Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T08:21:57.290Z Has data issue: false hasContentIssue false
  • English
  • Français

A Hybrid Method for Dynamic Mesh Generation Based on Radial Basis Functions and Delaunay Graph Mapping

Published online by Cambridge University Press:  28 May 2015

Li Ding ,
Tongqing Guo  and
Zhiliang Lu
Li Ding
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
Tongqing Guo
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
Zhiliang Lu*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
*
*Corresponding author. Email: [email protected] (Z. L. Lu)
Get access

Abstract

Aiming at complex configuration and large deformation, an efficient hybrid method for dynamic mesh generation is presented in this paper, which is based on Radial Basis Functions (RBFs) and Delaunay graph mapping. Based on the computational mesh, a set of very coarse grid named as background grid is generated firstly, and then the computational mesh can be located at the background grid by Delaunay graph mapping technique. After that, the RBFs method is applied to deform the background grid by choosing partial mesh points on the boundary as the control points. Finally, Delaunay graph mapping method is used to relocate the computational mesh by employing area or volume weight coefficients. By applying different dynamic mesh methods to a moving NACA0012 airfoil, it can be found that the RBFs-Delaunay graph mapping hybrid method is as accurate as RBFs and is as efficient as Delaunay graph mapping technique. Numerical results show that the dynamic meshes for all test cases including one two-dimensional (2D) and two three-dimensional (3D) problems with different complexities, can be generated in an accurate and efficient manner by using the present hybrid method.

Keywords

65Z05Dynamic mesh methodhybrid methodbackground gridradial basis functionsdelaunay graph mapping
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015 , pp. 338 - 356
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Byun, C. and Guruswamy, G. P., A parallel, multi-block, moving grid method for aeroelastic applications on full aircraft, AIAA Paper 98-4782, September 1998.Google Scholar
[2]Reuther, J., Jameson, A., Farmer, J., Martinelli, L. and Saunders, D., Aerodynamics shape optimization of complex aircraft configurations via an adjoint formulation, AIAA Paper 960094, January 1996.Google Scholar
[3]Jones, W. T. and Samareh-Abolhassani, J., A grid generation system for multi-disciplinary design optimization, AIAA Paper 95-1689, June 1995.Google Scholar
[4]Huang, W., Lu, Z. L. and Guo, T. Q.et al., Numerical method of static aeroelastic correction andjigshape design for large airliners, Science China Tech. Sci., 55(9) (2012), pp. 2447–2453.Google Scholar
[5]Batina, J. T., Unsteady Euler algorithm with unstructured dynamic mesh for complex-aircraft aeroelastic analysis, AIAA J., 29(3) (1991), pp. 327–333.Google Scholar
[6]Venkatakrishnan, V. and Mavriplis, D. J., Implicit method for the computation of unsteady flows on unstructured grids, J. Comput. Phys., 127(2) (1996), pp. 380–397.Google Scholar
[7]Farhat, C., Degand, C., Koobus, B. and Lesoinne, M., Torsional springs for two-dimensional dynamic unstructured fluid meshes, Comput. Methods Appl. Mech. Eng., 163 (1998), pp. 231–245.CrossRefGoogle Scholar
[8]Witteveen, J. A. S., Explicit and robust inverse distance weighting mesh deformation for CFD, AIAA 2010-165, January 2010.Google Scholar
[9]Witteveen, J. A. S. and Bijl, H., Explicit mesh deformation using inverse distance weighting interpolation, AIAA 2009-3996, June 2009.Google Scholar
[10]Bar-Yoseph, P. Z., Mereu, S. and Chippada, S., Automatic monitoring of element shape quality in 2D and 3D computational mesh dynamics, Comput. Mech., 27(5) (2001), pp. 378–395.Google Scholar
[11]Nielsen, E. J. and Anderon, W. K., Recent improvements in aerodynamic design optimization on unstructured meshes, AIAA J., 40(6) (2002), pp. 1155–1163.Google Scholar
[12]Sheta, E. F., Yang, H. Q. and Hanchi, S. D., Solid brickanalogy for automatic grid deformation for Fluid-Structure interaction, AIAA 2006-3219, June 2006.Google Scholar
[13]Frank, R., Scattered data interpolation: Tests of some methods, Math. Comput., 38 (1982), pp. 181–200.Google Scholar
[14]Wu, Z. M., Multivariate compactly supported positive definite radial functions, Adv. Comput. Math., 4 (1995), pp. 283–292.Google Scholar
[15]Bernal, F. and Gutierrez, G., Solving delay differential equations through BRF collocation, Adv. Appl. Math. Mech., 1 (2009), pp. 257–272.Google Scholar
[16]Liu, X. Q., Qin, N. and Xia, H., Fast dynamic grid deformation based on Delaunay graph mapping, J. Comput. Phys., 211(2) (2006), pp. 405–423.Google Scholar
[17]Ding, L., Lu, Z. L. and Guo, T. Q., An efficient dynamic mesh generation method for complex multi-block structured grid, Adv. Appl. Math. Mech., 6(1) (2014), pp. 120–134.Google Scholar
[18]Spekreijse, S. P., Prananta, B. B. and Kok, J. C., A simple, robust and fast algorithm to compute deformations of multi-block structured grids, NLR-TP-2002-105, 2002.Google Scholar
[19]Zhou, X., Li, S. X. and Chen, B., Spring-interpolation approach for generating unstructureddynamic meshes, Acta Aeronautica Et Astronautica Sinica, 31(7) (2010), pp. 1389–1395.Google Scholar
[20]Buhmann, M. D., Radial basis functions, Acta Numer., 9 (2000), pp. 1–38.Google Scholar
[21]Shu, C., Ding, H. and Yeo, K. S., Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 192 (2003), pp. 941–954.CrossRefGoogle Scholar
[22]Faul, A. C. and Powell, M. J. D., Proof of convergence of an interactive technique for thin plate spline interpolation in two dimensions, Adv. Comput. Math., 11 (1999), pp. 183–192.CrossRefGoogle Scholar
[23]Wendland, H., Fast evaluation of radial basis functions: methods based on partition of unity, Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, 2002, pp. 473–483.Google Scholar
[24]De Boer, A., Van Der Schoot, M. S. and Bijl, H., Mesh deformation based on radial basis function interpolation, Comput. Struct., 85 (2007), pp. 784–795.CrossRefGoogle Scholar
[25]Botsch, M. and Kobbelt, L., Real-time shape editing using radial basis functions, Comput. Graphics Forum, 24(3) (2005), pp. 611–621.Google Scholar
[26]Rendall, T. C. S. and Allen, C. B., Efficient mesh motion using radial basis functions with data reduction algorithms, J. Comput. Phys., 228 (2009), pp. 6231–6249.CrossRefGoogle Scholar
[27]Rendall, T. C. S. and Allen, C. B., Improved radial basis function fluid-structure coupling via efficient localized implementation, Int. J. Numer. Methods Eng., 78(10) (2009), pp. 1188–1208.Google Scholar
[28]ANASYS Software Corporation, ANASYS FLUENT 14.0 User Manual, Printer in U.S.A, 2011.Google Scholar