예조건화 방법론의 Navier-Stokes 방정식에의 적용

Application of Preconditioning to Navier-Stokes Equations

  • 이상현 (울산대학교 수송시스템공학부)
  • 발행 : 2004.03.01

초록

본 연구의 목적은 예조건화 방법론을 난류모델을 포함한 Navier-Stokes 방정식에 적용하는 것이다. 가상 음속 개념을 적용하였다 공간차분을 위해 Roe의 FDS를 사용하였고, 시간 적분을 위해 LU-SGS 기법을 사용하였다. 알고리즘을 검증하기 위하여 NACA 날개 주위의 저속유동, 초음속 노즐 유동을 계산하였다. 본 연구에서 개발된 알고리즘은 저속유동 및 초음속 유동의 계산에서 충분한 계산 성능을 보이는 것으로 판단된다.

The objective of this study is to apply preconditioning to Wavier-Stokes equations with a turbulence model. The concept of a pseudo sonic speed was adopted. Roe's FDS was used for spatial discretization, LU-SGS scheme was used for time integration. In order to test the algorithms, the low speed flows around NACA airfoils and the flows through supersonic nozzle were calculated. The algorithm developed in the present study shows good performance in the calculations of low speed viscous flows and supersonics flows.

키워드

참고문헌

  1. J. S. Sheun, K. H. Chen, and Y. H. Choi, 'A Coupled Implicit Method for Chemical Non-Equilibrium Flows at All Speeds,' Journal of Computational Physics 106, 1993, pp.306-318
  2. K. H. Chen, and J. S. Shuen, 'Three Dimenstional Coupled Implicit Methods for Spray Combustion Flows at All Speeds,' AIAA, 1994, pp.94-3047
  3. L. D. Dailey, and R. H. Pletcher, 'Evaluation of Multigrid Acceleration for Preconditioned Time-Accurate Navier-Stokes Algorithms,' AIAA 1995, pp.95-1668
  4. J. R. Edwards, and C. J. Roy, '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. J. R. Edwards, and M. S. Liou, 'Low Diffusion Flux Splitting Methods for Flows at All Speeds,' AIAA Journal, Vol. 36. No.9, 1998, pp.l610-1617
  6. J. S-Y. Hsieh, and V. Yang, 'A Preconditioning Flux-Difference Scheme for Chemically Reacting Flows at All Mach Numbers,' International Journal of CFD, Vol. 8, 1997, pp.31-49
  7. 이상현, '저속 압축성 유동장 해석을 위한 예조건화 방법론 연구 I,' 항공우주학회지 29권, 7호, pp.87-95
  8. Y- H. Choi, and C. L. Mercle, 'The application of Preconditioning in Viscous Flows,' Journal of Computational Physics 106, 1993, pp.207-223
  9. F. R. Menter, Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA Journal, Vol. 32, No.8, 1994, pp.l598-1605
  10. P. L. Roe, Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes, Journal of Computational Physics, Vol. 43, No.3, 1981, pp.352-372
  11. C. Crown, 'Supersonic Nozzle Design,' NACA Technical Report 1651, June, 1948
  12. Pinkerton, R. M., 'Calculated and Measured Pressure Distributions over the Midspan Section of the NACA 4412 Airfoil,' Report 563, NACA, 1936