气体动理论BGK格式的网格自适应方法

doi:10.7527/S1000-6893.2013.0385

Abstract

Abstract:

An adaptive mesh refinement method based on the gas-kinetic BGK (Bhatnagr-Gross-Kroor) scheme is proposed in this paper to improve the accuracy and computational efficiency of gas-kinetic BGK schemes for shock capturing. In the present work, a linked list based on a quadrilateral is applied to describe the topology of the meshes. In the reconstruction stage, the van Leer limiter is introduced to ensure the accuracy of physical quantities reconstruction at the interface between the coarse meshes and the refined meshes. Some cases from transonic airfoil flow (Mach number Ma=0.85), supersonic flow over forward-facing step (Ma=3) to hypersonic flow around a cylinder (Ma=8.03) are presented to verify the adaptive mesh method for the BGK scheme. It is found that the proposed method can greatly improve the computational efficiency without reducing accuracy. The approach provides a numerical technique for the BGK scheme to compute complex flows efficiently.

Key words: BGK, gas-kinetic scheme, quadrilateral mesh, adaptive mesh refinement, hypersonic flow, airfoil

CLC Number:

V211.3
O354

ZHANG He, ZHONG Chengwen, GONG Jian, BI Zhixian, HAN Shuguang. Adaptive Mesh Refinement for Gas-kinetic BGK Scheme[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2014, 35(3): 687-694.

References

[1] Xu K. A gas-kinetic BGK scheme for the Naver-Stokes equations and its connection with artificial dissipation and Godunov method[J]. Journal of Computational Physics, 2001, 171(1): 289-335.

[2] Manuel T, Xu K. Stability and consistency of kinetic upwinding for advection-diffusion equations[J]. Journal of Numerical Analysis, 2006, 26(1): 686-722.

[3] Chit O J, Omar A A, Asrar W, et al. Hypersonic flow simulation by the gas-kinetic Bhatnagr-Gross-Krook[J]. AIAA Journal, 2005, 43(7): 1427-1433.

[4] Li Z H, Zhang H X. Gas-kinetic unified algorithm for aerodynamics from rarefied to continuum flow regime using Boltzmann model equation, AIAA-2006-1175[R]. Res-ton: AIAA, 2006.

[5] Xu K, Josyula E. Gas-kinetic scheme for rarefied flow simulation[J]. Mathematics and Computers in Simulation, 2006, 72(2): 253-256.

[6] Cai C P, Tang H Z, Xu K. Gas-kinetic BGK scheme for three dimensional magnetohydrodynamics, AIAA-2007-1441[R]. Reston: AIAA, 2007.

[7] Xu K, Li Z H. Microchannel flow in the slip regime: gas-kinetic BGK-Burnett solutions[J]. Journal of Fluid Mechanics, 2004, 513(1): 87-110.

[8] Li Z H, Zhang H X, Fu S. Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation[J]. Science in China Series G-Physics, Mechanics & Astronomy, 2005, 48(4): 496-512.

[9] Li Q B, Xu K, Fu S. A high-order gas-kinetic Navier-Stokes flow solver[J]. Journal of Computational Physics, 2010, 229 (1): 6715-6731.

[10] Liu S, Zhong C W. Modified unified kinetic scheme for all flow regimes[J]. Physical Review E, 2012, 85(6): 066705.

[11] Xu K, Huang J C. A unified gas-kinetic scheme for con-tinuum and rarefied flows[J]. Journal of Computational Physics, 2010, 229(20): 7747-7764.

[12] Kim C A, Jameson A, Martinelli L, et al. An accurate LED-BGK solver on unstructured adaptive meshes, AIAA-1997-328[R]. Reston: AIAA, 1997.

[13] Ni G X, Jiang S, Xu K. Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes[J]. Journal of Computational Physics, 2008, 227(1): 3015-3031.

[14] Shen Q. Rarefied gas dynamics[M]. Beijing: National Defense Industry Press, 2003: 45. (in Chinese) 沈青. 稀薄气体动力学[M]. 北京: 国防工业出版社, 2003: 45.

[15] Darren L, De Z. A quadtree-based adaptively-refined Cartesian-grid algorithm for solution of the Euler equations[D]. Ann Arbor: Department of Aerospace Engineering, the University of Michigan, 1993.

[16] Woodward P, Colella P. The numerical simulation of two dimensional fluids with strong shock[J]. Journal of Computational Physics, 1984, 54(1): 115-173.

[17] Xiong S W, Zhong C W, Zhuo C S, et al. Numerical simulation of flow around an airfoil with gas-kinetic BGK scheme[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(6): 1099-1105. (in Chinese) 熊生伟, 钟诚文, 卓丛山, 等. 气体运动论BGK格式的翼型绕流数值模拟[J]. 航空学报, 2010, 31(6): 1099-1105.

[18] Wieting A R. Experimental study of shock wave interface heating on a cylindrical leading edge, NASA TM-100484[R]. Hampton, V A: NASA Langley Research Center, 1987.

[19] Yoshihara H, Sacher P. Test cases for inviscid flow field methods, AGARD AR-211[R]. Langley Field, V A: AGARD, 1985.

Adaptive Mesh Refinement for Gas-kinetic BGK Scheme

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