The paper contains a stability analysis of the plane-wave Riemann problem for the two-dimensional hyperbolic conservation laws for an ideal compressible gas. It is proved that the contact discontinuity in the plane-wave Riemann problem is unstable under perturbations. T... View more
[ATP1984] D. A. Anderson, J. C. Tannehill, R. H. Pletcher, "Computational Fluid Mechanics and Heat Transfer", HEMISPHERE Publishing Corporation, 1984.
[CF1948] R. Courant and K. 0. Friedrichs, "Supersonic Flow and Shock Waves", Interscience, New York, 1948 [DMG;2004]M. Dumbser, J. M. Moschetta and J. Gressier, "A Matrix stability analysis of the carbuncle phenomenon", J. Comput. Phys., 197, 647-670 (2004) [EIN1988] B. Einfeldt, "On Godunov-type methods for gas dynamics", SIAM J.
Numer. Anal., 25, 294-318 (1988).
[GRE1998]J. Gressier and J.-M. Moschetta "Robustness versus Accuracy in ShockWave Computations", International Journal of Numerical Methods in Fluids, July 1999.
[KL1989] H. O. Kreiss and J. Lorenz, "Initial-Boundary Value Problems and the Navier-Stokes Equations", Academic Press 1989.
[LAX2006] P. D. Lax, "Hyperbolic Partial Differential Equations", Courant Lecture Notes 14, 2006.
[LEV2002] R. J. LeVeque, "Finite Volume Methods for Hyperbolic Problems", Cambridge University Press, Cambridge, 2002.
[LL1959] L. D. Landau and E. M. Lifchitz, "Fluid Mechanics", Addison-Wesley Publishing, 1957.
[MA1983] A. Majda, "The stability of multi-dimensional shock fronts", Memories of the AMS Number 275, 1983.
[PEIM1988] K.M. Perry and S. T Imlay, "Blunt Body Flow Simulations", AIAA Paper, 88-2924,1988.