T. Allahviranloo, N. Ahmady, and E. Ahmady, Numerical solution of fuzzy differential equations by predictor???corrector method, Information Sciences, vol.177, issue.7, pp.1633-1647, 2007.
DOI : 10.1016/j.ins.2006.09.015

C. Altmann, T. Belat, M. Gutnic, P. Helluy, H. Mathis et al., A local time-stepping Discontinuous Galerkin algorithm for the MHD system, CEM- RACS 2008?Modelling and numerical simulation of complex fluids, pp.33-54, 2009.
DOI : 10.1051/proc/2009038

URL : https://hal.archives-ouvertes.fr/inria-00594611

M. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, Journal of Computational Physics, vol.82, issue.1, pp.64-84, 1989.
DOI : 10.1016/0021-9991(89)90035-1

M. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, Journal of Computational Physics, vol.53, issue.3, pp.484-512, 1984.
DOI : 10.1016/0021-9991(84)90073-1

T. Coupez and E. Hachem, Solution of high-Reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.65-85, 2013.
DOI : 10.1016/j.cma.2013.08.004

URL : https://hal.archives-ouvertes.fr/hal-00866734

M. Ersoy, F. Golay, and L. Yushchenko, Abstract, Open Mathematics, vol.11, issue.8, pp.1392-1415, 2013.
DOI : 10.2478/s11533-013-0252-6

R. Eymard, G. T. , and R. Herbin, Finite volume methods, in Handbook of numerical analysis, Handb. Numer. Anal, vol.VII, pp.713-1020, 2000.

D. Fuster, G. Agbaglah, C. Josserand, S. Popinet, and S. Zaleski, Numerical simulation of droplets, bubbles and waves: state of the art, Fluid Dynamics Research, vol.41, issue.6, pp.41-065001, 2009.
DOI : 10.1088/0169-5983/41/6/065001

URL : https://hal.archives-ouvertes.fr/hal-01445431

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, of Applied Mathematical Sciences, 1996.
DOI : 10.1007/978-1-4612-0713-9

F. Golay, M. Ersoy, L. Yushchenko, and D. Sous, Block-based adaptive mesh refinement scheme using numerical density of entropy production for three-dimensional two-fluid flows, International Journal of Computational Fluid Dynamics, vol.1, issue.1, pp.29-67, 2015.
DOI : 10.1016/S0045-7825(99)00099-7

URL : https://hal.archives-ouvertes.fr/hal-01226163

F. Golay and P. Helluy, Numerical schemes for low Mach wave breaking, International Journal of Computational Fluid Dynamics, vol.45, issue.2, pp.69-86, 2007.
DOI : 10.1016/S0021-9991(02)00058-X

URL : https://hal.archives-ouvertes.fr/hal-00139634

E. Hachem, S. Feghali, R. Codina, and T. Coupez, Immersed stress method for fluid-structure interaction using anisotropic mesh adaptation, International Journal for Numerical Methods in Engineering, vol.230, issue.4, pp.805-825, 2013.
DOI : 10.1002/nme.4481

URL : https://hal.archives-ouvertes.fr/hal-00815641

E. Hairer, S. P. Nørsett, and G. Wanner, Solving ordinary differential equations. I, of Springer Series in Computational Mathematics, 1993.
DOI : 10.1007/978-3-662-12607-3

P. Houston, J. Mackenzie, E. Süli, and G. Warnecke, A posteriori error analysis for numerical approximations of Friedrichs systems, Numerische Mathematik, vol.82, issue.3, pp.433-470, 1999.
DOI : 10.1007/s002110050426

A. Ka?eniauskas, Development of efficient interface sharpening procedure for viscous incompressible flows, Informatica, vol.19, pp.487-504, 2008.

S. Karni and A. Kurganov, Local error analysis for approximate solutions of hyperbolic conservation laws, Advances in Computational Mathematics, vol.36, issue.1, pp.79-99, 2005.
DOI : 10.1007/s10444-005-7099-8

A. Karni, G. Kurganov, and . Petrova, A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems, Journal of Computational Physics, vol.178, issue.2, pp.323-341, 2002.
DOI : 10.1006/jcph.2002.7024

S. Kokh, Aspects numériques et théoriques de la modélisation des écoulements diphasiques compressibles par des méthodes de capture d'interface, 2001.

S. Koshizuka, H. Tamako, and Y. Oka, A particle method for incompressible viscous flow with fluid fragmentations, Computational Fluid Dynamics Journal, vol.4, pp.29-46, 1995.

A. Kurganov and E. Tadmor, Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numerical Methods for Partial Differential Equations, vol.160, issue.5, pp.584-608, 2002.
DOI : 10.1002/num.10025

P. D. Lax and X. Liu, Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes, SIAM Journal on Scientific Computing, vol.19, issue.2, pp.319-340, 1998.
DOI : 10.1137/S1064827595291819

R. Liska and B. Wendroff, Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations, SIAM Journal on Scientific Computing, vol.25, issue.3, pp.995-1017, 2003.
DOI : 10.1137/S1064827502402120

F. Losasso, F. Gibou, and R. Fedkiw, Simulating water and smoke with an octree data structure, ACM Transactions on Graphics, vol.23, issue.3, pp.457-462, 2004.
DOI : 10.1145/1015706.1015745

J. Martin and W. Moyce, Part IV. An Experimental Study of the Collapse of Liquid Columns on a Rigid Horizontal Plane, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.244, issue.882, pp.312-324, 1952.
DOI : 10.1098/rsta.1952.0006

URL : https://hal.archives-ouvertes.fr/hal-00518739

C. Min and F. Gibou, A second order accurate level set method on non-graded adaptive cartesian grids, Journal of Computational Physics, vol.225, issue.1, pp.300-321, 2007.
DOI : 10.1016/j.jcp.2006.11.034

A. N. Sambe, D. Sous, F. Golay, P. Fraunié, and R. Marcer, Numerical wave breaking with macro-roughness, European Journal of Mechanics - B/Fluids, vol.30, issue.6, pp.577-588, 2011.
DOI : 10.1016/j.euromechflu.2011.03.002

URL : https://hal.archives-ouvertes.fr/hal-00979010

C. W. Schulz-rinne, J. P. Collins, and H. M. Glaz, Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics, SIAM Journal on Scientific Computing, vol.14, issue.6, pp.1394-1414, 1993.
DOI : 10.1137/0914082

K. Shyue, An eulerian interface-sharpening algorithm for compressible gas dynamics, in Modeling, Simulation and Optimization of Complex Processes-HPSC 2012, pp.221-231, 2014.

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics, 2009.

M. J. Williamschen and C. Groth, Parallel Anisotropic Block-Based Adaptive Mesh Refinement Algorithm For Three-Dimensional Flows, 21st AIAA Computational Fluid Dynamics Conference, pp.1-22, 2013.
DOI : 10.2514/6.2013-2442

P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of Computational Physics, vol.54, issue.1, pp.115-173, 1984.
DOI : 10.1016/0021-9991(84)90142-6

P. R. Woodward, Trade-offs in designing explicit hydrodynamical schemes for vector computers, Parallel computations, pp.153-171, 1982.

K. Yiu, D. Greaves, S. Cruz, A. Saalehi, and A. Borthwick, Quadtree grid generation: Information handling, boundary fitting and CFD applications, Computers & Fluids, vol.25, issue.8, pp.25-759, 1996.
DOI : 10.1016/S0045-7930(96)00029-1

M. Zhang and W. Wu, A two dimensional hydrodynamic and sediment transport model for dam break based on finite volume method with quadtree grid, Applied Ocean Research, vol.33, issue.4, pp.297-308, 2011.
DOI : 10.1016/j.apor.2011.07.004

T. Zhang and Y. X. Zheng, Conjecture on the Structure of Solutions of the Riemann Problem for Two-Dimensional Gas Dynamics Systems, SIAM Journal on Mathematical Analysis, vol.21, issue.3, pp.593-630, 1990.
DOI : 10.1137/0521032

Z. Zheng and C. Groth, Block-based adaptive mesh refinement finite-volume scheme for hybrid multiblock meshes, 7st conference on Computational Fluid Dynamics (ICCFD7), pp.1-19, 2012.