Developing Hybrid cell-edge and cell-node Dissipative Compact Scheme for Complex Geometry Flows

详细信息    查看全文

• 作者：XiaoGang Deng (1) (2)
  Yi Jiang (1) (3)
  MeiLiang Mao (1) (3)
  HuaYong Liu (1)
  GuoHua Tu (1)
  
• 关键词：high ; order compact scheme ; Hybrid cell ; edge and cell ; node Dissipative Compact Scheme (HDCS) ; Weighted Compact Nonlinear Scheme (WCNS) ; Complex Geometry ; Geometric Conservation Law (GCL)
• 刊名：SCIENCE CHINA Technological Sciences
• 出版年：2013
• 出版时间：October 2013
• 年：2013
• 卷：56
• 期：10
• 页码：2361-2369
• 全文大小：999KB
• 参考文献：1. Tim C, Lele S K. Computational aeroacoustics: progress on nonlinear problems of sound generation. Prog Aerosp Sci, 2004, 40: 345鈥?16 CrossRef
  2. Ghosal S. An analysis of numerical errors in large-eddy simulations of turbulence. J Comput Phys, 1996, 125:187鈥?06 CrossRef
  3. Lele S K. Compact finite difference schemes with spectral-like resolution. J Comput Phys, 1992, 103: 16鈥?2 CrossRef
  4. Rizzetta D, Visbal M, Morgan P. A high-order compact finite-dierence scheme for large-eddy simulation of active flow control. Prog Aerosp Sci, 2008, 44: 397鈥?26 CrossRef
  5. Fu D X, Ma Y W. A high-order accurate difference schemes for complex flow fields. J Comput Phys, 1997, 134: 1鈥?5 CrossRef
  6. Deng X G, Maekawa H, Shen Q. A class of high-order dissipative compact schemes. AIAA paper 96-1972, 1996
  7. Deng X G, Zhang H X. Developing high-order weighted compact nonlinear schemes. J Comput Phys, 2000, 165: 22鈥?4 CrossRef
  8. Deng X G, Maekawa H. Compact high-order accurate nonlinear schemes. J Comput Phys, 1997, 130: 77鈥?1 CrossRef
  9. Harten A, Engquist B, Osher S, et al. Uniformly high-order essentially non-oscillatory schemes, III. J Comput Phys, 1987, 71: 231鈥?03 CrossRef
  10. Jiang G, Shu C W. Efficient implementation of weighted ENO. J Comput Phys, 1996, 181: 202鈥?28 CrossRef
  11. Wang Z J. High-order methods for the Euler and Navier-Stokes equations on unstructured grids. Prog Aerosp Sci, 2007, 43: 1鈥?1 CrossRef
  12. Deng X G, Mao M L, Tu G H, et al. Geometric conservation law and applications to high-order finite difference schemes with stationary grids. J Comput Phys, 2011, 230: 1100鈥?115 CrossRef
  13. Deng X G, Min Y B, Mao M L, et al. Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids. J Comput Phys, 2013, 239: 90鈥?11 CrossRef
  14. Deng X G, Mao M L, Jiang Y, et al. New high-order hybrid cell-edge and cell-node weighted compact nonlinear schemes. AIAA paper 2011-3857, 2011
  15. Thomas L G, Xavier G, Christophe C. Multi-size-mesh, multi-time-step algorithm for noise computation around an airfoil in curvilinear meshes. AIAA 2007-3504, 2007
  16. Bodony D J. Analysis of sponge zones for computational fluid mechanics. J Comput Phys, 2006, 212: 681鈥?02 CrossRef
  17. Deng X G, Mao M L, Tu G H, et al. Extending weighted compact nonlinear schemes to complex grids with characteristic-based interface conditions. AIAA J, 2010, 48: 2840鈥?851 CrossRef
  18. Verhaagen N G, Elsayed M. Leading-edge radius effects on 50掳 delta wing flow. AIAA paper 2 2009-540, 2009
  19. Jameson A. Time dependent calculations using multigrid with applications to unsteady flows past airfoils and wings. AIAA Paper 91-1596, 1991
  20. Jiang Y, Deng X G, Mao M L, et al. Large eddy simulation based on seventh-order dissipative compact scheme. The Ninth Asian Computational Fluid Dynamics Conference, Nanjing, China, 2012
  
• 作者单位：XiaoGang Deng (1) (2)
  Yi Jiang (1) (3)
  MeiLiang Mao (1) (3)
  HuaYong Liu (1)
  GuoHua Tu (1)
  
  1. State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang, 621000, China
  2. National University of Defense Technology, Changsha, 410073, China
  3. China Aerodynamics Research and Development Center, P.O. Box 211, Mianyang, 621000, China
  
• ISSN：1869-1900

文摘

Developing high resolution finite difference scheme and enabling the use of this scheme on complex geometry are the aims of this study. High resolution has been achieved by Dissipative Compact Schemes (DCS), however, according to the recent research, applications of DCS on complex geometry may have serious problem for that the Geometric Conservation Law (GCL) is not satisfied, and this may cause numerical instability. To cope with this problem, a new scheme named Hybrid cell-edge and cell-node Dissipative Compact Scheme (HDCS) has been formulated. The formulation of the HDCS contains two steps. First, a new central compact scheme is formulated for the purpose of conveniently fulfilling the GCL, and then dissipation is added on the central scheme by high-order dissipative interpolation of cell-edge variables. The solutions of Euler and Navier-Stokes equations show that the HDCS can be applied successfully on complex geometry, while the DCS may suffer numerical instabilities. Moreover, high resolution of the HDCS may be observed in the test of scattering of acoustic waves by multiple cylinders.