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

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

DOI QR Code

3차원 유동 시뮬레이션을 위한 Supercompact 다중 웨이블릿

Supercompact Multiwavelets for Three Dimensional Flow Field Simulation

  • 발행 : 2005.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 supercompact 다중 웨이블릿 기법과 이 기법의 유동 시뮬레이션 데이터에의 적용을 발표한다. Supercompact 웨이블릿 방법은 간결한 지원(support)을 제공할 수 있고 또 속성이 다른 떨어져 있는 데이터와(예: 충격파의 불연속구간 또는 와동을 가로지르는 부분) 불필요한 상호작용을 피할 수 있는 점에서 유동 시뮬레이션 데이터를 위한 적합한 웨이블릿 방법이라 할 수 있다. 데이터 압축을 위한 임계처리법(thresholding)은 다중 웨이블릿의 공분산 벡터 구조 기반 하에 적용된다. 본 논문은 3차원으로의 기법 확장이 설명 분석되었다. 수치실험은 본 방법이 여러 이론적인 이점을 제공할 수 있고 실제 결과에 있어서 큰 데이터 압축 비율을 산출 할 수 있음을 보여준다.

This paper presents a supercompact multi-wavelet scheme and its application to fluid simulation data. The supercompact wavelet method is an appropriate wavelet for fluid simulation data in the sense that it can provide compact support and avoid unnecessary interaction with remotely located data (e.g. across a shock discontinuity or vortices). thresholding for data compression is applied based on a covariance vector structure of multi-wavelets. The extension of this scheme to three dimensions is analyzed. The numerical tests demonstrate that it can allow various analytic advantages as well as large data compression ratios in actual practice.

키워드

참고문헌

  1. Engquist, B., Osher, S., and Zhong, S., 'Fast wavelets based algorithms for linear evolution equations', lCASE Report, 1992
  2. Harten, A., 'Multiresolution algorithm for the numerical solution of hyperbolic conservation laws', Comm. Pure Appl. Math., Vol. 48, 1995, pp. 1305-1342 https://doi.org/10.1002/cpa.3160481201
  3. Harten, A., 'Multiresolution algorithm for the numerical solution of hyperbolic conservation laws', CAM report 93-03(1993) pp. 153-192
  4. Gerritsen, M., Designing an efficient solution strategy for fluid flows, Ph.D. thesis, Stanford University, 1996
  5. Sweldens, W., 'The lifting scheme: a new philosophy in biorthogonal wavelet constructions', Proc. SPlE, 1995, pp. 68-79
  6. Daubechies, I., 'Orthonormal Basis of Compactly Supported Wavelets', Comm. Pure Appl. Math., Vol. 41, 1988, pp. 909-996 https://doi.org/10.1002/cpa.3160410705
  7. Geronimo, J., Hardin, D., and Massopust, P., 'Fractal Functions and Wavelet Expansions based on several Scaling Functions', J. Approx. Theory, Vol. 78, 1994, pp. 373-401 https://doi.org/10.1006/jath.1994.1085
  8. Strang, G. and Strela, V., 'Orthogonal Multiwavelets with Vanishing Moments', J.Opt. Eng., Vol. 33, 1994, pp. 2104-2107 https://doi.org/10.1117/12.172247
  9. Alpert, B., 'A class of bases in $L^2$ for the Sparse Representation of Integral Operators', SIAM Journal on Mathematical Analysis, 1993, pp. 246-262
  10. Harten, A., 'Discrete multi-resolution analysis and generalized wavelets', Applied Numerical Mathematics, Vol. 12, 1993, pp. 152-192
  11. Harten, A., 'Multiresolution representation and numerical algorithms: a brief review', Tech. Rep. 94-59, lCASE report, 1994
  12. Downie, T. R. and Silverman, B. W., 'The Discrete Multiple Wavelet Transform and 임계처리법 (thresholding)', IEEE trans on Sig Proc
  13. Lee D., Beam R. M., Warming R. F., 'Supercompact Multi-Wavelets for flow field simulation', Computers and Fluids, Vol. 30(7-8), 2001, pp. 783-805 https://doi.org/10.1016/S0045-7930(01)00029-9
  14. Rott, N., 'On the Viscous Core of a Line Vortex', Journal of Applied Mathematics and Physics, Vol. 9b, No. 5/6, 1958, pp. 543-553
  15. Dacles-Mariani, J., Zilliac, G. G., Chow, J. S., and Bradshaw, P., 'Numerical/Experimental Study of a Wingtip Vortex in the Near Field', AlAA Journal, Vol. 33, No.9, 1995, pp. 1561-1568
  16. Rogers, S. E., Kwak, D., and Kiris, C, 'Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations', AIAA Journal, Vol. 29, No.4, 1991, pp. 603-610 https://doi.org/10.2514/3.10627
  17. Cox, M. and Ellsworth, D., 'Managing Big Data for Scientific Visualization', ACM SIGGRAPH '97 Course #4, Exploring Gigabyte Datasets in Real-Time: Algorithms, Data Management, and Time-Critical Design, 1997