Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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On the Suitability of Centered and Upwind-Biased Compact Difference Schemes for Large Eddy Simulations (III) - Dynamic Error Analysis -

LES에서 중심 및 상류 컴팩트 차분기법의 적합성에 관하여 (III) -동적 오차 해석 -

  • 박노마 (서울대학교 기계항공공학부) ;
  • 유정열 (서울대학교 기계항공공학부) ;
  • 최해천 (서울대학교 기계항공공학부)
  • Published : 2003.07.01
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Abstract

The suitability of high-order accurate, centered and upwind-biased compact difference schemes for large eddy simulation is evaluated by a dynamic analysis. Large eddy simulation of isotropic turbulence is performed with various dissipative and non-dissipative schemes to investigate the effect of numerical dissipation on the resolved solutions. It is shown by the present dynamic analysis that upwind schemes reduce the aliasing error and increase the finite differencing error. The existence of optimal upwind scheme that minimizes total numerical error is verified. It is also shown that the finite differencing error from numerical dissipation is the leading source of numerical errors by upwind schemes. Simulations of a turbulent channel flow are conducted to show the existence of the optimal upwind scheme.

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References

  1. Park, N., Yoo, J. Y. and Choi, H., 2003, 'On the Suitability of Centered and Upwind-biased Compact Different Schemes for Large Eddy Simulation: Part II- Static Error Analysis,' Trans. Of the KSME B, Vol. 27, No. 7, pp. 984-994 https://doi.org/10.3795/KSME-B.2003.27.7.984
  2. Fedioun, I., Lardjane, N. and Gokalp, I., 2001, 'Revisiting Numerical Errors in Direct and Large Eddy Simulations of Turbulence: Physical and Spectral Space Analysis,' J. Comput. Phys., Vol. 174, pp.816-851 https://doi.org/10.1006/jcph.2001.6939
  3. Ghosal, S., 1996, 'An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence,' J. Comput. Phys., Vol. 125, pp. 187-206 https://doi.org/10.1006/jcph.1996.0088
  4. Park, N., Yoo, J. Y. and Choi, H., 2003, 'On the Suitability of Centered and Upwind-biased Compact Different Schemes for Large Eddy Simulation: Part 1-Numerical Test,' Trans. Of the KSME B, Vol. 27, No. 7, pp. 973-983 https://doi.org/10.3795/KSME-B.2003.27.7.973
  5. Zhong, X., 1998, 'High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition,' J. Comput. Phys., Vol. 144, pp. 662-709 https://doi.org/10.1006/jcph.1998.6010
  6. Anderson, W., Thomas, J. and Van Leer, B., 1986, 'Comparison of Finite Volume Flux Vector Splitting for the Euler Equations,' AIAA Journal, Vol. 24, pp. 1453-1460 https://doi.org/10.2514/3.9465
  7. Harten, A., Engquist, B., Osher, S. and Chakravarthy, S., 1987, 'Uniformly High Order Accurate Essentially Non-Oscillatory Schemes III,' J. Comput. Phys., Vol. 71, pp. 231-303 https://doi.org/10.1016/0021-9991(87)90031-3
  8. Liu, X. D., Osher, S. and Chan, T., 1994, 'Weighted Essentially Non-Oscillatory Schemes,' J. Comput. Phys., Vol. 115, pp. 200-212 https://doi.org/10.1006/jcph.1994.1187
  9. Jiang, G. S. and Shu, C. W., 1996, 'Efficient Implementation of Weighted ENO Schemes,' J. Comput. Phys., Vol. 126, pp. 202-228 https://doi.org/10.1006/jcph.1996.0130
  10. Steger, J. L. and Warming, R. F., 'Flux Vector Splitting of the Inviscid Gas Dynamics Equations with Applications to Finite Difference Methods,' J. Comput. Phys., Vol. 40, pp. 263-293 https://doi.org/10.1016/0021-9991(81)90210-2
  11. Lele, S. K., 1992, 'Compact Finite-Difference Schemes with Spectral-Like Resolution,' J. Comput. Phys., Vol. 103, pp. 16-42 https://doi.org/10.1016/0021-9991(92)90324-R
  12. Comte-Bellot, G. and Corrsin, S., 1971, 'Simple Eulerian Time Correlation of Full- and Narrow-Band Velocity Signals in Grid-Generated, 'Isotropic' Turbulence,' J. Fluid Mech., Vol. 48, pp. 273-337 https://doi.org/10.1017/S0022112071001599
  13. Carati, D., Jansen, K. and Lund, T., 'A Family of Dynamic Models for Large-Eddy Simulation,' Annual Research Briefs, Center for Turbulence Research
  14. Metais, O. and Lesieur, M., 1992, 'Spectral Large-Eddy Simulation of Isotropic and Stably Stratified Tubulence,' J. Fluid Mech., Vol. 239, pp. 157-194 https://doi.org/10.1017/S0022112092004361
  15. Germano, M., Piomelli, U., Moin, P. and Cabot, W., 1991, 'A Dynamic Subgrid-Scale Eddy Viscosity Model,' Phys. Fluids A, Vol. 3, pp. 1760-1765 https://doi.org/10.1063/1.857955
  16. Tolstykh, A. I. and Lipavskii, M. V., 1998, 'On Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing,' J. Comput. Phys., Vol. 140, pp. 205-232 https://doi.org/10.1006/jcph.1998.5887
  17. Blaisdell, G. A., Spyropoulus, E. T. and Qin, J. H., 1996, 'The Effect of the Formulation of Nonlinear Terms on Aliasing Errors in Spectral Methods,' Appl. Numer. Math., Vol. 21, pp. 207-219 https://doi.org/10.1016/0168-9274(96)00005-0
  18. Zang, T. A., 1991, 'On the Rotation and Skew-Symmetric Forms for Incompressible Flow Simulations,' Appl. Numer. Math., Vol. 7, pp. 27-40 https://doi.org/10.1016/0168-9274(91)90102-6
  19. Kravchenko, G. and Moin, P., 1997, 'On the Effect of Numerical Errors in Large-Eddy Simulations of Turbulent Flows,' J. Comput. Phys., Vol. 131, pp. 310-322 https://doi.org/10.1006/jcph.1996.5597
  20. van Leer, B., 1982, 'Flux-Vector Splitting for the Euler Equations,' Lecture Notes in Physics, Vol. 170(Springer-Verlag, New York/Berlin), p. 507-512 https://doi.org/10.1007/3-540-11948-5_66
  21. Liu, M. S. and Steffen, Jr., C. J., 1993, 'A New Flux Splitting Scheme,' J. Comput. Phys., Vol. 107, pp 23-39 https://doi.org/10.1006/jcph.1993.1122
  22. Roe, P. L., 1981, 'Approximate Riemann Solvers, Parameter Vectors and Difference Schemes,' J. Comput. Phys., Vol. 43, pp. 357-372 https://doi.org/10.1016/0021-9991(81)90128-5
  23. Meinke, M., Schroder, W., Krause, E. and Rister, Th., 2002, 'A Comparison of Second- and Sixth-order Methods for Large-Eddy Simulations,' Computers & Fluids, Vol. 31, pp. 695-718 https://doi.org/10.1016/S0045-7930(01)00073-1
  24. Mossi, M. and Sagaut, P., 2003, 'Numerical Investigation of Fully Developed Channel Flow Using Shock-Capturing Schemes,' Computers & Fluids, Vol. 32, pp. 249-274 https://doi.org/10.1016/S0045-7930(02)00003-8
  25. Garnier, E., Mossi, M., Sagaut, P., Comte, P. and Deville, M., 1999, 'On the Use of Shock-Capturing Schemes for Large-Eddy Simulation,' J. Comput. Phys., Vol. 153, pp. 273-311 https://doi.org/10.1006/jcph.1999.6268
  26. Wei, T. and Willmarth, W. W., 1989, 'Reynolds-Number Effects on the Structure of a Turbulent Channel Flow,' J. Fluid Mech., Vol. 204, pp. 57-95 https://doi.org/10.1017/S0022112089001667
  27. Jeong, J. and Hussain, F., 1995, 'On the Identification of a Vortex,' J. Fluid Mech., Vol. 285, pp 69-94 https://doi.org/10.1017/S0022112095000462