Numerical approximations of shock waves sometimes suffer from instabilities called carbuncles. Techniques for suppressing carbuncles are trial-and-error and lack in reliability and generality, partly because theoretical knowledge about carbuncles is equally unsatisfacto... View more
[CBGS02] J.-F. Coulombel, S. Benzoni-Gavage, and D. Serre, Note on a paper by Robinet, Gressier, Casalis & Moschetta, J. Fluid Mech. 469 (2002), 401-405.
[DMG03] M. Dumbser, J.-M. Moschetta, and J. Gressier, A matrix stability analysis of the carbuncle phenomenon, submitted to Elsevier Science, 2003.
[KRW96] D. Kr¨oner, M. Rokyta, and M. Wierse, A Lax-Wendroff type theorem for upwind finite volume schemes in 2-D, East-West J. Numer. Math. 4 (1996), 279-292.
P. Lax and B. Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217-237.
K.W. Morton and P. Roe, Vorticity-preserving Lax-Wendroff-type schemes for the system wave equation, SIAM J. Sci. Comput. 23 (2001), no. 1, 170-192.
S. Osher and F. Solomon, Upwind difference schemes for hyperbolic systems of conservation laws, Math. Comp. 38 (1982), 339-373.
K.M. Peery and S.T. Imlay, Blunt-body flow simulations, AIAA paper 88-2904, 1988.
Numer. Meth. Fluids 18 (1994), 555-574.
[LW60] [MR01] [OS82] [PI88] [Qui94] [Roe81] [SO89] [RGCJ00] J.-Ch. Robinet, J. Gressier, G. Casalis, and J.-M. Moschetta, Shock wave instability and the carbuncle phenomenon: same intrinsic origin?, J. Fluid Mech. 417 (2000), 237-263.
P.L. Roe, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (1981), 357-372.