Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-02T18:56:10.985Z Has data issue: false hasContentIssue false
  • English
  • Français

Dissipation Improvement of MUSCL Scheme for Computational Aeroacoustics

Published online by Cambridge University Press:  05 May 2011

San-Yin Lin ,
Sheng-Chang Shih  and
Jen-Jiun Hu
San-Yin Lin*
Affiliation:
Institute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
Sheng-Chang Shih*
Affiliation:
Far East College, Tainan, Taiwan 712, R.O.C.
Jen-Jiun Hu*
Affiliation:
Insititute of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
*Professor
**Associate Professor
***Graduate student
Get access

Abstract

An upwind finite-volume scheme is studied for solving the solutions of two dimensional Euler equations. It based on the MUSCL (Monotone Upstream Scheme for Conservation Laws) approach with the Roe approximate Riemann solver for the numerical flux evaluation. First, dissipation and dispersion relation, and group velocity of the scheme are derived to analyze the capability of the proposed scheme for capturing physical waves, such as acoustic, entropy, and vorticity waves. Then the scheme is greatly enhanced through a strategy on the numerical dissipation to effectively handle aeroacoustic computations. The numerical results indicate that the numerical dissipation strategy allows that the scheme simulates the continuous waves, such as sound and sine waves, at fourth-order accuracy and captures the discontinuous waves, such a shock wave, sharply as well as most of upwind schemes do. The tested problems include linear wave convection, propagation of a sine-wave packet, propagation of discontinuous and sine waves, shock and sine wave interaction, propagation of acoustic, vorticity, and density pulses in an uniform freestream, and two-dimensional traveling vortex in a low-speed freestream.

Keywords

Upwind finite-volume schemeDissipationDispersionGroup velocity
Type
Articles
Information
Journal of Mechanics , Volume 17 , Issue 1 , March 2001 , pp. 39 - 47
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Osher, S., “Convergence of Generalized MUSCL Schemes,” SIAM Journal Numerical Analysis, 22, pp. 947–961 (1985).Google Scholar
2Yee, H. C., “A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods,” NASA Technical Memorandum 101088 (1989).Google Scholar
3Harten, A., “High Resolution Schemes for Hyperbolic Conservation Laws,” Journal of Computational Physics, 49, pp. 357–393 (1983).Google Scholar
4Jiang, G. S. and Shu, C. W., “Efficient Implementation of Weighted ENO Schemes,” ICASE Report No. 95-73 (1995).Google Scholar
5Gottlieb, D. and Orszag, S. A., Numerical Analysis of Spectral Methods, SIAM Philadelphia (1977).Google Scholar
6Lele, S. K., “Compact Finite Difference Schemes with Spectral-like Resolution,” Journal of Computational Physics, 103, pp.16–42 (1992).Google Scholar
7Tam, C. K. W. and Webb, J. C., “Dispersion- Relation-Preserving Finite Difference Schemes for Computational Acoustics,” Journal of Computational Physics, 107, pp. 262–281 (1993).Google Scholar
8Chakravarthy, S. R. and Osher, S., “A New Class of Very High Accurate TVD Schemes for Hyperbolic Conservation Laws,” AIAA Paper 85-0363 (1985).Google Scholar
9Lin, S. Y. and Chin, Y. S., “Comparison of Higher Resolution Euler Schemes for Aeroacoustic Computations,” AIAA Journal, 33(2), pp. 237–245 (1995).Google Scholar
10Roe, P. L., “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,” Journal of Computational Physics, 43, pp. 357–372 (1981).Google Scholar
11Whitham, G. B., Linear and Nonlinear Waves, Wiley, New York (1974).Google Scholar
12Lu, P. J., and Yeh, D. Y., “Transonic Flutter Suppression Using Active Acoustic Excitations,” AIAA Paper, 93-3285, July (1993).Google Scholar
13Trefethen, L. N., “Group Velocity in Finite Difference Schemes,” SIAM Review, 24(2), pp. 113–135 (1982).Google Scholar
14Cockburn, B., Lin, S. Y., and Shu, C. W., “TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws III: One Dimensional Systems,” Journal of Computational Physics, 84(1), pp. 90–113 (1989).Google Scholar
15Lin, S. Y. and Hu, J. J., “Weighted ENO Scheme for Aeroacoustic Computations and Its Boundary Condition Treatment,” AIAA Paper 99-0361, Jan(1999).Google Scholar
16Rai, M. M., “Navier-Stokes Simulations of Blade-Vortex Interaction Using High-Order Accurate Upwind Schemes,” AIAA Paper, 87-0543, Jan. (1987).Google Scholar
17Sculley, M. P., “Computation of Helicopter Rotor Wake Geometry and Its Influence on Rotor Harmonic Loads,” ASRL TR-178-1, Aeroelastic and Structure Research Laboratory, Massachuseets Institute of Technology, March (1975).Google Scholar