Journal of the Korean Society of Propulsion Engineers (한국추진공학회지)

The Korean Society of Propulsion Engineers (한국추진공학회)
권호 표지

Convergence Characteristics of Preconditioned Euler Equations

예조건화된 오일러 방정식의 수렴특성

  • 이상현 (울산대학교 수송시스템공학부)
  • Published : 2004.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

The convergence characteristics of preconditioned Euler equations were studied. A perturbation analysis was conducted to understand the behavior of the preconditioned Euler equations. Various speed flows in a two-dimensional channel with a 10％ circular arc in the middle of the channel were calculated. Roe's FDS scheme was used for spatial discretization and the LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of pressure and velocity were maintained regardless of the Mach numbers but that the convergence characteristics of temperature were strongly related to the Mach number and became worse as the Mach number decreased. The perturbation analysis well explained the trend of the convergence characteristics and showed that the convergence characteristics are strongly related with the behavior o( the Preconditioning matrix.

예조건화된 오일러 방정식의 수렴특성에 대한 연구를 수행하였다. 지배방정식의 거동을 이해하기 위하여 섭동 해석을 수행하였다. 중앙부에 10％ 원호를 가진 2차원 관을 통과하는 다양한 마하수의 비점성 유동장에 대해 수치 계산을 수행하였다. 공간차분은 Roe의 FDS를 사용하고 시간적분은 LU-SGS 기법을 사용하였다. 압력 및 속도의 수렴특성은 마하수와 상관없이 일정하게 유지되었으나, 온도의 수렴성은 마하수가 작아질수록 악화되는 것으로 나타났다. 섭동 해석을 통해 이러한 지배방정식의 수렴특성을 설명할 수 있었으며, 수렴특성이 예조건화 행렬의 거동 특성에 의해 결정된다는 사실을 알 수 있었다.

Keywords

References

  1. Shuen, J. S., Chen, K. H., and Choi, Y., 'A Coupled Implicit Method for ChemicalNon-Equilibrium Flows at All Speeds,'Journal of Computational Physics 106, 1993, pp.306-318
  2. Chen, K. H., and Shuen, J. S., 'Three Dimensional Coupled Implicit Methods for Spray Combustion Flows at All Speeds,' AIAA 1994, pp.94-3047
  3. Dailey, L. D., and Pletcher, R. H., 'Evaluation of Multigrid Acceleration for Preconditioned Time-Accurate NavierStokes Algorithms,' AIAA 1995, pp.95-1668
  4. Edwards, J. R., and Roy, C. J., 'Preconditioned Multigrid Methods for Two Dimensional Combustion Calculations at All Speeds,' AIAA Journal, Vol. 36, No.2, February, 1998, pp.185-192 https://doi.org/10.2514/2.7500
  5. Edwards, J. R., and Liou M. S., 'Low Diffusion Flux Splitting Methods for Flows at All Speeds,' AIAA Journal, Vol. 36. No.9, 1998, pp.1610-1617 https://doi.org/10.2514/2.587
  6. Hsieh, J. S-Y., and Yang V., 'A Preconditioning Flux-Difference Scheme for Chemically Reacting Flows at All Mach Numbers,' International Journal of CFD, Vol. 8. 1997, pp.31-49
  7. Buelow, P..E, and Schwer, D. A., Feng, J, Merkle, C. L., and Choi, D., 'Three Dimensional Coupled Implicit Methods for Spray Combustion Flows at All Speeds,' AIAA 1994, pp.94-3047
  8. 이상현, '저속 압축성 유동장 해석을 위한 예조건화 방법론 연구 I,'항공우주학회지, 29권, 7호, 2001, pp.87-95
  9. 이상현, '저속 압축성 유동장 해석을 위한 예조건화 방법론 연구 II - 온도장 계산 성능 개선,' 공우주학회지, 29권, 8호, 2001, pp.26-36
  10. Roe, P. L., 'Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,' Journal of Computational Physics, Vol. 43, No. 3, 1981, pp.352-372
  11. Lee, D., 'Design Criteria for Local Euler Preconditioning,' Journal of Computational Physics. Vol. 144, 1998, pp.423-459 https://doi.org/10.1006/jcph.1998.5993
  12. Yoon, S., and Jameson, A., 'Lower-Upper Method for the Euler and Navier-Stokes Equation,' AIAA Journal, Vol. 26, No.9, 1988, pp.1025-1026 https://doi.org/10.2514/3.10007
  13. Sesterhenn, J., Muller, B., and H. Thomann,'On Cancellation Problem In Calculating Low Mach number Flows,' Journal of Computational Physics. Vol.151, 1999, pp.597-615 https://doi.org/10.1006/jcph.1999.6211