M. G. Briscoe and A. A. Kovitz, Experimental and theoretical study of the stability of plane shock waves reflected normally from perturbed flat walls,J .F l u i dM e c h, pp.5-7

V. M. Kontorovich, Conserning the stability of shock waves,Z h .E k s p .T e o r .F i z

P. Clavin, L. He, and F. A. , WilliamsMultidimensional stability analysis of overdriven gaseous detonations ,P h y s .F l u i d s9, pp.3-7

P. Clavin and F. A. Williams, Analytical studies of the dynamics of gaseous detonations,P h i l .T r a n s, R. Soc. A, vol.243, pp.1-35, 1950.

M. S. Longuet-higgins, At h e o r yo ft h eo r i g i no fm i c r o s e i s m s ,P h i l .T r a n s .R .S o, pp.597-624

J. Larsson, I. Bermejo-moreno, and S. K. Lele, Reynolds-and Mach-number effects in canonical shockturbulence interaction, pp.2-9

J. Larsson and S. K. , Direct numerical simulation of canonical shock/turbulence interaction, Physics of Fluids, vol.21, issue.12, p.126101, 2009.
DOI : 10.1063/1.3275856

P. Clavin, Instability and nonlinear patterns of overdriven detonation in gases,inNonlinear PDE's in condensed matter and reactive flows,H .B e r e s t y c k ia n dY .P o m e a u ,e d s, pp.49-97, 2002.

P. Clavin and B. Denet, Diamond Patterns in the Cellular Front of an Overdriven Detonation, Physical Review Letters, vol.88, issue.4, p.4502, 2002.
DOI : 10.1103/PhysRevLett.88.044502

T. G. Golda, P. D. Hough, and G. Gay, APPSPACK (Asynchronous parallel pattern search package); software available at http

R. J. Leveque and M. J. Berger, Clawpack Software, www.clawpack.org [15] R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, 2002.

S. F. Shandarin and Y. Zeldovich, The large-scale structure of the universe: Turbulence, intermittency, structures in a self-gravitating medium Reviews of Modern Physics, pp.185-198, 1989.

S. N. Gurbatov, A. I. Saichev, and S. F. , Large-scale structure of the Universe. The Zeldovich approximation and the adhesion model, Physics-Uspekhi, vol.55, issue.3, pp.223-249, 2012.
DOI : 10.3367/UFNe.0182.201203a.0233

M. Vergalossa, B. Dubrulle, U. Frisch, and N. , Noullez Burgers'equation, Devil's staircases and the mass distribution for large-scale structures Astron, Astrophys, vol.289, pp.325-356, 1994.

L. Gilling, Tugen, Synthetic turbulence generator http://vbn.aau.dk/en/publications/tugen(3e097a90- b3d8-11de-a179-000ea68e967b).html [20] B. Denet , Are small scale of turbulence able to wrinkle a premixed flame at large scale,Com b, Theor. Mod, vol.2, issue.2, pp.167-178, 1998.

F. Grasso and S. Pirozzoli, Shock-wave?vortex interactions: shock and vortex deformations, and sound production,T h e o r .C o m p .F l u i dD y n, pp.4-6
DOI : 10.1007/s001620050121

A. Rault, G. Chiavassa, and R. Donat, Shock-wave?vortex interactions at high Mach numbers, Journal of Scientific Computing, vol.19, issue.1/3, pp.347-371, 2003.
DOI : 10.1023/A:1025316311633

G. Taylor, On the dissipation of eddies,T h eS c i e n t i fi cP a pe r so fS i rG e o ff r e yI n g r a mT a y l o r2, pp.96-101

S. K. Lele, Compact finite difference schemes with spectral like resolution,J .C o m p u t .P h y s, pp.0-3, 1992.

G. Jourdan, L. Houas, L. Schwaederlé, G. Layes, R. Carrey et al., An e wv a r i a b l ei n c l i n a t i o n shock tube for multiple investigations, pp.5-5

Y. Sun, Z. Wang, and Y. Liu, High-order multidomain spectral difference method for the Navier-Stokes equations on unstructured hexahedral grids, pp.3-4

A. Jameson, A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy, Journal of Scientific Computing, vol.37, issue.1, pp.348-358, 2010.
DOI : 10.1007/s10915-009-9339-4

A. Jameson, P. Vincent, and P. Castonguay, On the Non-linear Stability of Flux Reconstruction Schemes, Journal of Scientific Computing, vol.56, issue.2, pp.434-445, 2012.
DOI : 10.1007/s10915-011-9490-6

P. Ro-e, Approximate Riemann solvers, parameter vectors, and difference schemes,J .C o m p u t .P h y s, pp.357-372, 1981.

A. Harten, High resolution schemes for hyperbolic conservation laws, pp.357-393

P. O. Persson and J. Peraire, Sub-cell shock capturing for discontinuous Galerkin methods,A I A AP, 44th AIAA Aerospace Sciences Meeting and Exhibit, pp.1-13, 2006.

P. O. Persson, Shock Capturing for High-Order Discontinuous Galerkin Simulation of Transient Flow Problems, 21st AIAA Computational Fluid Dynamics Conference, pp.2013-30611, 2013.
DOI : 10.2514/6.2013-3061

J. S. Hesthaven and T. Warburton, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications,S p r i n g e rS c i e n c e + B u s i n e s sM e d i a
DOI : 10.1007/978-0-387-72067-8

G. E. Barter and D. L. , Shock capturing with PDE-based artificial viscosity for DGFEM: Part I. formulation,J .C o m p u t .P h y s REFERENCES REFERENCES According to (A16) for ? 5/3, equation (A18) has two pairs of imaginary roots REFERENCES 17 REFERENCES REFERENCES 19 REFERENCES Also note that the element-wise viscosities from Eq, C12) are made C 0 continuous as suggested in [33] by means of bilinear interpolation of the common values of ? evaluated at the elements' interfaces. REFERENCES 21, pp.2-9

D. Figure and =. Mv, 4: time evolution of numerical Schlieren plots (? * = tu 1 /H ? 1/2). (a) ? * =0.021 (b) ? * =0, p.120

D. Figure and =. Mv, 8: time evolution of numerical Schlieren plots (? * = tu 1