T. V. Bazhenova, L. G. Gvozdeva, and Y. V. Zhilin, Change in the shape of the diffracting shock wave at a convex corner, Acta Astronautica, vol.6, issue.3, pp.401-412, 1979.

G. Ben-dor, Handbook of Shock Waves, Oblique Shock Wave Reflections, vol.2, pp.68-179, 2000.

C. Besset and E. Blanc, Propagation of vertical shock waves in the atmosphere, The Journal of the Acoustical Society of America, vol.95, issue.4, pp.1830-1839, 1994.

J. P. Best, A generalisation of the theory of geometrical shock dynamics, Shock Waves, vol.1, issue.4, pp.251-273, 1991.

C. J. Catherasoo and B. Sturtevant, Shock dynamics in non-uniform media, Journal of Fluid Mechanics, vol.127, pp.539-561, 1983.

S. Gottlieb and C. W. Shu, Total variation diminishing Runge-Kutta schemes. Mathematics of computation of the, vol.67, pp.73-85, 1998.

W. D. Henshaw, N. F. Smyth, and D. W. Schwendeman, Numerical shock propagation using geometrical shock dynamics, Journal of Fluid Mechanics, vol.171, pp.519-545, 1986.

H. T. Huynh, Accurate monotone cubic interpolation, SIAM Journal on Numerical Analysis, vol.30, issue.1, pp.57-100, 1993.

H. Jourdren, HERA: a hydrodynamic AMR platform for multi-physics simulations, Adaptive Mesh Refinement-Theory and Applications, pp.283-294, 2005.

B. I. Kvasov, Monotone and convex interpolation by weighted quadratic splines, Advances in Computational Mathematics, vol.40, pp.91-116, 2014.

W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, ACM siggraph computer graphics, vol.21, issue.4, pp.163-169, 1987.

Y. Noumir, A. L. Guilcher, N. Lardjane, R. Monneau, and A. Sarrazin, A fast-marching like algorithm for geometrical shock dynamics, Journal of Computational Physics, vol.284, pp.206-229, 2015.

S. Osher and C. W. Shu, High-order essentially nonoscillatory schemes for HamiltonJacobi equations, SIAM Journal on Numerical Analysis, vol.28, issue.4, pp.907-922, 1991.

K. Oshima, Propagation of spacially non-uniform shock waves, ISAS report, vol.30, issue.6, p.195, 1965.

K. Oshima, K. Sugaya, M. Yamamoto, and T. Totoki, Diffraction of a plane shock wave around a corner, ISAS report, vol.30, issue.2, pp.51-82, 1965.

M. Pandey and V. D. Sharma, Kinematics of a shock wave of arbitrary strength in a non-ideal gas, Quarterly of Applied Mathematics, vol.67, issue.3, pp.401-418, 2009.

J. Ridoux, Contribution au développement d'une méthode de calcul rapide de propagation des ondes de souffle en présence d'obstacles, 2017.

J. Ridoux, N. Lardjane, L. Monasse, and F. Coulouvrat, Comparison of Geometrical Shock Dynamics and Kinematic models for shock wave propagation, Shock Waves, vol.27, issue.5, pp.1-16, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01511489

P. Romon, Introduction à la géométrie différentielle discrète. Ellipses, 2013.

D. W. Schwendeman, A numerical scheme for shock propagation in three dimensions, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.416, pp.179-198, 1850.
DOI : 10.1098/rspa.1988.0033

D. W. Schwendeman, Numerical shock propagation in non-uniform media, Journal of Fluid Mechanics, vol.188, pp.383-410, 1988.
DOI : 10.1017/s0022112088000771

D. W. Schwendeman, A new numerical method for shock wave propagation based on geometrical shock dynamics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.441, pp.331-341, 1912.
DOI : 10.1098/rspa.1993.0064

D. W. Schwendeman, A higher-order Godunov method for the hyperbolic equations modelling shock dynamics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.455, pp.1215-1233, 1984.
DOI : 10.1098/rspa.1999.0356

URL : http://rspa.royalsocietypublishing.org/content/royprsa/455/1984/1215.full.pdf

D. W. Schwendeman, On converging shock waves of spherical and polyhedral form, Journal of Fluid Mechanics, vol.454, pp.365-386, 2002.

D. W. Schwendeman and G. B. Whitham, On converging shock waves, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.413, pp.297-311, 1845.
DOI : 10.1098/rspa.1987.0116

V. D. Sharma and C. Radha, On one-dimensional planar and nonplanar shock waves in a relaxing gas, Physics of Fluids, vol.6, issue.6, pp.2177-2190, 1994.
DOI : 10.1063/1.868220

V. D. Sharma and C. Radha, Three dimensional shock wave propagation in an ideal gas, International Journal of Non-Linear Mechanics, vol.30, issue.3, pp.305-322, 1995.
DOI : 10.1016/0020-7462(95)00005-9

W. Shi and C. K. Cheung, Performance evaluation of line simplification algorithms for vector generalization, The Cartographic Journal, vol.43, issue.1, pp.27-44, 2006.
DOI : 10.1179/000870406x93490

URL : http://hdl.handle.net/10397/32700

B. W. Skews, The shape of a diffracting shock wave, Journal of Fluid Mechanics, vol.29, issue.02, pp.297-304, 1967.

B. W. Skews, Shock wave diffraction on multi-facetted and curved walls, Shock Waves, vol.14, issue.3, pp.137-146, 2005.
DOI : 10.1007/s00193-005-0266-5

D. A. Tariq, J. B. Bdzil, and D. S. Stewart, Level set methods applied to modeling detonation shock dynamics, Journal of Computational Physics, vol.126, issue.2, pp.390-409, 1996.

G. B. Whitham, A new approach to problems of shock dynamics. Part I: Twodimensional problems, Journal of Fluid Mechanics, vol.2, issue.2, pp.145-171, 1957.

G. B. Whitham, A new approach to problems of shock dynamics. Part II: Threedimensional problems, Journal of Fluid Mechanics, vol.5, issue.3, pp.369-386, 1959.

G. B. Whitham, Linear and Nonlinear Waves, chapter 8: Shock Dynamics, 1999.
DOI : 10.1002/9781118032954