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Migration from Compressible Code to Preconditioned Code

압축성 코드에서 예조건화 코드로의 이전

  • 한상훈 (부산대학교 대학원 항공우주공학과) ;
  • 김명호 (국방과학연구소) ;
  • 최정열 (부산대학교 항공우주공학과)
  • Published : 2007.03.31

Abstract

Comprehensive mathematical comparison of numerical dissipation vector was made for a compressible and the preconditioned version Roe's Riemann solvers. Choi and Merkle type preconditioning method was selected from the investigation of the convergence characteristics of the various preconditioning methods for the flows over a two-dimensional bump. The investigation suggests a way of migration from a compressible code to a preconditioning code with a minor changes in Eigenvalues while maintaining the same code structure. Von Neumann stability condition and viscous Jacobian were considered additionally to improve the stability and accuracy for the viscous flow analysis. The developed code was validated through the applications to the standard validation problems.

이차원 범프 유동에 대한 다양한 예조건화 행렬의 수렴 특성을 살펴 Choi 와 Merkle 의 예조건화 행렬을 선택하여, 압축성 및 예조건화 Roe의 Riemann 해법의 수치 소산항을 수학적으로 비교하였다. 이 결과 코드의 구조는 동일하게 유지한 채, 고유치의 작은 수정만으로 압축성 해법을 예조건화 해법으로 이전할 수 있는 방법을 알 수 있었다. 아울러 점성 유동 영역에서의 안정성 및 정확성을 향상시키기 위하여 von Neumann 안정 조건 및 점성 자코비안을 고려하였으며, 개발된 코드는 표준 검증 문제에 적용하여 검증을 수행하였다.

Keywords

References

  1. Turkel, E., 'Preconditioned Methods for Solving the Incompressible and Low Speed Compressible Equations', Journal of Computational Physics, Vol. 72, No.2, 1987, pp. 277-298 https://doi.org/10.1016/0021-9991(87)90084-2
  2. Choi, Y, and Merkle, C., 'The application of Preconditioning in Viscous Flows', Journal of Computational Physics, Vol. 107, 1993, pp. 207-223
  3. Chen, K. H., and Shuen, J. S., 'Three Dimensional Coupled Implicit Methods for Spray Combustion Flows at All speeds', AlAA Paper 94-3047, 1994
  4. Weiss, J., and Smith, W., 'Preconditioning Applied to Variable and Constant Density Flows', AlAA Journal, Vol. 33, No. 11, 1995, pp. 2050-2057
  5. Edwards, J. R., and Roy, C. J., 'Preconditioned Multigrid Methods for Two-Dimensional Combustion Calculations at All Speeds', AlAA Journal, Vol. 36, No 2, 1998, pp. 185-192
  6. Edwards, J. R., and Thomas, J. L., 'Development of o(Nm2 ) Preconditioned Multigrid Solvers for Euler and Navier-Stokes Equations', AlAA Journal, Vol. 38, No.4, 2000, pp. 717-720
  7. 김명호, 이기수, 최정열, 김귀순, 김성룡, 정인석, 'Myrinet 및 Fast Ethernet 환경에서의 병렬처리성능', 한국항공우주학회지, 제 30권 제 6호, 2002년, 9월, pp. 21-30
  8. Roe, P. L., 'Characteristic-Based Schemes for the Euler Equations', Annual Review of Fluid Mechanics, Vol. 18, 1986, pp. 337-365 https://doi.org/10.1146/annurev.fl.18.010186.002005
  9. 원수희, 정인석, 신재렬, 최정열, '무딘 물체 주위 고 마하수 유동해석의 문제점과 해결책', 한국항공우주학회지, 제 34권 제 6호, 2002년, 6월, pp. 18-28
  10. Yoon, S., and Jameson, A, 'Lower- Upper Symmetric Gauss Seidal Method for the Using the Navier-Stokes Equations', AIAA Journal, Vol. 26, No.9, 1988, pp. 1025-1026 https://doi.org/10.2514/3.10007
  11. Shuen, S., and Yoon, S., 'Numerical Study of Chemically Reacting Flows Using a Lower-Upper Symmetric Sucessive Overrelaxation Scheme', AIAA Journal, Vol. 27, No. 12, 1989, pp. 1752-1760 https://doi.org/10.2514/3.10331
  12. Hsieh, S. Y., and Yang, V., 'A Preconditioned Flux-Differencing Scheme for Chemically Reacting Flows at all Mach Numbers', International Journal of CFD, Vol. 8, 1997, pp. 31-49
  13. Ghia, U., Ghia, K. N., and Shin, C. T, 'High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and Multigrid Method', Journal of Computational Physics, Vol. 8, 1982, pp. 387-411
  14. Armaly, B. F., Durst, F., Oereira, K. C. F., and Schonung, B., 'Experimental and Theoretical Investigation of Backward-Facing Step Flow', Journal of Fluid Mechanics, Vol. 127, 1983, pp. 473-496 https://doi.org/10.1017/S0022112083002839
  15. Cuffel, R. F., Back, L. H., and P. F. Massier, 'Transonic Flow Field in a Supersonic Nozzle with Small Throat Radius of Curvature', AIAA Journal, Vol. 7, No.7, 1969, pp. 1364-1366 https://doi.org/10.2514/3.5349
  16. ritton, D. J., 'Experiments on the Flow Past a Circular Cylinder at Low Reynolds Numbers', Journal of Fluid Mechanics, Vol. 6, 1959, pp. 547- 567 https://doi.org/10.1017/S0022112059000829
  17. Buelow, P. E. O., Schwer, D. A, Feng, J., and Merkle, C. L., 'A Preconditioned Dual -Time, Diagonalized ADI Scheme for Unsteady Computations', AIAA Paper 97-2101, 1997