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摘 要:为解决带有复杂几何边界条件的高速流体计算问题,提出基于非结构网格的Gas-Kinetic方法.对于二维非结构网格,以三角形网格作为计算单元,形成在该网格控制单元中物理量导数求解的新方法.通过物理量导数得到在控制体积元边界上的通量,然后用每个计算时间步中求出的边界通量和控制体积元中的物理量,求出下一计算时间步所需的新物理量,依次进行计算直到计算结果收敛为止.采用NACA0012翼型进行数值计算验证,结果表明该方法简单高效,适用于低速和高速流体的计算.
关键词:非结构网格;Gas-Kinetic方法;可压缩流动
中图分类号:O35;O241;TP301.6;TB115
文献标志码:A
Gas-Kinetic method based on unstructured meshes
HE Bing1,FENG Weibing1,ZHANG Wu1,WU Pin1,BAI Wen2,LI Li2
(1. School of Computer Eng. & Sci.,Shanghai Univ.,Shanghai 200072,China;
2. Aeronautics Computing Technique Research Institute,China Aviation Industry Corp. I,Xi’an 710069,China)
Abstract:To solve the computation problem of high-speed fluid considering the condition of complicated geometrical boundary,a Gas-Kinetic method based on unstructured meshes is proposed. In the method,triangle mesh is taken as the computation element for 2D unstructured mesh,and a new method of solution on physical quantity derivatives in the mesh control elements is presented. The flux on the boundary of control volume units is obtained by physical quantity derivatives. Then the flux on boundary and the physical quantities in mesh control units,which are solved at each calculation time step,are used to solve the new physical quantities at the next calculation time step,and the calculation goes on in turn until the numerical results reach convergence. NACA0012 airfoil is used to validate the numerical computation and the results show that the method is simple and efficient. So it can be applied to the computation on low-speed and high-speed fluid.
Key words:unstructured mesh;Gas-Kinetic method;compressible flow
0 引 言
以Boltzmann方程为基础的流体力学计算方法最近成为CFD领域的研究热点,BGK模型在求解Boltzmann方程中有着重要作用.由于Boltzmann 方程从分子热运动的角度描述气体运动,因此BGK模型不仅适用于连续介质气体运动,还适用于稀薄气体运动的数值模拟,而且能很好求解复杂边界形状的流动问题.目前,求解BGK模型的方法主要有Lattice Boltzmann Method (LBM)[1,2]和Gas-Kinetic[3]方法.LBM在低速流体中应用广泛,发展比较成熟,但是对于高速流体问题,目前还没有很好的解决方法.Gas-Kinetic方法可以用于高速流体计算,从亚音速到高超音速问题均可进行计算.由于在计算实际问题时需要考虑复杂的几何边界条件,因此发展非结构网格方法[4]显得非常必要.本文提出1种基于非结构网格的Gas-Kinetic方法.该方法属于有限体积方法,其关键是求出控制体积元边界上的通量,在每个时间步中求出边界通量,可以用控制体积元中的物理量和边界上的通量求出下一时间步所需新的物理量,依次进行计算直到计算结果收敛为止.本文以三角形网格作为计算单元进行求解,数值计算结果验证该方法的正确性.
1 二维BGK模型
5 结 论
应用属于有限体积方法的Gas-Kinetic方法,在计算界面通量时用改进的TVD格式处理激波间断,并在计算过程中提出1种比较简单的处理非结构网格中物理量导数的方法,计算结果已验证计算的正确性.通过对NACA0012翼型从跨音速到超音速问题的计算表明Gas-Kinetic方法可以适用于从低速到高速的流体问题计算,具有很好的发展前景.
参考文献:
[1] QIAN Y H,D’HUMIèRES D,LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Lett,1992,17(6):479-484.
[2] CHEN Shiyi,DOOLEN G D. Lattice Boltzmann method for fluid flows[J]. Ann Rev Fluid Mech,1998,30:329-367.
[3] XU Kun. A Gas-Kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J]. J Comput Phys,2001,171(1):289-335.
[4] NI Guoxi,JIANG Song,XU Kun. Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes[J]. J Comput Phys,2008,227(6):3 015-3 031.
[5] 孙喜明,杨京龙,姚朝晖. BGK方法在非结构网格上的应用[J]. 计算物理,2002,19(6):9-15.
(编辑 廖粤新)
“本文中所涉及到的图表、注解、公式等内容请以PDF格式阅读原文”
关键词:非结构网格;Gas-Kinetic方法;可压缩流动
中图分类号:O35;O241;TP301.6;TB115
文献标志码:A
Gas-Kinetic method based on unstructured meshes
HE Bing1,FENG Weibing1,ZHANG Wu1,WU Pin1,BAI Wen2,LI Li2
(1. School of Computer Eng. & Sci.,Shanghai Univ.,Shanghai 200072,China;
2. Aeronautics Computing Technique Research Institute,China Aviation Industry Corp. I,Xi’an 710069,China)
Abstract:To solve the computation problem of high-speed fluid considering the condition of complicated geometrical boundary,a Gas-Kinetic method based on unstructured meshes is proposed. In the method,triangle mesh is taken as the computation element for 2D unstructured mesh,and a new method of solution on physical quantity derivatives in the mesh control elements is presented. The flux on the boundary of control volume units is obtained by physical quantity derivatives. Then the flux on boundary and the physical quantities in mesh control units,which are solved at each calculation time step,are used to solve the new physical quantities at the next calculation time step,and the calculation goes on in turn until the numerical results reach convergence. NACA0012 airfoil is used to validate the numerical computation and the results show that the method is simple and efficient. So it can be applied to the computation on low-speed and high-speed fluid.
Key words:unstructured mesh;Gas-Kinetic method;compressible flow
0 引 言
以Boltzmann方程为基础的流体力学计算方法最近成为CFD领域的研究热点,BGK模型在求解Boltzmann方程中有着重要作用.由于Boltzmann 方程从分子热运动的角度描述气体运动,因此BGK模型不仅适用于连续介质气体运动,还适用于稀薄气体运动的数值模拟,而且能很好求解复杂边界形状的流动问题.目前,求解BGK模型的方法主要有Lattice Boltzmann Method (LBM)[1,2]和Gas-Kinetic[3]方法.LBM在低速流体中应用广泛,发展比较成熟,但是对于高速流体问题,目前还没有很好的解决方法.Gas-Kinetic方法可以用于高速流体计算,从亚音速到高超音速问题均可进行计算.由于在计算实际问题时需要考虑复杂的几何边界条件,因此发展非结构网格方法[4]显得非常必要.本文提出1种基于非结构网格的Gas-Kinetic方法.该方法属于有限体积方法,其关键是求出控制体积元边界上的通量,在每个时间步中求出边界通量,可以用控制体积元中的物理量和边界上的通量求出下一时间步所需新的物理量,依次进行计算直到计算结果收敛为止.本文以三角形网格作为计算单元进行求解,数值计算结果验证该方法的正确性.
1 二维BGK模型
5 结 论
应用属于有限体积方法的Gas-Kinetic方法,在计算界面通量时用改进的TVD格式处理激波间断,并在计算过程中提出1种比较简单的处理非结构网格中物理量导数的方法,计算结果已验证计算的正确性.通过对NACA0012翼型从跨音速到超音速问题的计算表明Gas-Kinetic方法可以适用于从低速到高速的流体问题计算,具有很好的发展前景.
参考文献:
[1] QIAN Y H,D’HUMIèRES D,LALLEMAND P. Lattice BGK models for Navier-Stokes equation[J]. Europhysics Lett,1992,17(6):479-484.
[2] CHEN Shiyi,DOOLEN G D. Lattice Boltzmann method for fluid flows[J]. Ann Rev Fluid Mech,1998,30:329-367.
[3] XU Kun. A Gas-Kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method[J]. J Comput Phys,2001,171(1):289-335.
[4] NI Guoxi,JIANG Song,XU Kun. Efficient kinetic schemes for steady and unsteady flow simulations on unstructured meshes[J]. J Comput Phys,2008,227(6):3 015-3 031.
[5] 孙喜明,杨京龙,姚朝晖. BGK方法在非结构网格上的应用[J]. 计算物理,2002,19(6):9-15.
(编辑 廖粤新)
“本文中所涉及到的图表、注解、公式等内容请以PDF格式阅读原文”