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Extending Seventh-Order Dissipative Compact Scheme Satisfying Geometric Conservation Law to Large Eddy Simulation on Curvilinear Grids

Published online by Cambridge University Press:  29 May 2015

Yi Jiang ,
Meiliang Mao ,
Xiaogang Deng  and
Huayong Liu
Yi Jiang*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
Meiliang Mao
Affiliation:
Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
Xiaogang Deng
Affiliation:
National University of Defense Technology, Changsha 410073, China
Huayong Liu
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, China
*
*Corresponding author. Email: yijiang@mail.ustc.edu.cn (Y. Jiang)
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Abstract

Seventh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS-E8T7) is extended to a new implicit large eddy simulation named HILES on stretched and curvilinear meshes. Although the conception of HILES is similar to that of monotone integrated LES (MILES), i.e., truncation error of the discretization scheme itself is employed to model the effects of unresolved scales, HDCS-E8T7 is a new high-order finite difference scheme, which can eliminate the surface conservation law (SCL) errors and has inherent dissipation. The capability of HILES is tested by solving several benchmark cases. In the case of flow past a circular cylinder, the solutions of HILES fulfilling the SCL have good agreement with the corresponding experiment data, however, the flowfield is gradually contaminated when the SCL error is enlarged. With the help of fulling the SCL, ability of HILES for handling complex geometry has been enhanced. The numerical solutions of flow over delta wing demonstrate the potential of HILES in simulating turbulent flow on complex configuration.

Keywords

76Fxx76GxxImplicit large eddy simulationhigh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS)geometric conservation law (GCL)complex geometry
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 4 , August 2015 , pp. 407 - 429
Copyright
Copyright © Global-Science Press 2015 

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References

[1]Ghosal, S., An analysis of numerical errors in large-eddy simulations of turbulence, J. Comput. Phys., 125 (1996), pp. 187–206Google Scholar
[2]Kravchenko, A. G. and Moin, P., On the effect of numerical errors in large eddy simulations of turbulent flows, J. Comput. Phys., 131(2) (1997), pp. 310–322.CrossRefGoogle Scholar
[3]Chow, Fotini Katopodes and Moin, Parviz, A further study of numerical errors in large-eddy simulations, J. Comput. Phys., 184 (2003), pp. 366–380Google Scholar
[4]Park, Noma, Yoo, Jung Yul and Choi, Haecheon, Discretization errors in large eddy simulation: on the suitability of centered and upwind-biased compact difference schemes, J. Comput. Phys., 198 (2004), pp. 580–616.Google Scholar
[5]Kawamura, T. and Kuwahara, K., Computation of high Reynolds number flow around a circular cylinder with surface roughness, AIAA-paper, 84–0340.Google Scholar
[6]Boris, J. P., Grinstein, F. F., Oran, E. S. and Kolbe, R. L., New insights into large eddy simulation, Fluid Dyn. Res., 10 (1992), pp. 199–228.Google Scholar
[7]Boris, J. P., More for LES: a brief historical perspective of MILES, in: Grinstein, F. F., Margolin, L. G., Rider, W. J. (Eds.), Implicit Large Eddy Simulation, Cambridge University Press, 2007, pp. 9–38.Google Scholar
[8]Margolin, L. G. and Rider, W. J., Numerical regularization: The numerical analysis of implicit subgrid models, in: Grinstein, F. F., Margolin, L. G., Rider, W. J. (Eds.), Implicit Large Eddy Simulation, Cambridge University Press, 2007, pp. 195–221.Google Scholar
[9]Visbal, M. R. and Rizzetta, D. P., Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes, J. Fluids Eng., 124(4) (2002), PP. 836–847.Google Scholar
[10]Shen, Yiqing and Zha, Gecheng, Large eddy simulation using a new set of sixth order schemes for compressible viscous terms, J. Comput. Phys., 229 (2010), pp. 8296–8312.Google Scholar
[11]Vuillot, F., Lupoglazoff, N. and Huet, M., Effect of chevrons on double stream jet noise from hybrid CAA computations, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 4–7 January 2011, Orlando, Florida.CrossRefGoogle Scholar
[12]Rizzetta, Donald P., Visbal, Miguel R. and Morgan, Philip E., A high-order compact finite-difference scheme for large-eddy simulation of active flow control, Progress Aerospace Sci., 44 (2008), pp. 397–426.Google Scholar
[13]Lele, S. K., Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992), pp. 16–42.Google Scholar
[14]Wang, Z. J., High-order methods for the Euler and Navier-Stokes equations on unstructured grids, Progress Aerospace Sci., 43 (2007), pp. 1–41.Google Scholar
[15]Ekaterinaris, J. A., High-order accurate, low numerical diffusion methods for aerodynamics, Progress Aerospace Sci., 41(3–4) (2005), pp. 192–300.Google Scholar
[16]Deng, X. G., Mao, M. L., Tu, G. H., Liu, H. Y. and Zhang, H. X., Geometric conservation law and applications to high-order finite difference schemes with stationary grids, J. Comput. Phys., 230 (2011), pp. 1100–1115.Google Scholar
[17]Visbal, R. M. and Gaitonde, D. V., On the use of higher-order finite-difference schemes on curvilinear and deforming meshes, J. Comput. Phys., 181 (2002), pp. 155–185.Google Scholar
[18]Nonomura, T., Iizuka, N. and Fujii, K., Freestream and vortex preservation properties of high-order WENO and WCNS on curvilinear grids, Comput. Fluids, 39 (2010), pp. 197–214.Google Scholar
[19]Thomas, P. D. and Lombard, C. K., Geometric conservation law and its application to flow computations on moving grids, AIAA J., 17(10) (1979), pp. 1030–1037.CrossRefGoogle Scholar
[20]Pulliam, T. H. and Steger, J. L., On implicit finite-difference simulations of three-dimensional flow, AIAA Paper 78–10, 1978.Google Scholar
[21]Deng, Xiaogang, Jiang, Yi, Mao, Meiliang, Liu, Huayong and Tu, Guohua, Developing hybrid cell-edge and cell-node dissipative compact scheme for complex geometry flows, Sci. China Tech. Sci., 56 (2013), pp. 2361–2369.Google Scholar
[22]Deng, Xiaogang, Jiang, Yi, Mao, Meiliang, Liu, Huayong, Li, Song and Tu, Guohua, A family of hybrid cell-edge and cell-node dissipative compact schemes satisfying geometric conservation law, submitted to Computers & Fluids.Google Scholar
[23]Xie, Peng and Liu, Chaoqun, Weighted compact and non-compact scheme for shock tube and shock entropy interaction, AIAA, 2007–509.Google Scholar
[24]Tam, C. K. W. and Webb, J. C., Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys., 107 (1993), pp. 262–281.Google Scholar
[25]Hsu, John M. and Jameson, Antony, An Implicit-explicit hybrid scheme for calculating complex unsteady flows, AIAA, 2002–0714.Google Scholar
[26]Gordnier, R. E. and Visbal, M. R., Numerical simulation of delta-wing roll, AIAA Paper 93–0554, January 1993.Google Scholar
[27]Deng, Xiaogang, Min, Yaobing, Mao, Meiliang, Liu, Huayong, Tu, Guohua and Zhang, Hanxin, Further studies on geometric conservation law and applications to high-order finite difference schemes with stationary grids, J. Comput. Phys., 239 (2013), pp. 90–111.Google Scholar
[28]Kim, J. W. and Lee, D. J., Characteristic interface conditions for multiblock high-order computation on singular structured grid, AIAA J., 41(2) (2003), pp. 2341–2348.Google Scholar
[29]Deng, X. G., Mao, M. L., Tu, G. H., Zhang, Y. F. and Zhang, H. X., Extending weighted compact nonlinear schemes to complex grids with characteristic-based interface conditions, AIAA J., 48(12) (2010), pp. 2840–2851.Google Scholar
[30]Jiang, Yi, Mao, Meiliang, Xiaogang, Deng, Liu, Huayong, Li, Song and Yan, Zhenguo, Extending seventh-order hybrid cell-edge and cell-node dissipative compact scheme to complex grids, The 4th Asian Symposium on Computational Heat Transfer and Fluid Flow, Hong Kong, 3–6 June 2013.Google Scholar
[31]Kim, John, Moin, Parviz and Moser, Robert, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177 (1987), pp. 133–166.CrossRefGoogle Scholar
[32]Rizzetta, D. P., Visbal, M. R. and Blaisdell, G. A., A time-implicit high-order compact differencing and filtering scheme for large-eddy simulation, int. J. Numer. Meth. Fluids, 42 (2003), pp. 665–693.Google Scholar
[33]Lenormand, E., Sagaut, P. and Phuoc, L. Ta, Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number, int. J. Numer. Meth. Fluids, 32 (2000), pp. 369–406.Google Scholar
[34]Suh, Jungsoo, Frankel, Steven H., Mongeau, Luc and Plesniak, Michael W., Compressible large eddy simulations of wall-bounded turbulent flows using a semi-implicit numerical scheme for low Mach number aeroacoustics, J. Comput. Phys., 215 (2006), pp. 526–551.CrossRefGoogle Scholar
[35]Kravchenko, G. and Moin, P., Numerical studies of flow over a circular cylinder at Re=3900, Phys. Fluids, 12 (2000), pp. 403–417.Google Scholar
[36]Poinsot, T. and Lele, S. T., Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys., 101 (1992), pp. 104–129.CrossRefGoogle Scholar
[37]Bodony, Daniel J., Analysis of sponge zones for computational fluid mechanics, J. Comput. Phys., 212 (2006), pp. 681–702.CrossRefGoogle Scholar
[38]Kravchenko, A. G. and Moin, P., B-spline methods and zonal grids for numerical simulations of turbulent flows, Flow Physics and Computation Division, Department of Mechanical Engineering, Stanford University, Report No. TF-73, Stanford, CA, Feb. 1998.Google Scholar
[39]Verhaagen, N. G. and Elsayed, M., Leading-edge radius effects on 50° delta wing flow, AIAA paper 2009–540, 47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition 5–8 January 2009, Orlando, Florida.Google Scholar