitting scheme is constructed, and numerical stability conditions to ascertain the time step are discussed. As the application of the newly developed GKUA, several unsteady varying processes of one- and two-dimensional flows with different Knudsen number are simulated, and the unsteady transport phenomena and rarefied effects are revealed and analyzed. It is validated that the GKUA solver is competent for simulations of unsteady gas dynamics covering various flow regimes.

Keywords

82C4074H15Unsteady flowcovering various flow regimeskinetic theory of gasesBoltzmann model equationgas-kinetic unified algorithmdiscrete velocity ordinate methodShakov kinetic modelRykov kinetic model
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 5 , October 2015 , pp. 569 - 596
Copyright
Copyright © Global-Science Press 2015 

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