CONSTRUCRION AND ANALYSIS OF A NEW COMPUTABLE MODEL FOR BOLTZMANN EQUATION

Peng Aoping; Li Zhihui; Wu Junlin; Pi Xingcai; Jiang Xinyu

doi:10.6052/0459-1879-21-104

Volume 53 Issue 9

Sep. 2021

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Chinese Journal of Theoretical and Applied Mechanics > 2021 > 53(9): 2582-2594. > DOI: 10.6052/0459-1879-21-104 CSTR: 32045.14.0459-1879-21-104

Peng Aoping, Li Zhihui, Wu Junlin, Pi Xingcai, Jiang Xinyu. Construcrion and analysis of a new computable model for Boltzmann equation. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2582-2594. DOI: 10.6052/0459-1879-21-104

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CONSTRUCRION AND ANALYSIS OF A NEW COMPUTABLE MODEL FOR BOLTZMANN EQUATION

*.
Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, Sichuan, China
†.
National Laboratory for Computational Fluid Dynamics, Beihang University, Beijing 100191, China

Received Date: March 16, 2021
Accepted Date: July 22, 2021
Available Online: July 23, 2021

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Abstract

Abstract

Due to large differences of geometric scale between the components of near space vehicles, the multi-scale complex non-equilibrium flow phenomenon will appear in many flow field regions when vehicles flying at high Mach number and high altitudes. In those regions the gas molecular velocity distribution functions are related to the local molecular velocities and macroscopic parameters, such as velocities, temperatures, heat flux vectors and stress tensors. By analyzing the first-order Chapman−Enskog approximate solution of Boltzmann equation, a new computable collision relaxation model is constructed, which considers the influence of heat flux vector and stress tensor, and satisfies the high-order collision moments of Boltzmann equation. The basic properties such as conservation law and H theorem are analyzed mathematically. The compatibility between the new model equation and Boltzmann equation is proved. The relationships between the new model and old models such as Shakhov and Belyi models are given. The expression of the collision relaxation parameter is determined by using molecular collision dynamics. As examples, one dimensional shock profiles and two dimensional flows around a flat plate and two side-by-side cylinders in near space environments are simulated by gas kinetic unified algorithm with different models. By comparing with results of DSMC method, it shows that in one dimensional problems the results of Shakhov model with heat flux is better than the new model because of smaller 1D shear stress, but in two dimension the new model can capture the position of shock wave better than the other two models due to higher dimensional shear stresses leading to more distinct viscosity effect. Especially for macro parameters in shock waves, the results of the new model accord with those of DSMC better. Then the validity and reliability of the new model is verified. These results illuminate that the collision relaxation model is influenced by multi-parameters together in the flow field when the non-equilibrium effects are quite distinct.

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References

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