HIGH-ORDER ADAPTIVE-GRID METHOD FOR THE ANALYSIS OF UNSTEADY COMPRESSIBLE FLOW

비정상 압축성 유동 해석을 위한 고차 정확도 적응 격자 기법의 연구

  • 장세명 (군산대학교 공과대학 기계자동차공학부) ;
  • Published : 2008.09.30

Abstract

The high-order numerical method based on the adaptive mesh refinement(AMR) on the quadrilateral unstructured grids has been developed in this paper. This adaptive-grid method, originally developed with MUSCL-TVD scheme, is now extended to the WENO (weighted essentially no-oscillatory) scheme with the Runge-Kutta time integration of fifth order in spatial and temporal accuracy. The multidimensional interpolation was studied in the preliminary research, which allows us to maintain the same order of accuracy for the computation of numerical flux between two adjacent cells of different levels. Some standard benchmark tests are done to validate this method for checking the overall capacity and efficiency of the present adaptive-grid technique.

Keywords

References

  1. 2004, Colonius T. and Lele S.K., "Computational Acoustics: Progress on Nonlinear Problems of Sound Generation," Progress in Aerospace Science, Vol.40, pp.345-416 https://doi.org/10.1016/j.paerosci.2004.09.001
  2. 1994, Liu X.D., Osher S. and Chan T., "Weighted Essentially Non-Oscillatory Schemes," J. Computational Physics, Vol.115, pp.200-212 https://doi.org/10.1006/jcph.1994.1187
  3. 1996, Jiang G. and Shu C.W., "Efficient Implementation of Weighted ENO Schemes," J. Computational Physics, Vol.126, pp.202-228 https://doi.org/10.1006/jcph.1996.0130
  4. 1989, Berger M.J. and Colella P., "Local Adaptive Mesh Refinement for Shock Hydrodynamics," J. Computational Physics, Vol.82, pp.64-84 https://doi.org/10.1016/0021-9991(89)90035-1
  5. 1998, Berger M.J. and Leveque R.J., "Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems," SIAM J. Numerical Analysis, Vol.35, No.6, pp.2298-2316 https://doi.org/10.1137/S0036142997315974
  6. 2006, 장세명, Morris P.J., "적응 격자 고차 해상도 해법을 위한 다차원 내삽법," 한국전산유체공학회지, Vol.11, No.4, pp.39-47
  7. 2000, Chang S.M. and Chang K.S., "On the Shock-Vortex Interaction in Schardin's Problem," Shock Waves, Vol.10, No.5, pp.333-343 https://doi.org/10.1007/s001930000061
  8. 2004, Chang S.M., Chang K.S. and Lee S., "Reflection and Penetration of a Shock Wave Interacting with a Starting Vortex," AIAA J., Vol.42, No.4, pp.796-805 https://doi.org/10.2514/1.9560
  9. 1993, Zeeuw D.D. and Powell K.G., "An Adaptively Refined Cartesian Mesh Solver for Euler Equations," J. Computational Physics, Vol.104, pp. 56-68 https://doi.org/10.1006/jcph.1993.1007
  10. 1986, Oden J.T., Strouboulis T. and Devloo P., "Adaptive Finite Element Methods for the Analysis of Inviscid Compressible Flow," Computer Methods in Applied Mechanics and Engineering, Vol.59, pp.327-362 https://doi.org/10.1016/0045-7825(86)90004-6
  11. 1997, Toro E.F., Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag
  12. 2001, Kermani M.J. and Plett E.G., "Modified Entropy Correction Formula for the Roe Scheme," AIAA2001-0083, AIAA Annual Meeting, Reno, Nevada, USA
  13. 2004, Bogey C. and Bailly C., "A Family of Low Dispersive and Low Dissipative Explicit Schemes for Flow and Noise Computations," J. Computational Physics, Vol.194, pp. 194-214 https://doi.org/10.1016/j.jcp.2003.09.003
  14. 2002, Prozzoli S., "Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction Problems," J. Computational Physics, Vol.210, pp.554-583 https://doi.org/10.1016/j.jcp.2005.04.023
  15. 1984, Woodward P. and Colella P., "Numerical Simulation of Two-dimensional Fluid Flow with Strong Shocks," J. Computational Physics, Vol.54, pp.115-173 https://doi.org/10.1016/0021-9991(84)90142-6
  16. 2005, 장세명, 장근식, "충격파-와동 간섭의 파라메터 연구," 대한기계학회논문집 B권, Vol.29, No.8, pp.921-926