气体动理论BGK格式的网格自适应方法
收稿日期: 2013-05-09
修回日期: 2013-09-13
网络出版日期: 2013-10-10
基金资助
国家“863”计划（2011AA7025042）
Adaptive Mesh Refinement for Gas-kinetic BGK Scheme
Received date: 2013-05-09
Revised date: 2013-09-13
Online published: 2013-10-10
Supported by
National High-tech Research and Development Program of China (2011AA7025042)
为了提高气体动理论BGK（Bhatnagr-Gross-Krook）格式在超声速流动问题计算时激波捕捉的准确性与计算效率，提出了一种适用于气体动理论BGK格式的网格自适应加密方法。该方法采用基于四边形的链表技术来描述网格的拓扑结构，在物理量重构过程中，使用了在四边形网格中表现优异的van Leer限制器，以保证粗细网格过渡处物理量重构的精度。用跨声速翼型绕流（马赫数Ma=0.85）、超声速前台阶流（Ma=3）和高超声速圆柱绕流（Ma=8.03）等多个典型算例验证了BGK自适应网格方法。计算结果表明，自适应网格BGK方法在保证数值精度的前提下，可大幅度提高计算效率。这为该方法用于高效地解决复杂问题提供了一种选择。
张贺 , 钟诚文 , 宫建 , 毕志献 , 韩曙光 . 气体动理论BGK格式的网格自适应方法[J]. 航空学报, 2014 , 35(3) : 687 -694 . DOI: 10.7527/S1000-6893.2013.0385
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.
[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.
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