Journal of the Korean Society for Aeronautical & Space Sciences (한국항공우주학회지)

The Korean Society for Aeronautical and Space Sciences (한국항공우주학회)
권호 표지
DOI QR코드

DOI QR Code

Temperature Preconditioning for Improving Convergence Characteristics in Calculating Low Mach Number Flows, I: Euler Equations

저속 유동 계산의 수렴성 개선을 위한 온도예조건화 I: 오일러 방정식

  • 이상현 (울산대학교 항공우주공학과)
  • Published : 2007.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

A temperature preconditioning that modulates the derivative of density with respect to temperature is proposed to improve the convergence characteristics of the preconditioned Euler equations. Flows in a two-dimensional channel with a 10% circular bump in the middle of the channel were calculated at different speeds. The numerical dissipation terms of the Roe’s FDS scheme according to the temperature preconditioning are derived. It is shown that the temperature preconditioning accelerates convergence of the preconditioned Euler equations.

예조건화 오일러 방정식의 수렴특성을 개선하기 위하여 밀도에 대한 온도의 미분항의 크기를 조절하는 온도예조건화 방법을 제시하고자 한다. 다양한 마하수의 원형 턱이 있는 이차원 관내 유동을 계산하였다. 온도예조건화에 맞는 새로운 Roe의 FDS 기법의 수치 소산항을 유도하여 사용하였다. 온도예조건화는 예조건화 오일러 방정식의 수렴 속도를 증가시키는 것으로 나타났다

Keywords

References

  1. Turkel, E., 'Preconditioning Techniques in Computational Fluid Dynamics', Annual Review of Fluid Mechanics, Vol. 31, pp. 385-416, 1999 https://doi.org/10.1146/annurev.fluid.31.1.385
  2. Choi, Y. H., and Merkle, C. L., 'The Application of Preconditioning in Viscous Flows', Journal of Computational Physics. Vol. 105, pp. 207-223, 1993 https://doi.org/10.1006/jcph.1993.1069
  3. Shuen, J. S., Chen, K. H, and Choi, Y., 'A Coupled Implicit Method for Chemical Non-Equilibrium Flows at All Speeds', Journal of Computational Physics, Vol. 106, pp. 306-318, 1993 https://doi.org/10.1016/S0021-9991(83)71110-1
  4. Chen, K. H, and Shuen, J. S., 'Three Dimensional Coupled Implicit Methods for Spray Combustion Flows at All Speeds', AIAA paper 94-3047, 1994
  5. Dailey, L. D., and Pletcher, R H, 'Evaluation of Multigrid Acceleration for Preconditioned Time-Accurate Navier-Stokes Algorithms', AIAA paper 95-1668, 1995
  6. Weiss, J. M., Smith, W. A., 'Preconditioning applied to variable and constant density flows', AIAA Journal, Vol. 33, No.11, pp. 2050-2057, 1995 https://doi.org/10.2514/3.12946
  7. Edwards, J. R, and Roy, C. J., 'Preconditioned Multigrid Methods for Two Dimensional Combustion Calculations at All Speeds', AIAA Journal, Vol. 36, No.2, pp. 185-192, 1998 https://doi.org/10.2514/2.7500
  8. Lee, S-H., 'Convergence Characteristics of Preconditioned Euler Equations', Journal of Computational Physics. Vol. 208, pp. 266-288, 2005 https://doi.org/10.1016/j.jcp.2005.02.014
  9. 이상현, '예조건화 오일러 방정식의 계산오차 문제', 한국항공우주학회지. 35권 7호, pp. 586-591, 2007 https://doi.org/10.5139/JKSAS.2007.35.7.586
  10. Guillard, S., and Viozat, c., 'On the Behaviour of Upwind Schemes in the Low Mach Number Limit', Computers & Fluid, Vol. 28, pp. 63-86, 1999 https://doi.org/10.1016/S0045-7930(98)00017-6