D. Balsara, Second-order accurate schemes for magnetohydrodynamics with divergence-free reconstruction, The Astrophysical Journal Supplement Series, vol.151, pp.149-184, 2004.

D. Balsara and M. Dumbser, Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers, Journal of Computational Physics, pp.687-715, 2015.

A. Barlow, P. Maire, W. Rider, R. Rieben, and M. Shashkov, Arbitrary Lagrangian-Eulerian methods for modeling high-speed compressible multimaterial flows, Journal of Computational Physics, vol.322, pp.603-665, 2016.

T. Barth and P. Frederickson, Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction, 1990.

T. Barth and D. Jespersen, The design and application of upwind schemes on unstructured meshes, pp.89-0366, 1989.

D. J. Benson, Computational methods in lagrangian and eulerian hydrocodes, Computer Methods in Applied Mechanics and Engineering, vol.99, issue.2, pp.235-394, 1992.

,

M. Berndt, J. Breil, S. Galera, M. Kucharik, P. Maire et al., Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods, Journal of Computational Physics, vol.230, pp.6664-6687, 2011.

S. Bertoluzza, S. D. Pino, and E. Labourasse, A conservative slide line method for cell-centered semi-Lagrangian and ALE schemes in 2D, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), vol.50, pp.187-214, 2016.

P. Bochev, D. Ridzal, and M. Shashkov, Fast optimization-based conservative remap of scalar fields through aggregate mass transfer, Journal of Computational Physics, vol.246, pp.37-57, 2013.

W. Boscheri, An efficient high order direct ALE ADER finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics, International Journal for Numerical Methods in Fluids, vol.84, pp.76-106, 2017.

W. Boscheri, An efficient high order direct ale ader finite volume scheme with a posteriori limiting for hydrodynamics and magnetohydrodynamics, International Journal for Numerical Methods in Fluids, vol.84, issue.2, pp.76-106, 2017.

W. Boscheri, High order direct arbitrary-lagrangian-eulerian (ale) finite volume schemes for hyperbolic systems on unstructured meshes, Archives of Computational Methods in Engineering, vol.24, issue.4, pp.751-801, 2017.

W. Boscheri, D. Balsara, and M. Dumbser, Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers, Journal of Computational Physics, vol.267, pp.112-138, 2014.

W. Boscheri and M. Dumbser, Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes, Communications in Computational Physics, vol.14, pp.1174-1206, 2013.

W. Boscheri and M. Dumbser, A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3d, Journal of Computational Physics, vol.275, pp.484-523, 2014.

W. Boscheri and M. Dumbser, High order accurate direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on moving curvilinear unstructured meshes, Computers and Fluids, vol.136, pp.48-66, 2016.

W. Boscheri and M. Dumbser, Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes, Journal of Computational Physics, vol.346, pp.449-479, 2017.

W. Boscheri, M. Dumbser, and D. Balsara, High-order ader-weno ale schemes on unstructured triangular meshes-application of several node solvers to hydrodynamics and magnetohydrodynamics, International Journal for Numerical Methods in Fluids, vol.76, issue.10, pp.737-778, 2014.

W. Boscheri, M. Dumbser, and D. Balsara, High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes -Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics, International Journal for Numerical Methods in Fluids, vol.76, pp.737-778, 2014.

W. Boscheri, M. Dumbser, and M. Righetti, A semi-implicit scheme for 3d free surface flows with high-order velocity reconstruction on unstructured voronoi meshes, International journal for numerical methods in fluids, vol.72, issue.6, pp.607-631, 2013.

W. Boscheri, M. Dumbser, and O. Zanotti, High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes, Journal of Computational Physics, vol.291, pp.120-150, 2015.

W. Boscheri and R. Loubère, High order accurate direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for non-conservative hyperbolic systems with stiff source terms, Communications in Computational Physics, vol.21, pp.271-312, 2017.

W. Boscheri, R. Loubère, and M. Dumbser, Direct arbitrarylagrangian-eulerian ader-mood finite volume schemes for multidimensional hyperbolic conservation laws, Journal of Computational Physics, vol.292, pp.56-87, 2015.

W. Boscheri, R. Loubère, and M. Dumbser, Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD finite volume schemes for multidimensional hyperbolic conservation laws, Journal of Computational Physics, vol.292, pp.56-87, 2015.

W. Boscheri, G. R. Pisaturo, and M. Righetti, High-order divergence-free velocity reconstruction for free surface flows on unstructured voronoi meshes, International Journal for Numerical Methods in Fluids, vol.90, issue.6, pp.296-321, 2019.

W. Boscheri, M. Semplice, and M. Dumbser, Central WENO Subcell Finite Volume Limiters for ADER Discontinuous Galerkin Schemes on Fixed and Moving Unstructured Meshes. Communications in Computational Physics, vol.25, pp.311-346, 2019.

S. Busto, J. Ferrín, E. F. Toro, and M. E. Vázquez-cendón, A projection hybrid high order finite volume/finite element method for incompressible turbulent flows, Journal of Computational Physics, vol.353, pp.169-192, 2018.

E. Caramana, The implementation of slide lines as a combined force and velocity boundary condition, Journal of Computational Physics, vol.228, pp.3911-3916, 2009.

E. Caramana, D. Burton, M. Shashkov, and P. Whalen, The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, Journal of Computational Physics, vol.146, pp.227-262, 1998.

G. Carré, S. D. Pino, B. Després, and E. Labourasse, A cellcentered Lagrangian hydrodynamics scheme on general unstructured meshes in arbitrary dimension, Journal of Computational Physics, vol.228, pp.5160-5183, 2009.

M. Castro, J. Gallardo, J. López, and C. Parés, Well-balanced high order extensions of godunov's method for semilinear balance laws, SIAM Journal of Numerical Analysis, vol.46, pp.1012-1039, 2008.

M. Castro, J. Gallardo, and A. Marquina, Approximate Osher-Solomon schemes for hyperbolic systems, Applied Mathematics and Computation, vol.272, pp.347-368, 2016.

M. Castro, J. Gallardo, and C. Parés, High-order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallowwater systems, Mathematics of Computation, vol.75, pp.1103-1134, 2006.

M. Castro, A. Pardo, and C. Parés, Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique, Mathematical Models and Methods in Applied Sciences, vol.17, issue.12, pp.2055-2113, 2007.

M. Castro, A. Pardo, C. Parés, and E. Toro, On some fast wellbalanced first order solvers for nonconservative systems, Mathematics of computation, vol.79, issue.271, pp.1427-1472, 2010.

M. J. Castro, E. Fernández, A. Ferriero, J. A. García, and C. Parés, High order extensions of Roe schemes for two dimensional nonconservative hyperbolic systems, Journal of Scientific Computing, vol.39, pp.67-114, 2009.

M. J. Castro-díaz and E. D. Fernández-nieto, A class of computationally fast first order finite volume solvers: Pvm methods, SIAM J. Scientific Computing, vol.34, issue.4, 2012.

J. Cheng and C. Shu, A high order ENO conservative Lagrangian type scheme for the compressible Euler equations, Journal of Computational Physics, vol.227, pp.1567-1596, 2007.

J. Cheng and C. Shu, 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, pp.7191-7206, 2010.

S. Clain, S. Diot, and R. Loubère, A high-order finite volume method for systems of conservation laws-multidimensional optimal order detection (MOOD), Computational Physics, vol.230, issue.10, pp.4028-4050, 2011.

G. Clair, B. Després, and E. Labourasse, A new method to introduce constraints in cell-centered Lagrangian schemes, Computer Methods in Applied Mechanics and Engineering, pp.56-65, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00789201

G. Clair, B. Després, and E. Labourasse, A one-mesh method for the cell-centered discretization of sliding, Computer Methods in Applied Mechanics and Engineering, vol.269, pp.315-333, 2014.

A. Claisse, B. Després, E. Labourasse, and F. Ledoux, A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes, Journal of Computational Physics, vol.231, pp.4324-4354, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01437591

I. Cravero, G. Puppo, M. Semplice, and G. Visconti, Cweno: uniformly accurate reconstructions for balance laws, Mathematics of Computation, vol.87, issue.312, pp.1689-1719, 2018.

M. Cremonesi, A. Frangi, and U. Perego, A lagrangian finite element approach for the analysis of fluid-structure interaction problems, International Journal for Numerical Methods in Engineering, vol.84, issue.5, pp.610-630, 2010.

M. Cremonesi, A. Frangi, and U. Perego, A lagrangian finite element approach for the simulation of water-waves induced by landslides, Computers & Structures, vol.89, pp.1086-1093, 2011.

M. Cremonesi, S. Meduri, U. Perego, and A. Frangi, An explicit lagrangian finite element method for free-surface weakly compressible flows, Computational Particle Mechanics, vol.4, issue.3, pp.357-369, 2017.

G. Dal-maso, P. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl, vol.74, pp.483-548, 1995.

A. Dedner, F. Kemm, D. Kröner, C. D. Munz, T. Schnitzer et al., Hyperbolic divergence cleaning for the MHD equations, Journal of Computational Physics, vol.175, pp.645-673, 2002.

B. Després, Numerical Methods for Eulerian and Lagrangian Conservation Laws, 2017.

S. Diot, S. Clain, and R. Loubère, Improved detection criteria for the multi-dimensional optimal order detection (MOOD) on unstructured meshes with very highorder polynomials, Computers and Fluids, vol.64, pp.43-63, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00637123

S. Diot, R. Loubère, and S. Clain, The MOOD method in the threedimensional case: Very-high-order finite volume method for hyperbolic systems, International Journal of Numerical Methods in Fluids, vol.73, pp.362-392, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00764114

V. Dobrev, T. Ellis, T. Kolev, and R. Rieben, Curvilinear Finite elements for Lagrangian hydrodynamics, International Journal for Numerical Methods in Fluids, vol.65, pp.1295-1310, 2011.

V. Dobrev, T. Ellis, T. Kolev, and R. Rieben, High-order curvilinear finite elements for axisymmetric lagrangian hydrodynamics, Computers & Fluids, vol.83, issue.0, pp.58-69, 2013.

V. Dobrev, T. Kolev, and R. Rieben, High-order curvilinear finite element methods for lagrangian hydrodynamics, SIAM Journal on Scientific Computing, vol.34, issue.5, pp.606-641, 2012.

M. Dumbser, Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes with time-accurate local time stepping for hyperbolic conservation laws, Computer Methods in Applied Mechanics and Engineering, vol.280, pp.57-83, 2014.

M. Dumbser and D. Balsara, A new, efficient formulation of the HLLEM Riemann solver for general conservative and nonconservative hyperbolic systems, Journal of Computational Physics, vol.304, pp.275-319, 2016.

M. Dumbser, D. Balsara, E. Toro, and C. Munz, A unified framework for the construction of one-step finite-volume and discontinuous Galerkin schemes, Journal of Computational Physics, vol.227, pp.8209-8253, 2008.

M. Dumbser and W. Boscheri, High-order unstructured lagrangian one-step weno finite volume schemes for non-conservative hyperbolic systems: applications to compressible multi-phase flows, Computers & Fluids, vol.86, pp.405-432, 2013.

M. Dumbser, W. Boscheri, M. Semplice, and G. Russo, Central weighted eno schemes for hyperbolic conservation laws on fixed and moving unstructured meshes, SIAM Journal on Scientific Computing, vol.39, issue.6, pp.2564-2591, 2017.

M. Dumbser, C. Enaux, and E. Toro, Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws, Journal of Computational Physics, vol.227, pp.3971-4001, 2008.

M. Dumbser and M. Kaeser, Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems, Journal of Computational Physics, vol.221, pp.693-723, 2007.

M. Dumbser and M. Kaeser, Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems, Journal of Computational Physics, vol.221, pp.693-723, 2007.

M. Dumbser and M. Käser, Arbitrary high order non-oscillatory finite volume schemes on unstructured meshes for linear hyperbolic systems, Journal of Computational Physics, vol.221, pp.693-723, 2007.

M. Dumbser, M. Käser, V. Titarev, and E. Toro, Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems, Journal of Computational Physics, vol.226, pp.204-243, 2007.

M. Dumbser and R. Loubère, A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes, Journal of Computational Physics, vol.319, pp.163-199, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01972911

M. Dumbser and E. F. Toro, On universal Osher-type schemes for general nonlinear hyperbolic conservation laws, Communications in Computational Physics, vol.10, pp.635-671, 2011.

M. Dumbser and E. F. Toro, A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems, Journal of Scientific Computing, vol.48, pp.70-88, 2011.

M. Dumbser, O. Zanotti, R. Loubère, and S. Diot, A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws, Journal of Computational Physics, vol.278, pp.47-75, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01914588

B. Einfeldt, C. D. Munz, P. L. Roe, and B. Sjögreen, On godunovtype methods near low densities, Journal of Computational Physics, vol.92, pp.273-295, 1991.

F. Fambri, M. Dumbser, S. Köppel, L. Rezzolla, and O. Zanotti, ADER discontinuous Galerkin schemes for generalrelativistic ideal magnetohydrodynamics, Monthly Notices of the Royal Astronomical Society (MNRAS), 2018.

F. Fambri, M. Dumbser, and O. Zanotti, Space-time adaptive aderdg schemes for dissipative flows: Compressible navier-stokes and resistive mhd equations, Computer Physics Communications, vol.220, pp.297-318, 2017.

F. Vilar, Cell-centered discontinuous Galerkin discretization for two-dimensional Lagrangian hydrodynamics. Computers and Fluids, vol.64, pp.64-73, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01093675

F. Vilar, M. , P. Abgrall, and R. , Cell-centered discontinuous Galerkin discretizations for two-dimensional scalar conservation laws on unstructured grids and for one-dimensional Lagrangian hydrodynamics, Computers and Fluids, vol.46, issue.1, pp.498-604, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00538165

F. Vilar, M. , P. Abgrall, and R. , A discontinuous Galerkin discretization for solving the two-dimensional gas dynamics equations written under total Lagrangian formulation on general unstructured grids, Journal of Computational Physics, vol.276, pp.188-234, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00950782

E. Gaburro, Well balanced arbitrary-lagrangian-eulerian finite volume schemes on moving nonconforming meshes for nonconservative hyperbolic systems, 2018.

E. Gaburro, W. Boscheri, S. Chiocchetti, C. Klingenberg, V. Springel et al., High order direct arbitrarylagrangian-eulerian schemes on moving voronoi meshes with topology changes, 2019.

E. Gaburro, M. J. Castro, and M. Dumbser, Well-balanced arbitrarylagrangian-eulerian finite volume schemes on moving nonconforming meshes for the euler equations of gas dynamics with gravity, Monthly Notices of the Royal Astronomical Society, vol.477, issue.2, pp.2251-2275, 2018.

E. Gaburro, M. J. Castro, and M. Dumbser, A well balanced diffuse interface method for complex nonhydrostatic free surface flows, Computers & Fluids, vol.175, pp.180-198, 2018.

E. Gaburro, M. Dumbser, and M. J. Castro, Direct arbitrarylagrangian-eulerian finite volume schemes on moving nonconforming unstructured meshes, Computers and Fluids, vol.159, pp.254-275, 2017.

E. Gaburro, M. Dumbser, and M. J. Castro, Reprint of: Direct arbitrary-lagrangian-eulerian finite volume schemes on moving nonconforming unstructured meshes, Computers & Fluids, 2018.

S. Galera, P. Maire, and J. Breil, A two-dimensional unstructured cell-centered multi-material ale scheme using vof interface reconstruction, Journal of Computational Physics, vol.229, pp.5755-5787, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00453534

S. Godunov, Finite difference methods for the computation of discontinuous solutions of the equations of fluid dynamics, Mathematics of the USSR: Sbornik, vol.47, pp.271-306, 1959.

L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Computers & Mathematics with Applications, vol.39, issue.9, pp.135-159, 2000.

L. Gosse, A well-balanced scheme using non-conservative products designed for hyperbolic systems of conservation laws with source terms, Mathematical Models and Methods in Applied Sciences, vol.11, issue.02, pp.339-365, 2001.

J. Greenberg, A. Leroux, R. Baraille, and A. Noussair, Analysis and approximation of conservation laws with source terms, SIAM Journal on Numerical Analysis, vol.34, issue.5, pp.1980-2007, 1997.

J. M. Greenberg and A. Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996.

A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III, Journal of Computational Physics, vol.71, pp.231-303, 1987.

A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, Uniformly high order essentially non-oscillatory schemes, III. Journal of Computational Physics, vol.71, pp.231-303, 1987.

A. Hidalgo and M. Dumbser, Ader schemes for nonlinear systems of stiff advection-diffusion-reaction equations, Journal of Scientific Computing, vol.48, issue.1-3, pp.173-189, 2011.

C. Hu and C. Shu, A high-order weno finite difference scheme for the equations of ideal magnetohydrodynamics, Journal of Computational Physics, vol.150, pp.561-594, 1999.

C. Hu and C. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, Journal of Computational Physics, vol.150, issue.1, pp.97-127, 1999.

S. Idelsohn, M. Mier-torrecilla, and E. Oñate, Multi-fluid flows with the Particle Finite Element Method, Comput. Methods Appl. Mech. Engrg, vol.198, pp.2750-2767, 2009.

S. R. Idelsohn, E. Oñate, and F. D. Pin, The Particle Finite Element Method: a powerful tool to solve incompressible flows with freesurfaces and breaking waves, International Journal for Numerical Methods in Engineering, vol.61, pp.964-984, 2004.

H. Jackson, On the eigenvalues of the ader-weno galerkin predictor, Journal of Computational Physics, vol.333, pp.409-413, 2017.

J. R. Cavalcanti, M. Dumbser, D. D. Junior, and C. F. , A Conservative Finite Volume Scheme with Time-Accurate Local Time Stepping for Scalar Transport on Unstructured Grids, Advances in Water Resources, vol.86, pp.217-230, 2015.

R. Käppeli and S. Mishra, A well-balanced finite volume scheme for the euler equations with gravitation, Astronomy and Astrophysics, vol.587, p.94, 2016.

M. Käser and A. Iske, ADER schemes on adaptive triangular meshes for scalar conservation laws, Journal of Computational Physics, vol.205, pp.486-508, 2005.

P. Knupp, Achieving finite element mesh quality via optimization of the jacobian matrix norm and associated quantities. part ii -a framework for volume mesh optimization and the condition number of the jacobian matrix, Int. J. Numer. Meth. Engng, vol.48, pp.1165-1185, 2000.

M. Kucharik, J. Breil, S. Galera, P. Maire, M. Berndt et al., Hybrid remap for multi-material ALE, Computers and Fluids, vol.46, pp.293-297, 2011.

M. Kucharik, R. Loubère, L. Bednàrik, and R. Liska, Enhancement of Lagrangian slide lines as a combined force and velocity boundary condition, Computers & Fluids, vol.83, pp.3-14, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00986377

M. Kucharik and M. Shashkov, One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian-Eulerian methods, Journal of Computational Physics, vol.231, pp.2851-2864, 2012.

A. Larese, R. Rossi, E. Oñate, and S. Idelsohn, Validation of the Particle Finite Element Method (PFEM) for Simulation of the Free-Surface Flows, Engineering Computations, vol.25, pp.385-425, 2008.

R. J. Leveque, Balancing source terms and flux gradients in high-resolution godunov methods: the quasi-steady wavepropagation algorithm, Journal of Computational Physics, vol.146, issue.1, pp.346-365, 1998.

D. Levy, G. Puppo, and G. Russo, Central WENO schemes for hyperbolic systems of conservation laws, M2AN Math. Model. Numer. Anal, vol.33, issue.3, pp.547-571, 1999.

D. Levy, G. Puppo, and G. Russo, A third order central WENO scheme for 2D conservation laws, Applied Numerical Mathematics, vol.33, pp.415-421, 2000.

D. Levy, G. Puppo, and G. Russo, A fourth-order central WENO scheme for multidimensional hyperbolic systems of conservation laws, SIAM Journal on Scientific Computing, vol.24, pp.480-506, 2002.

Z. Li, X. Yu, and Z. Jia, The cell-centered discontinuous Galerkin method for Lagrangian compressible Euler equations in two dimensions, Computers and Fluids, vol.96, pp.152-164, 2014.

R. Liska, M. S. Váchal, and B. Wendroff, Synchronized flux corrected remapping for ALE methods, Computers and Fluids, vol.46, pp.312-317, 2011.

W. Liu, J. Cheng, and C. Shu, High order conservative Lagrangian schemes with Lax-Wendroff type time discretization for the compressible Euler equations, Journal of Computational Physics, vol.228, pp.8872-8891, 2009.

R. Loubere, M. Dumbser, and S. Diot, A new family of high order unstructured mood and ader finite volume schemes for multidimensional systems of hyperbolic conservation laws, Communications in Computational Physics, vol.16, issue.3, pp.718-763, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00949831

R. Loubère, P. Maire, and P. Váchal, A second-order compatible staggered Lagrangian hydrodynamics scheme using a cellcentered multidimensional approximate Riemann solver, Procedia Computer Science, vol.1, pp.1931-1939, 2010.

R. Loubère, P. Maire, and P. Váchal, 3D staggered Lagrangian hydrodynamics scheme with cell-centered Riemann solver-based artificial viscosity, International Journal for Numerical Methods in Fluids, vol.72, pp.22-42, 2013.

R. Loubère, P. H. Maire, and P. Váchal, Staggered Lagrangian hydrodynamics based on cell-centered Riemann solver, vol.10, pp.940-978, 2010.

R. Ma, X. Chang, L. Zhang, X. He, and M. Li, On the geometric conservation law for unsteady flow simulations on moving mesh, Procedia Engineering, vol.126, pp.639-644, 2015.

P. Maire, A high-order cell-centered lagrangian scheme for twodimensional compressible fluid flows on unstructured meshes, Journal of Computational Physics, vol.228, pp.2391-2425, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00322369

P. Maire, A high-order one-step sub-cell force-based discretization for cell-centered lagrangian hydrodynamics on polygonal grids, Computers and Fluids, vol.46, issue.1, pp.341-347, 2011.

P. Maire, A unified sub-cell force-based discretization for cellcentered lagrangian hydrodynamics on polygonal grids, International Journal for Numerical Methods in Fluids, vol.65, pp.1281-1294, 2011.

P. Maire and B. Nkonga, Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics, Journal of Computational Physics, vol.228, pp.799-821, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00290717

G. D. Maso, P. Lefloch, and F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl, vol.74, pp.483-548, 1995.

A. Mignone, G. Bodo, S. Massaglia, T. Matsakos, O. Tesileanu et al., Pluto: A numerical code for computational astrophysics, The Astrophysical Journal Supplement Series, vol.170, issue.1, p.228, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00398331

A. Mignone, C. Zanni, P. Tzeferacos, B. Van-straalen, P. Colella et al., The pluto code for adaptive mesh computations in astrophysical fluid dynamics, The Astrophysical Journal Supplement Series, vol.198, issue.1, p.7, 2011.

C. Munz, On Godunov-type schemes for Lagrangian gas dynamics, SIAM Journal on Numerical Analysis, vol.31, pp.17-42, 1994.

J. Von-neumann and R. Richtmyer, A method for the calculation of hydrodynamics shocks, Journal of Applied Physics, vol.21, pp.232-237, 1950.

E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, and B. Suarez, Possibilities of the Particle Finite Element Method for fluid-soilstructure interaction problems, Journal of Computational Mechanics, vol.48, pp.307-318, 2011.

E. Oñate, S. Idelsohn, M. Celigueta, and R. Rossi, Advances in the Particle Finite Element Method for the Analysis of Fluid-Multibody Interaction and Bed Erosion in Free-surface Flows, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.1777-1800, 2008.

A. L. Ortega and G. Scovazzi, A geometrically-conservative, synchronized, flux-corrected remap for arbitrary Lagrangian-Eulerian computations with nodal finite elements, Journal of Computational Physics, vol.230, pp.6709-6741, 2011.

S. Osher and F. Solomon, Upwind difference schemes for hyperbolic conservation laws, Math. Comput, vol.38, pp.339-374, 1982.

R. Pakmor, F. Marinacci, and V. Springel, Magnetic fields in cosmological simulations of disk galaxies, The Astrophysical Journal Letters, vol.783, issue.1, p.20, 2014.

R. Pakmor, V. Springel, A. Bauer, P. Mocz, D. J. Munoz et al., Improving the convergence properties of the moving-mesh code arepo, Monthly Notices of the Royal Astronomical Society, vol.455, issue.1, pp.1134-1143, 2015.

C. Parés, Numerical methods for nonconservative hyperbolic systems: a theoretical framework, SIAM Journal on Numerical Analysis, vol.44, pp.300-321, 2006.

F. D. Pin, S. R. Idelsohn, E. Oñate, and R. Aubry, The ALE/Lagrangian Particle Finite Element Method: A new approach to computation of free-surface flows and fluid-object interactions, Computers and Fluids, vol.36, pp.27-38, 2007.

S. D. Pino, A curvilinear finite-volume method to solve compressible gas dynamics in semi-Lagrangian coordinates, Comptes Rendus de l'Académie des Sciences -Series I -Mathematics, vol.348, pp.1027-1032, 2010.

J. Qiu and C. W. Shu, Hermite weno schemes and their application as limiters for runge-kutta discontinuous galerkin method ii: Two dimensional case, Computers & Fluids, vol.34, issue.6, pp.642-663, 2005.

B. Re, C. Dobrzynski, and A. Guardone, An interpolation-free ale scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids, Journal of Computational Physics, vol.340, pp.26-54, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01633476

W. Reed and T. Hill, Triangular mesh methods for neutron transport equation, Los Alamos Scientific Laboratory, 1973.

V. V. Rusanov, Calculation of Interaction of Non-Steady Shock Waves with Obstacles, J. Comput. Math. Phys. USSR, vol.1, pp.267-279, 1961.

S. Sambasivan, M. Shashkov, and D. Burton, A finite volume cellcentered Lagrangian hydrodynamics approach for solids in general unstructured grids, International Journal for Numerical Methods in Fluids, vol.72, pp.770-810, 2013.

T. Schwartzkopff, C. Munz, and E. Toro, ADER: A high order approach for linear hyperbolic systems in 2d, Journal of Scientific Computing, vol.17, issue.1-4, pp.231-240, 2002.

G. Scovazzi, Lagrangian shock hydrodynamics on tetrahedral meshes: A stable and accurate variational multiscale approach, Journal of Computational Physics, vol.231, pp.8029-8069, 2012.

L. Sedov, Similarity and Dimensional Methods in Mechanics, 1959.

M. Semplice, A. Coco, and G. Russo, Adaptive mesh refinement for hyperbolic systems based on third-order compact WENO reconstruction, Journal of Scientific Computing, vol.66, issue.2, pp.692-724, 2016.

V. Springel, E pur si muove: Galilean-invariant cosmological hydrodynamical simulations on a moving mesh, vol.401, pp.791-851, 2010.

V. Springel, Moving-mesh hydrodynamics with the arepo code, Proceedings of the International Astronomical Union, vol.6, issue.S270, pp.203-206, 2010.

A. Stroud, Approximate Calculation of Multiple Integrals, 1971.

M. Tavelli and W. Boscheri, A high order parallel eulerianlagrangian algorithm for advection-diffusion problems on unstructured meshes, International Journal for Numerical Methods in Fluids

V. Titarev and E. Toro, ADER: Arbitrary high order Godunov approach, Journal of Scientific Computing, vol.17, issue.1-4, pp.609-618, 2002.

V. Titarev and E. Toro, ADER schemes for three-dimensional nonlinear hyperbolic systems, Journal of Computational Physics, vol.204, pp.715-736, 2005.

E. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, second edn, 1999.

E. Toro and V. Titarev, Solution of the generalized Riemann problem for advection-reaction equations, Proc. Roy. Soc. London, pp.271-281, 2002.

E. F. Toro and V. A. Titarev, Derivative Riemann solvers for systems of conservation laws and ADER methods, Journal of Computational Physics, vol.212, issue.1, pp.150-165, 2006.

B. Van-leer, Towards the ultimate conservative difference scheme II: Monotonicity and conservation combined in a second order scheme, Journal of Computational Physics, vol.14, pp.361-370, 1974.

B. Van-leer, Towards the ultimate conservative difference scheme V: A second order sequel to Godunov's method, Journal of Computational Physics, vol.32, pp.101-136, 1979.

M. L. Wilkins, Calculation of elastic-plastic flow, Methods in Computational Physics, vol.3, 1964.

A. M. Winslow, Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh, J. Comput. Phys, vol.135, issue.2, pp.128-138, 1997.

O. Zanotti, F. Fambri, M. Dumbser, and A. Hidalgo, Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting, Computers and Fluids, vol.118, pp.204-224, 2015.