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The Study About Cloud of Points Reconstruction with the Framework of Meshfree Method for Viscous Flows

Published online by Cambridge University Press:  06 June 2017

Y. D. Wang ,
Y. Jing ,
J. Dai ,
Q. G. Lin ,
X. W. Cai ,
X. J. Ma ,
D. F. Ren  and
J. J. Tan
Y. D. Wang
Affiliation:
Shanghai Institute of Space PropulsionShanghai, China Shanghai Engineering Research Center of Space EngineShanghai, China School of Energy and Power EngineeringNanjing University of Science and TechnologyNanjing, China
Y. Jing
Affiliation:
Shanghai Institute of Space PropulsionShanghai, China Shanghai Engineering Research Center of Space EngineShanghai, China
J. Dai
Affiliation:
Shanghai Institute of Space PropulsionShanghai, China Shanghai Engineering Research Center of Space EngineShanghai, China
Q. G. Lin
Affiliation:
Shanghai Institute of Space PropulsionShanghai, China Shanghai Engineering Research Center of Space EngineShanghai, China
X. W. Cai
Affiliation:
China Ship Scientific Research CenterNational Key Laboratory of Science and Technology on HydrodynamicWuxi, China
X. J. Ma
Affiliation:
Shanghai Xinli Power Equipment Research InstituteShanghai, China
D. F. Ren
Affiliation:
School of Energy and Power EngineeringNanjing University of Science and TechnologyNanjing, China
J. J. Tan*
Affiliation:
School of Energy and Power EngineeringNanjing University of Science and TechnologyNanjing, China
*
*Corresponding author ([email protected])
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Abstract

A new method, called Cloud of Points (COP) Reconstruction, is proposed in the present work to extend the meshfree method to simulate viscous flows. With the characters of viscous flows, the anisotropic COP structure is distributed in boundary layer. The proposed method can improve the anisotropic COP structure to isotropic COP structure and reduce the condition number of the least square coefficient matrix for conventional meshfree method. The values of the new reconstructed points are calculated by the Lagrange interpolation. The accuracy and the robustness of the presented meshfree solver are demonstrated on a number of standard test cases, including the functions with analytical gradients and the viscous flows past NACA0012 airfoil. The comparison of the simulation results with the experimental data and other numerical simulation data are also investigated.

Keywords

Meshfree methodCloud of Points (COP) ReconstructionViscous flowMoving least square
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 2 , April 2018 , pp. 75 - 87
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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References

1. Lucy, L. B., “A Numerical Approach to the Testing of the Fission Hypothesis,” The Astronomical Journal, 82, pp. 1013–1024 (1977).Google Scholar
2. Liu, G. R., Mesh Free Method: Moving Beyond the Finite Element Method, CRC Press, Boca Raton (2003).Google Scholar
3. Liu, G. R. and Gu, Y. T., An Introduction to Meshfree Methods and Their Programming, Springer, Berlin (2005).Google Scholar
4. Liszka, T. and Orkisz, J., “The Finite Difference Method at Arbitrary Irregular Grids and Its Application in Applied Mechanics,” Computers and Structures, 11, pp. 83–95 (1980).CrossRefGoogle Scholar
5. Batina, J. T., “A Grid-Free Euler/Navier-Stokes Solution Algorithm for Complex Aircraft Applications,” 31st Aerospace Sciences Meeting, U.S. (1993).Google Scholar
6. Deshpande, S. M., Ghosh, A. K. and Mandal, J. C., “Least Squares Weak Upwind Methods for Euler Equations,” Fluid Mechanics Report, No. FM4, Department of Aerospace Engineering, Indian Institute of Science (1989).Google Scholar
7. Ghosh, A. K. and Deshpande, S. M., “Least Squares Kinetic Method for Inviscid Compressible Flows,” 12th Computational Fluid Dynamics Conference, U.S. (1995).CrossRefGoogle Scholar
8. Dauhoo, M. Z., Ghosh, A. K., Ramesh, V. and Deshpande, S. M., “q-LSKUM-A New Higher-Order Kinetic Upwind Method for Euler Equations Using Entropy Variables,” Computational Fluid Dynamics Journal, 9, pp. 272–77 (2000).Google Scholar
9. Cai, X. W. et al., “Application of Hybrid Cartesian Grid and Gridless Approach to Moving Boundary Flow Problems,” International Journal For Numerical Methods in Fluids, 72, pp. 994–1013 (2013).Google Scholar
10. Katz, A. J., “Gridless Methods for Computational Fluid Dynamics,” PH.D. Dissertation, Department of Aeronautics and Astronautics, Stanford University, California, U.S.A. (2009).Google Scholar
11. Morinishi, K., “An Implicit Gridless Type Solver for the Navier-Stokes Equations,” Computational Fluid Dynamics Journal, 9, pp. 551–560 (2000).Google Scholar
12. Liu, G. R. and Xu, G. X., “A Gradient Smoothing Method (GSM) for Fluid Dynamics Problems,” International Journal For Numerical Methods In Fluids, 58, pp. 1101–1133(2008).Google Scholar
13. Yao, J. Y. et al., “A Moving-Mesh Gradient Smoothing Method for Compressible CFD Problems, “ Mathematical Models & Methods in Applied Sciences, 23, pp. 273–305 (2013).Google Scholar
14. Munikrishna, N. and Balakrishnan, N. “Turbulent Flow Computations on a Hybrid Cartesian Point Distribution Using Meshless Solver LSFD-U,” Computers & Fluids, 40, pp. 118–138 (2011).Google Scholar
15. Namvar, M. and Jahangirian, A. “An Investigation of Mesh-Less Calculation for Compressible Turbulent Flows,” Computers & Fluids, 86, pp. 483–489 (2013).Google Scholar
16. Su, X. R., Yamamoto, S. and Nakahashi, K., “Analysis of a Meshless Solver for High Reynolds Number Flow,” International Journal for Numerical Methods in Fluids, 72, pp. 505–527 (2013).Google Scholar
17. Katz, A. and Jameson, A., “Edge-Based Meshless Methods for Compressible Viscous Flow with Applications to Overset Grids,” AIAA paper 2008-3989, AIAA 38th Fluid Dynamics Conference, Seattle, WA, (2008).Google Scholar
18. Kennett, D. J. et al., “An Implicit Meshless Method for Application in Computational Fluid Dynamics,” International Journal for Numerical Methods in Fluids, 71, pp. 1007–1028 (2013).CrossRefGoogle Scholar
19. Sridar, D. and Balakrishnan, N., “An Upwind Finite Difference Scheme for Meshless Solver,” Journal of Computational Physics, 189, pp. 1–29 (2003).Google Scholar
20. Liou, M. S., “A Sequel to AUSM, Part II : AUSM+-up for all Speeds,” Journal of Computational Physics, 214, pp. 137–170 (2006).Google Scholar
21. May, G. and Jameson, A. “Unstructured Algorithm for Inviscid and Viscous Flows Embedded in a Unified Solver Architecture: Flo3xx,” 43rd AIAA Aerospace Sciences Meeting and Exhibit, U.S. (2005).Google Scholar
22. Jawahar, P. and Hemant, K., “A High-Resolution Procedure for Euler and Navier-Stokes Computations on Unstructured Grids,” Journal of Computational Physics, 164, pp. 165–203 (2000).Google Scholar
23. Mavriplis, D., Jameson, A. and Martinelli, L., “Multigrid Solution of the Navier-Stokes Equations on Triangular Meshes,” AIAA paper 89-0120, AIAA 27th Aerospace Sciences Meeting, Reno, NV (1989).Google Scholar
24. Menter, F. R., “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA Journal, 32, pp. 269–289 (1994).CrossRefGoogle Scholar
25. Harris, C. D., “Two-Dimensional Aerodynamic Characteristics of the NACA0012 Airfoil in the Langley 8-foot Transonic Pressure Tunnel,” NASA-TM-81927, NASA Langley Research Center; Hampton, VA, U.S. (1981).Google Scholar