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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Harten, “High resolution schemes for hyperbolic conservation laws”, J. Comp. Phys, 49 pp357–393, 1983.
D.M. Causon, “Numerical computation of external transonic flows”, in Proc. of the 7th Gamm Conf. on Num. Meth. in Fl. Mech., Vieweg 1988.
P.K. Sweby, “High resolution schemes using flux limiters for hyperbolic conservation laws”, Siarn J. Num. Anal. 21 No 5 pp995–1011, 1984.
Lax P. and Wendroff B., “Systems of conservation laws”, Comm. on Pure and App. Math., 13 pp217–237, 1960.
Davis S.F. “T.V.D. finite difference schemes and artificial viscosity”, ICASE report
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.
Lax P. “Shock waves and entropy”, Proc. Symp at the Univ. of Wisconsin. E.H. Zarantonello, 110, ed. pp603-634, 1971.
Merriam M.L. “Smoothing and the second law”, Comp. Meth. in App. Mech. and Eng. 64 pp177–193, 1987.
Roe P.L. “Approximate Riemann solvers, parameter vectors and difference schemes”, J. Comp. Phys., 43 pp357–372, 1981.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer Fachmedien Wiesbaden
About this paper
Cite this paper
Clarke, N., Saunders, R., Causon, D.M. (1990). A Convenient Entropy Satisfying T.V.D. Scheme for Computational Aerodynamics. In: Wesseling, P. (eds) Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics. Notes on Numerical Fluid Mechanics (NNFM), vol 29. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-13975-1_7
Download citation
DOI: https://doi.org/10.1007/978-3-663-13975-1_7
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07629-0
Online ISBN: 978-3-663-13975-1
eBook Packages: Springer Book Archive