| 奇性方腔黏性流动的完全高精度紧致差分方法 |
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| 引用本文： | 王晓峰,袁合才. 奇性方腔黏性流动的完全高精度紧致差分方法[J]. 河南师范大学学报(自然科学版), 2012, 40(6): 14-18,22 |
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| 作者姓名： | 王晓峰 袁合才 |
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| 作者单位： | 河南科技学院数学科学学院,河南新乡453003;华北水利水电学院数学与信息科学学院,郑州450045 |
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| 基金项目： | 河南省教育厅自然科学研究项目 |
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| 摘 要： | 以涡量流函数形式的Navier-Stokes(N-S)方程为例,详细介绍了构造完全高精度紧致差分格式的一般方法.所建立的高精度差分格式,无论是在计算区域的内点还是在边界点上均可以达到4阶精度,且具有紧致性,与已有数值实验结果相比只需要用很少的网格(61×61)就可以求得较高计算精度的数值解,从而大大节省了计算时间,提高了计算效率.
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| 关 键 词： | 奇性方腔 完全高精度 紧致差分格式 伪时间导数 |
Fully Fourth-order Compact Finite Difference Schemes for Viscous Flow in Singular Square Cavity |
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| WANG Xiao-feng , YUAN He-cai. Fully Fourth-order Compact Finite Difference Schemes for Viscous Flow in Singular Square Cavity[J]. Journal of Henan Normal University(Natural Science), 2012, 40(6): 14-18,22 |
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| Authors: | WANG Xiao-feng YUAN He-cai |
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| Affiliation: | 1.School of Mathematical Sciences,Henan Institute of Science and Technology,Xinxiang 453003,China;2.College of Mathematics and Information Science,North China University of Water Conservancy and Electric Power,Zhengzhou 450045,China) |
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| Abstract: | This paper describes a fully higher-order compact finite difference scheme for solving 2D Navier-Stokes(N-S) equations representing streamfunction and vorticity form of the steady-state incompressible viscous fluid flows.The scheme maintains a fourth-order of spatial accuracy not only in the interior but also at the boundary.For the 2D driven cavity problem with known existing solutions,our coarse grids transient solutions are extremely close to the analytical ones even for high Reynolds numbers(Re=5 000).Comparisons are made with the established numerical results and excellent agreement is found in all the cases,both qualitatively and quantitatively. |
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| Keywords: | singular square cavity fully higher-order compact finite difference scheme pseudo-time derivative |
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