Advertisement

A Convenient Entropy Satisfying T.V.D. Scheme for Computational Aerodynamics

  • N. Clarke
  • R. Saunders
  • D. M. Causon
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)

Abstract

Conservative shock capturing methods for the unsteady Euler equations are reviewed and it is shown that the concepts of entropy satisfaction and total variation diminution can be applied to the classical Lax-Wendroff scheme. For an associated scheme to be efficient in applications, it is necessary that it be able to capture strong shock waves with high resolution. We describe a scheme which is efficient in both respects.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Harten, “High resolution schemes for hyperbolic conservation laws”, J. Comp. Phys, 49 pp357–393, 1983.MathSciNetADSzbMATHCrossRefGoogle Scholar
  2. [2]
    D.M. Causon, “Numerical computation of external transonic flows”, in Proc. of the 7th Gamm Conf. on Num. Meth. in Fl. Mech., Vieweg 1988.Google Scholar
  3. [3]
    P.K. Sweby, “High resolution schemes using flux limiters for hyperbolic conservation laws”, Siarn J. Num. Anal. 21 No 5 pp995–1011, 1984.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    Lax P. and Wendroff B., “Systems of conservation laws”, Comm. on Pure and App. Math., 13 pp217–237, 1960.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    Davis S.F. “T.V.D. finite difference schemes and artificial viscosity”, ICASE reportGoogle Scholar
  6. [6]
    Harten A., “The artificial compression method for computation of shocks and contact discontinuities: m. Self-adjusting hybrid schemes”, Math. of Comp. 32 No 142, pp363–389, 1978.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Lax P. “Shock waves and entropy”, Proc. Symp at the Univ. of Wisconsin. E.H. Zarantonello, 110, ed. pp603-634, 1971.Google Scholar
  8. [8]
    Merriam M.L. “Smoothing and the second law”, Comp. Meth. in App. Mech. and Eng. 64 pp177–193, 1987.MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. [9]
    Roe P.L. “Approximate Riemann solvers, parameter vectors and difference schemes”, J. Comp. Phys., 43 pp357–372, 1981.MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. [10]
    Roe P.L and Pike J., “Efficient construction and utilisation of approximate Riemann solutions”, Comp Meth. in App. Sc. and Eng. 6. Ed. R. Glowinski and J.L. Lions. pp.499-518, 1984.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • N. Clarke
    • 1
  • R. Saunders
    • 1
  • D. M. Causon
    • 1
  1. 1.Department of Mathematics and PhysicsManchester PolytechnicManchesterUK

Personalised recommendations