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

A Study of Monotonic Characteristics of AUSM - type Schemes in Shock Regions

충격파 영역에서의 AUSM 계열 수치기법의 단조성에 관한 연구

  • Published : 2002.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

The monotonic characteristics of AUSM-type shemes are proven by mathmatics and numerics. Qualitatively well-known characteristics are quantified by mathematics and the magnitude of oscillatory behaviors of each schemes could be compared directly. Moreover, it is also studied how the sonic transition position affects the oscillation in capturing the shocks. Lastly M-AUSMPW+, the latest improved AUSM-type scheme, is shown to have monotonic characeristics though all shock conditions.

AUSM계열 수치기법이 가지는 전동현상에 대해 수학적, 수치적 방법을 이용하여 이를 증명하였다. 이제까지 정성적으로 알려진 내용을 수학적 방법을 통해 정량화하여, 각 수치기법의 진동 크기에 대한 직접적인 비교를 수행하였다. 음속천이점 위치에 따른 각 수치기법의 특성을 파악할 수 있고 M-AUSMPW+수치기법은 전 마하수 영역에 걸쳐 단조성을 유지하면서 충격파를 포착하는 것을 확인할 수 있었다.

Keywords

References

  1. J. Gressier, P. Villedieu, and J-M Moshetta, Positivity of Flux Vector Splitting Schemes, J. of Computational Physics, 155, 199-220 (1999). https://doi.org/10.1006/jcph.1999.6337
  2. M. S. Liou, A Sequel to AUSM: AUSM+, J. of Computational Physics, 129, 364-382 (1996). https://doi.org/10.1006/jcph.1996.0256
  3. K. H. Kim, J. H. Lee, and O. H. Rho, "An Improvement of AUSM Schemes by Introducing the Pressure-based Weight Functions," Computers & Fluids, 27(3), 311-346 (1998). https://doi.org/10.1016/S0045-7930(97)00069-8
  4. K. H. Kim, C. Kim, and O. H. Rho, "Methods for the Accurate Computations of Hypersonic Flows, PART I: AUSMPW+ Scheme," accepted to J. of Computational Physics, (2001). https://doi.org/10.1006/jcph.2001.6873
  5. H. C. Yee, G. H. Kolpfer, and J. L. Montague, High-Resolution Shock Capturing Schemes for Inviscid and Viscous Hypersonic Flows, NASA TM 101088, 1989.
  6. D. Hanel, R. Schwane, and G. Seider, On the Accuracy of Upwind Schemes for the Solution of the Navier-Stokes Equations, AIAA paper 87-1105-CP, 1987.
  7. A. Harten, High Resolution Schemes for Hyperbolic Conservation Laws, J. of Computational Physics, 49, 357-393 (1983). https://doi.org/10.1016/0021-9991(83)90136-5
  8. P. K. Sweby, High Resolution TVD Schemes Using Flux Limiters, Lectures in Applied Mathematics, 22, 289-309 (1985).
  9. P. L. Roe, A Survey of Upwind Differencing Techniques, Lecture Notes in Physics, 323, 69 (1989). https://doi.org/10.1007/3-540-51048-6_6
  10. C. Hirsh, Numerical Computation of Internal and External Flows, Vol. 1,2, (John Wiley & Sons, 1990).