## 留言板

 引用本文: 林建国, 谢志华, 周俊陶. 任意精度的三点紧致显格式及其在CFD中的应用[J]. 应用数学和力学, 2007, 28(7): 843-852.
LIN Jian-guo, XIE Zhi-hua, ZHOU Jun-tao. Three-Point Explicit Compact Difference Scheme With Arbitrary Order of Accuracy and Its Applicatin in CFD[J]. Applied Mathematics and Mechanics, 2007, 28(7): 843-852.
 Citation: LIN Jian-guo, XIE Zhi-hua, ZHOU Jun-tao. Three-Point Explicit Compact Difference Scheme With Arbitrary Order of Accuracy and Its Applicatin in CFD[J]. Applied Mathematics and Mechanics, 2007, 28(7): 843-852.

## 任意精度的三点紧致显格式及其在CFD中的应用

###### 作者简介:林建国(1960- ),男,大连人,教授,博士生导师(联系人.Tel:+86-411-82931948;Fax:+86-411-84727632;E-mail:ljglin@126.com).
• 中图分类号: O241.82；X145

## Three-Point Explicit Compact Difference Scheme With Arbitrary Order of Accuracy and Its Applicatin in CFD

• 摘要: 通过在泰勒级数展开中运用逐阶迭代的方法，推导出了空间任意精度的三点紧致显格式的表达式，又由Fourier分析法得到了格式的数值弥散和耗散特性．与以往的高精度紧致差分格式不同，提出的格式不用隐式求解代数方程组并且可以达到任意精度．通过方波问题和顶盖方腔流的算例表明，格式在稀疏网格下可以得到很高的精度，不仅能节省计算量，而且易于编程，有很高的计算效率．
•  [1] Carpenter M H, Gottlieb D, Abarbanel S. The stability of numerical boundary treatments for compact high-order finite-difference schemes[J].Journal of Computational Physics,1993,108(2):272-295. [2] Lele S K. Compact finite difference schemes with spectral-like resolution[J].Journal of Computational Physics,1992,103(1):16-42. [3] Chu P C, FAN Chen-wu.A three-point combined compact difference scheme[J].Journal of Computational Physics,1998,140(2):370-399. [4] Mahesh K. A family of high order finite difference schemes with good spectral resolution[J].Journal of Computational Physics,1998,145(1):332-358. [5] Hixon R. Prefactored small-stencil compact schemes[J].Journal of Computational Physics,2000,165(2):522-541. [6] Tolstykh A I, Lipavskii M V.On performance of methods with third- and fifth-order compact upwind differencing[J].Journal of Computational Physics,1998,140(2):205-232. [7] MA Yan-wen, FU De-xun, Kobayashi N,et al.Numerical solution of the incompressible Navier-Stokes equations with an upwind compact difference scheme[J].International Journal for Numerical Methods in Fluids,1999,30(5):509-521. [8] MA Yan-wen, FU De-xun.Analysis of super compact finite difference method and application to simulation of vortex-shock interaction[J].International Journal for Numerical Methods in Fluids,2001,36(7):773-805. doi: 10.1002/fld.155 [9] Boersma B J. A staggered compact finite difference formulation for the compressible Navier-Stokes equations[J].Journal of Computational Physics,2005,208(2):675-690. [10] 袁湘江,周恒.计算激波的高精度数值方法[J].应用数学和力学,2000,21(5):441-450. [11] 刘儒勋,吴玲玲.非线性发展方程的小模板简化pade格式[J]. 应用数学和力学,2005,26(7):801-809. [12] Fomberg B, Ghrist M. Spatial finite difference approximations for wave-type equation[J].SIAM Journal on Numerical Analysis,1999,37(1):105-130. [13] 林建国,邱大洪.二阶非线性与色散性的Boussinesq类方程[J]. 中国科学,E辑,1998,28(6):567-573. [14] Spotz W F. High order compact finite difference schemes for computational mechanics[D].Austin:University of Texas, 1995. [15] Kalita J C, Dalal D C, Dass A K.A class of higher order compact schemes for the unsteady two-dimensional convection diffusion equation with variable convection coefficients[J].International Journal for Numerical Methods in Fluids,2002,38(12):1111-1131. doi: 10.1002/fld.263 [16] Ghia U, Ghia K N,Shin C T.High-Re solutions for imcompressible flow using the Navier-Stokes equation and a multigrid method[J].Journal of Computational Physics,1982,48(3):387-411.

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##### 出版历程
• 收稿日期:  2006-05-15
• 修回日期:  2007-04-26
• 刊出日期:  2007-07-15

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