Blast wave calculation, Communications on Pure and Applied Mathematics, vol.8, issue.2, pp.327-354, 1955. ,
DOI : 10.1002/cpa.3160080207
Numerical Solutions of Spherical Blast Waves, Journal of Applied Physics, vol.26, issue.6, pp.766-775, 1955. ,
DOI : 10.1063/1.1722085
URL : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA595878
A numerical method for a converging cylindrical shock, Journal of Fluid Mechanics, vol.18, issue.02, pp.185-200, 1957. ,
DOI : 10.1007/BF02036751
A numerical study of a converging cylindrical shock, Journal of Fluid Mechanics, vol.47, issue.04, pp.785-794, 1977. ,
DOI : 10.1016/0021-9991(71)90038-6
Similarity Q6 and dimensional methods in mechanics, 1959. ,
Numerical experiments using high-resolution schemes for unsteady, inviscid, compressible flows, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.42-44, pp.42-444675, 2004. ,
DOI : 10.1016/j.cma.2004.03.012
The numerical simulations of explosion and implosion in air: use of a modified Harten's TVD scheme, International Journal for Numerical Methods in Fluids, vol.2, issue.4, pp.661-680, 1999. ,
DOI : 10.1002/(SICI)1097-0363(19991030)31:4<661::AID-FLD866>3.0.CO;2-G
On the symmetric form of systems of conservation laws with entropy, Journal of Computational Physics, vol.49, issue.1, pp.151-164, 1983. ,
DOI : 10.1016/0021-9991(83)90118-3
Los Alamos National Laboratory LA-UR-03-8922, 2003. ,
Spherical Richtmyer-Meshkov instability for axisymmetric flow, Mathematics and Computers in Simulation, vol.65, issue.4-5, pp.4-5417, 2004. ,
DOI : 10.1016/j.matcom.2004.01.020
A high-order cell-centered Lagrangian scheme for compressible fluid flows in two-dimensional cylindrical geometry, Journal of Computational Physics, vol.228, issue.18, pp.6882-6915, 2009. ,
DOI : 10.1016/j.jcp.2009.06.018
URL : https://hal.archives-ouvertes.fr/inria-00372105
Two-dimensional central-upwind schemes for curvilinear grids and application to gas dynamics with angular momentum, Computer Physics Communications, vol.180, issue.11, pp.2283-2302, 2009. ,
DOI : 10.1016/j.cpc.2009.07.016
URL : http://arxiv.org/abs/0804.2979
A multislope MUSCL method on unstructured meshes applied to compressible Euler equations for axisymmetric swirling flows, Journal of Computational Physics, vol.229, issue.13, pp.4884-4906, 2010. ,
DOI : 10.1016/j.jcp.2010.03.004
URL : https://hal.archives-ouvertes.fr/hal-00484221
A cell-centered Lagrangian scheme with the preservation of symmetry and conservation properties for compressible fluid flows in two-dimensional cylindrical geometry, Journal of Computational Physics, vol.229, issue.19, pp.7191-7206, 2010. ,
DOI : 10.1016/j.jcp.2010.06.007
ReALE: A Reconnection Arbitrary-Lagrangian???Eulerian method in cylindrical geometry, Computers & Fluids, vol.46, issue.1, pp.59-69, 2011. ,
DOI : 10.1016/j.compfluid.2010.08.024
A class of implicit upwind schemes for Euler simulations with unstructured meshes, Journal of Computational Physics, vol.84, issue.1, pp.174-206, 1989. ,
DOI : 10.1016/0021-9991(89)90187-3
URL : https://hal.archives-ouvertes.fr/inria-00076037
The node-centred finite volume approach: Bridge between finite differences and finite elements, Computer Methods in Applied Mechanics and Engineering, vol.102, issue.1, pp.107-138, 1993. ,
DOI : 10.1016/0045-7825(93)90143-L
Unified construction of finite element and finite volume discretizations for compressible flows, Computer Methods in Applied Mechanics and Engineering, vol.39, issue.1, pp.1-32, 1996. ,
Finite element/volume solution to axisymmetric conservation laws, Journal of Computational Physics, vol.224, issue.2, pp.489-518, 2007. ,
DOI : 10.1016/j.jcp.2006.08.018
A penalty formulation for the throughflow modeling of turbomachinery, Computers & Fluids, vol.60, pp.86-98, 2012. ,
DOI : 10.1016/j.compfluid.2012.03.001
On the relation between finite element and finite volume schemes for compressible flows with cylindrical and spherical symmetry, Journal of Computational Physics, vol.230, issue.3, pp.680-694, 2011. ,
DOI : 10.1016/j.jcp.2010.10.012
Riemann solvers and numerical methods for fluid mechanics, 1997. ,
Numerical approximation of partial differential equations. No. 23 in Springer series in computational mathematics, 1994. ,
Finite element methods for flow problems, 2002. ,
DOI : 10.1002/0470013826
Theory and Practice of Finite Elements, Applied Mathematical Science, vol.159, 2004. ,
DOI : 10.1007/978-1-4757-4355-5
Finite volume methods for conservation laws and hyperbolic systems, 2002. ,
Approximate Riemann solvers, parameter vectors, and difference schemes, Journal of Computational Physics, vol.43, issue.2, pp.357-372, 1981. ,
DOI : 10.1016/0021-9991(81)90128-5
Roe Linearization for the van der Waals Gas, Journal of Computational Physics, vol.175, issue.1, pp.50-78, 2002. ,
DOI : 10.1006/jcph.2001.6915
Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme, Journal of Computational Physics, vol.14, issue.4, pp.361-370, 1974. ,
DOI : 10.1016/0021-9991(74)90019-9
Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings. 10th AIAA Computational Fluid Dynamics Conference, pp.1-13, 1991. ,
A Basic Toll Kit for Sparse Matrix Computations, 1994. ,
Efficient Unstructured Mesh Generation by Means of Delaunay Triangulation and Bowyer-Watson Algorithm, Journal of Computational Physics, vol.106, issue.1, pp.125-138, 1993. ,
DOI : 10.1006/jcph.1993.1097
Powerful spherical and cylindrical compression shocks in the neighbourhood of the centre and of the cylinder axis, Luftfahrtforschung, vol.19, pp.302-312, 1942. ,
On imploding Q7 cylindrical and spherical shock waves in a perfect gas, Journal of Fluid Mechanics, vol.560, issue.103, 2006. ,
Revisiting Wall Heating, Journal of Computational Physics, vol.162, issue.2, pp.395-410, 2000. ,
DOI : 10.1006/jcph.2000.6544
An experimental investigation of the stability of converging cylindrical shock waves in air, Experiments in Fluids, vol.33, issue.5, pp.315-322, 1987. ,
DOI : 10.1007/BF00277710
Stability of converging cylindrical shock waves, Shock Waves, vol.35, issue.2, pp.149-160, 1991. ,
DOI : 10.1007/BF01414910
Multi-material ALE computation in inertial confinement fusion code CHIC, Computers & Fluids, vol.46, issue.1, pp.161-167, 2011. ,
DOI : 10.1016/j.compfluid.2010.06.017
Focusing of Strong Shocks in an Annular Shock Tube, Shock Waves, vol.89, issue.3-4, pp.3-4205, 2006. ,
DOI : 10.1007/s00193-006-0035-0
Controlling the form of strong converging shocks by means of disturbances, Shock Waves, vol.5, issue.1-2, pp.29-42, 2007. ,
DOI : 10.1007/s00193-007-0087-9
On cylindrically converging shock waves shaped by obstacles, Physica D: Nonlinear Phenomena, vol.237, issue.14-17, pp.14-172203, 2008. ,
DOI : 10.1016/j.physd.2007.11.021
The interaction between shock waves and solid spheres arrays in a shock tube, Acta Mechanica Sinica, vol.20, issue.3, pp.219-227, 2004. ,