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Image of Journal of Applied Nonlinear Dynamics
ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Gas-Kinetic Unified Algorithm for Aerodynamics Covering Various Flow Regimes Using Computable Modeling of Boltzmann Equation

Journal of Environmental Accounting and Management 11(3) (2023) 243--269 | DOI:10.5890/JEAM.2023.09.001

Zhihui Li$^{1,3}$, Zheng Han$^1$, Aoping Peng$^{2,3}$, Junlin Wu${}^{2,3}$, Xuguo Li${}^{2,3}$

$^1$ National Laboratory for Computational Fluid Dynamics, Beihang University (BUAA), Beijing 100191, China

$^2$ Laboratory of Aerodynamics in Multiple Flow Regimes, CARDC, Mianyang, SiChuan, 621000, China

$^3$ China Aerodynamics Research and Development Center, P.O.Box 211, Mianyang 621000, China

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Abstract

The gas-kinetic unified algorithm solving the Boltzmann modeling velocity distribution function equation is developed and employed to study gas dynamic problems covering various flow regimes. Based on the computable modeling of Boltzmann equation, the modeled velocity distribution function equation covering to various flow regimes is presented. The discrete velocity ordinate method is developed and applied to remove the velocity space dependency of the distribution function. Based on the uncoupling technique on molecular movement and collision in the DSMC method, the gas-kinetic finite difference scheme is constructed to directly solve the discrete velocity distribution functions by using the unsteady time-splitting method from computational fluid dynamics. The discrete velocity numerical integration method with the Gauss-type weight function is developed to evaluate the macroscopic flow variables at each point in the physical space. The parallel implementation for the gas-kinetic numerical method is investigated to solve the three-dimensional complex flows. To validate the accuracy and feasibility of the present numerical method, one-dimensional shock wave problems, supersonic flows past two-dimensional circular cylinder and three-dimensional hypersonic flows past sphere and spacecraft shape covering various flow regimes are simulated with different Knudsen numbers and Mach numbers. The computational results are found in good agreement with the related theoretical, DSMC, N-S, and experimental data. The computing practice has confirmed that the present gas-kinetic algorithm probably provides a promising approach to resolve the hypersonic aerothermodynamics problems with the complete spectrum of flow regimes from the gas-kinetic point of view of solving the unified Boltzmann model equation.

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