基于非结构网络的翼身组合体绕流数值模拟
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摘要
非结构网格的生成与应用推动了CFD技术的发展，它使得针对复杂外形的
网格生成变得相对容易。通过控制背景网格，使非结构网格的尺度及疏密分布
随物面几何外形易于调整，与结构化网格相比，针对复杂外形的非结构网格质
量的根本改善大大提高了复杂外形绕流的流场计算精确度，这一网格生成方法
已经显示出是一种强有力的CFD技术。本文工作正是在这一技术发展背景下开
展的。
论文的工作包括以下几个方面：
（1）应用投影变换的方法生成了三维翼身组合体的表面网格。
（2）对决定三维非结构网格生成结果及疏密分布的背景网格生成技术做了深
入细致的研究，采用了三维空间多层背景网格，它是结合结构化Cartesian
和非结构背景网格各自优点的背景网格生成方法，通过本文实践证明，该
方法是成功的。
（3）由生成的三维初始推进面，应用推进阵面法完成了翼身组合体的三维空
间网格生成并尝试了一种新的推进选点准则，实践证明是可行的。应用网
格光顺技术，改进了初始生成的网格质量。
（4）应用格心格式的有限体积法对翼身组合体绕流进行了Euler方程的数值
模拟，同时引入各种加速收敛措施，与实验相比，得到了较为满意的计算
结果。
本文的工作表明，非结构网格生成及应用在计算流体力学中具有良好的发
展前景。
The Computational Fluid Dynamics (CFD) has been rapidly developed with the application of unstructured grids which makes it easier to generate the grids for complex geometries by controlling the background girds , it is pretty easy to refine the size and distribution of unstructured grids The computation accuracy of flow over complex geometries can be greatly enhanced due to the improvement of grid quality . The method has been shown that it is a very powerfiil technique for CFD.
This paper presents some works based on the unstructured grids, the main works of the paper are as follows:
1) generating the surface unstructured grids for combination of wing-body by means of projection transformation
2) A multi-domain method of grid generation is adopted to control quality and distribution of the unstructured grids , the method combines the advantage of both structured Cartesian and unstructured background grids.
3) generating the 3-D unstructured grids for the combination of wing-body by means of AFM (Advancing Front Method ) . using a new criterion for selecting the optimum point . The method is proved to be feasible . The grid quality is better than original method by means of deleting some small and distorted?elements and smoothing technique.
4) the EULER equation is solved for the combination of wingbody by means of the finite volume method on the unstructured grids . Several methods are used for quick convergence and the results are in correspondence with the experiment data.
What is done in the paper shows that the unstructured grid has the great potential power and it will be more widely used in the Computational Fluid Dynamics (CFD) in the future.
网格生成变得相对容易。通过控制背景网格，使非结构网格的尺度及疏密分布
随物面几何外形易于调整，与结构化网格相比，针对复杂外形的非结构网格质
量的根本改善大大提高了复杂外形绕流的流场计算精确度，这一网格生成方法
已经显示出是一种强有力的CFD技术。本文工作正是在这一技术发展背景下开
展的。
论文的工作包括以下几个方面：
（1）应用投影变换的方法生成了三维翼身组合体的表面网格。
（2）对决定三维非结构网格生成结果及疏密分布的背景网格生成技术做了深
入细致的研究，采用了三维空间多层背景网格，它是结合结构化Cartesian
和非结构背景网格各自优点的背景网格生成方法，通过本文实践证明，该
方法是成功的。
（3）由生成的三维初始推进面，应用推进阵面法完成了翼身组合体的三维空
间网格生成并尝试了一种新的推进选点准则，实践证明是可行的。应用网
格光顺技术，改进了初始生成的网格质量。
（4）应用格心格式的有限体积法对翼身组合体绕流进行了Euler方程的数值
模拟，同时引入各种加速收敛措施，与实验相比，得到了较为满意的计算
结果。
本文的工作表明，非结构网格生成及应用在计算流体力学中具有良好的发
展前景。
The Computational Fluid Dynamics (CFD) has been rapidly developed with the application of unstructured grids which makes it easier to generate the grids for complex geometries by controlling the background girds , it is pretty easy to refine the size and distribution of unstructured grids The computation accuracy of flow over complex geometries can be greatly enhanced due to the improvement of grid quality . The method has been shown that it is a very powerfiil technique for CFD.
This paper presents some works based on the unstructured grids, the main works of the paper are as follows:
1) generating the surface unstructured grids for combination of wing-body by means of projection transformation
2) A multi-domain method of grid generation is adopted to control quality and distribution of the unstructured grids , the method combines the advantage of both structured Cartesian and unstructured background grids.
3) generating the 3-D unstructured grids for the combination of wing-body by means of AFM (Advancing Front Method ) . using a new criterion for selecting the optimum point . The method is proved to be feasible . The grid quality is better than original method by means of deleting some small and distorted?elements and smoothing technique.
4) the EULER equation is solved for the combination of wingbody by means of the finite volume method on the unstructured grids . Several methods are used for quick convergence and the results are in correspondence with the experiment data.
What is done in the paper shows that the unstructured grid has the great potential power and it will be more widely used in the Computational Fluid Dynamics (CFD) in the future.
引文
[1] Rainald Lohner. "Generation of Three-Dimensional Unstructured Grids by the Advancing-Front Method" International Journal for Numerical Methods in Fluids. Vol.8 1135-1149 (1988)
[2] Shahyar Pizadenh. "Structured Background Grids for Generation of Unstructured Grids by Advancing-Front Method" AIAA Journal. Vol.31, No.2 February 1993
[3] 黄长征．乔志德． “跨音速流动的欧拉方程数值计算” 中国航空科技文献 HJL910078
[4] Parikh, P., Pirzadeh.S, and Lohner.R. "A Package for 3-D Unstructured Grids Generation Finite-Element Flow Solution and Flow Field Visualization" NASACR-182090, Sept. 1990
[5] Paul.Louis.George "The Advancing-Front Mesh Generation Method Revisited" Int. J. Num. Meth. Eng. Vol 37． 3605-3619 (1994)
[6] Peter. Hansbo "Generalized Laplacian Smoothing of Unstructured Grids" Communications in Numerical Methods in Engineering Vol.11, 455-464 (1995)
[7] 罗时钧． “跨音速无粘有旋流和有限体积法” 西北工业大学，上海交通大学讲义， 1984． 7
[8] Rainald Lohner. "Some Useful Data Structures for the Generation of Unstructured Grids" Communications in Applied Numerical Methods, Vol.4, 123-135 (1988)
[9] D.J.Mavriplis "Unstructured Mesh Generation and Adaptivity" ICASE (NASA-CR-195069) April (1995)
[10] W.Kyle Anderson "Grid Generation and Flow Solution Method for Euler Equations on Unstructured Grids" NASATM-4295
[11] Shahyar Pirzadeh. "Recent Progress in Unstructured Grid Generation" AIAA-92-0445
[12] S. H. Lo "Automatic Mesh Generation over Intersecting Surfaces" International Journal for Numerical Methods in Engineering Vol. 38, 943-954 (1995)
[13] Timothy D.Gatzke and Nigel P. Weatherill "Unstructured Grid Generation Using Interactive Three-Dimensional Boundary And Efficient Three-Dimensional Volume Methods" AIAA-93-3452-CP
[14] L.Stolcis, L.J.Johnston "Solution of the Euler Equations on Unstructured Grids for Two-Dimensional Compressible Flow" Aeronautical Journal. June/July 1990
[15] 朱自强等． “应用计算流体力学” 北京航空航天大学出版社．1998
[ 16] V.Parthasarathy and Y.Kallinderis "A New Multigrid Approach for 3D Unstructured, Adaptive Grids" AIAA 94-0078
[17] Chung-Jin Woan "Unstructured Surface Grid Generation on Unstructured Quilt of Patches23 AIAA 95-2202
[18] Hong Luo , Joseph D. Baum and Rainald Lohner "An Improved Finite Volume Scheme for Compressible Flows on Unstructured Grids" AIAA 95． 0348
[19] A.Jameson and D.Mavriplis "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh" AIAA-85-0435
[20] Carl Ollivier-Gooch "An Unstructured Mesh Improvement Toolkit with Application to Mesh improvement, Generation, and (De-)Refinement" AIAA 98-0218
[21] Merriam,M.L. "An Efficient Advancing Front Algorithm for Delaunay Triangulation" AIAA 91-0792
[22] M.Blanco and D.W.Zingg "A Fast Solver for the Euler Equations on Unstructured Grids Using a Newton-GMRES Method" AIAA 97-0331
[23] Paresh Parikh and Shahyar Pizadeh. "Unstructured Grid Solution To A Wing/pylon/store Configuration" Journal of Aircraft Vol. 31, No. 6, November-December 1994
[24] 宋曜利． “非结构化网格生成以及二维Euler方程数值解” 西北工业大学空气动力学硕士学位论文， 1997． 3
[25] 张小潘． “非结构网格生成及在机翼Euler方程计算中的应用” 西北工业大学空气动力学硕士学位论文， 1999． 3
[26] Leland H.Jorgensen and Edgar R.Nelson "experimental aerodynamic characteristic for slender bodies with thin wings and tail at angles of attack from 0°to 58° and mach numbers from 0． 6 to 2． 0" NASA TM X-3310
[2] Shahyar Pizadenh. "Structured Background Grids for Generation of Unstructured Grids by Advancing-Front Method" AIAA Journal. Vol.31, No.2 February 1993
[3] 黄长征．乔志德． “跨音速流动的欧拉方程数值计算” 中国航空科技文献 HJL910078
[4] Parikh, P., Pirzadeh.S, and Lohner.R. "A Package for 3-D Unstructured Grids Generation Finite-Element Flow Solution and Flow Field Visualization" NASACR-182090, Sept. 1990
[5] Paul.Louis.George "The Advancing-Front Mesh Generation Method Revisited" Int. J. Num. Meth. Eng. Vol 37． 3605-3619 (1994)
[6] Peter. Hansbo "Generalized Laplacian Smoothing of Unstructured Grids" Communications in Numerical Methods in Engineering Vol.11, 455-464 (1995)
[7] 罗时钧． “跨音速无粘有旋流和有限体积法” 西北工业大学，上海交通大学讲义， 1984． 7
[8] Rainald Lohner. "Some Useful Data Structures for the Generation of Unstructured Grids" Communications in Applied Numerical Methods, Vol.4, 123-135 (1988)
[9] D.J.Mavriplis "Unstructured Mesh Generation and Adaptivity" ICASE (NASA-CR-195069) April (1995)
[10] W.Kyle Anderson "Grid Generation and Flow Solution Method for Euler Equations on Unstructured Grids" NASATM-4295
[11] Shahyar Pirzadeh. "Recent Progress in Unstructured Grid Generation" AIAA-92-0445
[12] S. H. Lo "Automatic Mesh Generation over Intersecting Surfaces" International Journal for Numerical Methods in Engineering Vol. 38, 943-954 (1995)
[13] Timothy D.Gatzke and Nigel P. Weatherill "Unstructured Grid Generation Using Interactive Three-Dimensional Boundary And Efficient Three-Dimensional Volume Methods" AIAA-93-3452-CP
[14] L.Stolcis, L.J.Johnston "Solution of the Euler Equations on Unstructured Grids for Two-Dimensional Compressible Flow" Aeronautical Journal. June/July 1990
[15] 朱自强等． “应用计算流体力学” 北京航空航天大学出版社．1998
[ 16] V.Parthasarathy and Y.Kallinderis "A New Multigrid Approach for 3D Unstructured, Adaptive Grids" AIAA 94-0078
[17] Chung-Jin Woan "Unstructured Surface Grid Generation on Unstructured Quilt of Patches23 AIAA 95-2202
[18] Hong Luo , Joseph D. Baum and Rainald Lohner "An Improved Finite Volume Scheme for Compressible Flows on Unstructured Grids" AIAA 95． 0348
[19] A.Jameson and D.Mavriplis "Finite Volume Solution of the Two-Dimensional Euler Equations on a Regular Triangular Mesh" AIAA-85-0435
[20] Carl Ollivier-Gooch "An Unstructured Mesh Improvement Toolkit with Application to Mesh improvement, Generation, and (De-)Refinement" AIAA 98-0218
[21] Merriam,M.L. "An Efficient Advancing Front Algorithm for Delaunay Triangulation" AIAA 91-0792
[22] M.Blanco and D.W.Zingg "A Fast Solver for the Euler Equations on Unstructured Grids Using a Newton-GMRES Method" AIAA 97-0331
[23] Paresh Parikh and Shahyar Pizadeh. "Unstructured Grid Solution To A Wing/pylon/store Configuration" Journal of Aircraft Vol. 31, No. 6, November-December 1994
[24] 宋曜利． “非结构化网格生成以及二维Euler方程数值解” 西北工业大学空气动力学硕士学位论文， 1997． 3
[25] 张小潘． “非结构网格生成及在机翼Euler方程计算中的应用” 西北工业大学空气动力学硕士学位论文， 1999． 3
[26] Leland H.Jorgensen and Edgar R.Nelson "experimental aerodynamic characteristic for slender bodies with thin wings and tail at angles of attack from 0°to 58° and mach numbers from 0． 6 to 2． 0" NASA TM X-3310