publication . Other literature type . Article . 2000

Shock wave instability and the carbuncle phenomenon : same intrinsic origin?

Robinet, Jean-Christophe; Gressier, Jérémie; Casalis, Grégoire; Moschetta, Jean-Marc;
  • Published: 25 Aug 2000
  • Publisher: Cambridge University Press (CUP)
  • Country: France
Abstract
<jats:p>The theoretical linear stability of a shock wave moving in an unlimited homogeneous environment has been widely studied during the last fifty years. Important results have been obtained by Dýakov (1954), Landau &amp; Lifchitz (1959) and then by Swan &amp; Fowles (1975) where the fluctuating quantities are written as normal modes. More recently, numerical studies on upwind finite difference schemes have shown some instabilities in the case of the motion of an inviscid perfect gas in a rectangular channel. The purpose of this paper is first to specify a mathematical formulation for the eigenmodes and to exhibit a new mode which was not found by the previou...
Subjects
free text keywords: Mécanique des fluides, Shock wave instability, Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics, Classical mechanics, Linear stability, Normal mode, Euler equations, symbols.namesake, symbols, Carbuncle, medicine.disease, medicine, Inviscid flow, Perfect gas, Instability, Physics, Shock wave
35 references, page 1 of 3

Batten, P., Clarke, N., Lambert, C. & Causon, D. M. 1997 On the choice of waves speeds for the HLLC Riemann solver. SIAM J. Sci. Comput. 18, 1553{1570. [OpenAIRE]

Casalis, G. & Robinet, J.-Ch. 1997 Linear stability analysis in transonic di user flows. Aerospace Sci. Technol. 1, 37{47.

Dyakov, S. P. 1954 On the stability of shock waves. Sov. Phys. JETP 27, 288{295.

Dyakov, S. P. 1957 The interaction of shock waves with small perturbations. Sov. Phys. JETP 33, 948{974.

Einfeldt, B., Munz, C. D., Roe, P. L. & Sjo¨green, B. 1991 On Godunov-type methods near low densities. SIAM J. Numer. Anal. 92, 273{295. [OpenAIRE]

Flandrin, L., Charrier, P. & Dubroca, B. 1994 A robust nite volume method for computations on two-dimensional unstructured hybrid meshes. In Computational Fluid Dynamics. John Wiley & Sons.

Fowles, G. R. & Houwing, A. F. P. 1984 Instabilities of shock and detonation waves. Phys. Fluids 27, 1982{1990.

Godunov, S. K. 1959 A di erence scheme for numerical computation of discontinuous solutions of hydrodynamics equations. Math. Sbornik 47, 271{306.

Gressier, J. & Moschetta, J.-M. 1998a On the marginal stability of upwind schemes. In 16th ICNMFD, pp. 385{390. Springer.

Gressier, J. & Moschetta, J.-M. 1998b On the pathological behavior of upwind schemes. AIAA Paper 98-0110. [OpenAIRE]

Gressier, J. & Moschetta, J.-M. 1999 Robustness versus accuracy in shock wave computations. Intl J. Numer. Meth. Fluids (accepted).

Hafez, M. M. & Guo, W. H. 1999 Some anomalies of numerical simulation of shock waves. Part I: inviscid flows. Comput. Fluids 28, 701{719.

Harten, A., Lax, P. D. & Leer, B. van 1983 On upstream di erencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25, 35{61. [OpenAIRE]

Ivanov, M. M., Gimelshein, S. F. & Beylich, A. E. 1995 Hysteresis e ect in stationary reflection of shock waves. Phys. Fluids 7, 685{687.

Kontorovitch, V. M. 1957 Reflection and refraction of sound by shock waves. Sov. Phys. JETP 33, 1527.

35 references, page 1 of 3
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publication . Other literature type . Article . 2000

Shock wave instability and the carbuncle phenomenon : same intrinsic origin?

Robinet, Jean-Christophe; Gressier, Jérémie; Casalis, Grégoire; Moschetta, Jean-Marc;