Advertisement

Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics

  • Christopher K. W. Tam
  • Zhong Dong
Article

Abstract

High-order finite-difference schemes are less dispersive and dissipative but, at the same time, more isotropic than low-order schemes. They are well suited for solving computational acoustics problems. High-order finite-difference equations, however, support extraneous wave solutions which bear no resemblance to the exact solution of the original partial differential equations. These extraneous wave solutions, which invariably degrade the quality of the numerical solutions, are usually generated when solid-wall boundary conditions are imposed. A set of numerical boundary conditions simulating the presence of a solid wall for high-order finite-difference schemes using a minimum number of ghost values is proposed. The effectiveness of the numerical boundary conditions in producing quality solutions is analyzed and demonstrated by comparing the results of direct numerical simulations and exact solutions.

Keywords

Exact Solution Partial Differential Equation Ghost Acoustics Direct Numerical Simulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, D.A., Tannehill, J.C., and Pletcher, R.H. (1984). Computational Fluid Mechanics and Heat Transfer. McGraw-Hill, Washington.Google Scholar
  2. Bayliss, A., and Turkel, E. (1980). Radiation Boundary Conditions for Wave-Like Equations. Comm. Pure Appl. Math., 33, 707–725.Google Scholar
  3. Bayliss, A., and Turkel, E. (1982). Far Field Boundary Conditions for Compressible Flows. J. Comput. Phys., 48, 182–199.Google Scholar
  4. Briggs, R.J. (1964). Electron-Stream Interaction with Plasmas. MIT Press, Cambridge, MA.Google Scholar
  5. Engquist, B., and Majda, A. (1977). Absorbing Boundary Conditions for the Numerical Simulation of Waves. Math. Comp., 31, 629–651.Google Scholar
  6. Engquist, B., and Majda, A. (1979). Radiation Boundary Conditions for Acoustic and Elastic Wave Calculations. Comm. Pure Appl. Math., 32, 313–357.Google Scholar
  7. Givoli, D. (1991). Non-Reflecting Boundary Conditions. J. Comput. Phys., 94, 1–29.Google Scholar
  8. Jiang, H., and Wong, Y.S. (1990). Absorbing Boundary Conditions for Second-Order Hyperbolic Equations. J. Comput. Phys., 88, 205–231.Google Scholar
  9. Khan, M.M.S., Brown, W.H., and Ahuja, K.K. (1987). Computational Aeroacoustics as Applied to the Diffraction of Sound by Cylindrical Bodies. AIAA J., 25, 949–955.Google Scholar
  10. Oran, E.S., and Boris, J.P. (1987). Numerical Simulation of Reactive Flow. Elsevier, New York.Google Scholar
  11. Tam, C.K.W., and Hu, F.Q. (1989), Three Families of Instability Waves of High Speed Jets. J. Fluid Mech., 201, 447–483.Google Scholar
  12. Tam, C.K.W., and Webb, J.C. (1993). Dispersion-Relation-Preserving Schemes for Computational Acoustics. J. Comput. Phys., 107, 262–281.Google Scholar
  13. Tam, C.K.W., Webb, J.C., and Dong, Z. (1993). A Study of the Short Wave Components in Computational Acoustics. J. Comput. Acoustics, 1, 1–30.Google Scholar
  14. Thompson, K.W. (1990). Time-Dependent Boundary Conditions for Hyperbolic Systems, II. J. Comput. Phys., 89, 439–461.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Christopher K. W. Tam
    • 1
  • Zhong Dong
    • 1
  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA

Personalised recommendations