S. Adami, X. Hu, and N. Adams, A new surfacetension formulation for multi-phase SPH using a reproducing divergence approximation, J. Comput . Phys
DOI : 10.1016/j.jcp.2010.03.022

Y. Afshar, F. Schmid, A. Pishevar, and S. Worley, Exploiting seeding of random number generators for eecient domain decomposition parallelization of dissipative particle dynamics

B. J. Alder and T. E. Wainwright, Phase Transition for a Hard Sphere System, The Journal of Chemical Physics, vol.27, issue.5, p.????
DOI : 10.1063/1.1743956

M. Allen and D. Tildesley, Computer Simulation of Liquids

J. Anderson, Computational Fluid Dynamics Computational Fluid Dynamics: The Basics with Applications

J. B. Avalos and A. D. Mackie, Dissipative particle dynamics with energy conservation, Europhysics Letters (EPL), vol.40, issue.2
DOI : 10.1209/epl/i1997-00436-6

D. Barcarolo, D. L. Touzé, G. Oger, and F. De-vuyst, Adaptive particle reenement and dereenement applied to the smoothed particle hydrodynamics method, J. Comput. Phys

M. C. Payne, R. Kondor, and G. Csányi, Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons The Gaussian Approximation Potential, Phys. Rev. Lett

M. I. Baskes, Modiied embedded-atom potentials for cubic materials and impurities, Phys. Rev. B, p.????
DOI : 10.1103/physrevb.46.2727

M. Berger and P. Colella, Local adaptive mesh reenement for shock hydrodynamics, J. Comput. Phys
DOI : 10.1016/0021-9991(89)90035-1

M. J. Berger and J. Oliger, Adaptive mesh reenement for hyperbolic partial diierential equations
DOI : 10.21236/ada130162

URL : http://www.dtic.mil/dtic/tr/fulltext/u2/a130162.pdf

S. [. Bian, R. Litvinov, M. Qian, N. A. Ellero, and . Adams, Multiscale modeling of particle in suspension with smoothed dissipative particle dynamics, Physics of Fluids, vol.24, issue.1
DOI : 10.1063/1.2980039

H. Bock, K. E. Gubbins, and S. H. Klapp, Coarse Graining of Nonbonded Degrees of Freedom, Physical Review Letters, vol.30, issue.26
DOI : 10.1063/1.1711137

J. Brackbill, D. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2
DOI : 10.1016/0021-9991(92)90240-Y

J. K. Brennan, M. Lísal, J. D. Moore, S. Izvekov, I. V. Schweigert et al., Coarse-Grain Model Simulations of Nonequilibrium Dynamics in Heterogeneous Materials, The Journal of Physical Chemistry Letters, vol.5, issue.12, p.?????
DOI : 10.1021/jz500756s

L. [. Cieren, S. Colombet, R. Pitoiset, and . Namyst, Exastamp: A parallel framework for molecular dynamics on heterogeneous clusters. Euro-Par : Parallel Processing Workshops
DOI : 10.1007/978-3-319-14313-2_11

G. De-fabritiis, R. Delgado-buscalioni, P. V. Coveney, R. Delgado-buscalioni, and G. De-fabritiis, Multiscale modeling of liquids with molecular speciicity :::::::, . ¢ Cited on page Embedding molecular dynamics within uctuating hydrodynamics in multiscale simulations of liquids Concurrent triple-scale simulation of molecular liquids, Phys. Rev. Lett. Phys. Rev. E J. Chem. Phys, issue.(

N. Desbiens, E. Bourasseau, and J. Maillet, Potential optimization for the calculation of shocked liquid nitromethane properties, Molecular Simulation, vol.69, issue.13, p.????
DOI : 10.1021/jp9921102

URL : https://hal.archives-ouvertes.fr/hal-00515017

E. Bourasseau, J. Maillet, and L. Soulard, Molecular based equation of state for shocked liquid nitromethane, J. Hazard. Mater

J. Donea, P. Fasoli-stella, and S. Giulani, Lagrangian and eulerian nite element techniques for transient uid-structure interaction problems

O. Durand and L. Soulard, Large-scale molecular dynamics study of jet breakup and ejecta production from shock-loaded copper with a hybrid method Power law and exponential ejecta size distributions from the dynamic fragmentation of shock-loaded Cu and Sn metals under melt conditions, )

O. Durand and L. Soulard, Mass-velocity and size-velocity distributions of ejecta cloud from shock-loaded tin surface using atomistic simulations, Journal of Applied Physics, vol.117, issue.16
DOI : 10.1088/0034-4885/71/3/036601

URL : http://arxiv.org/pdf/1503.04976

O. Durand and L. Soulard, Modeling from molecular dynamics simulations of ejecta production induced by shock-loaded metallic surfaces Investigation of the static and dynamic fragmentation of metallic liquid sheets induced by random surface uctuations,

S. A. Dyachkov, A. N. Parshikov, and V. V. Zhakhovsky, Shock-produced ejecta from tin: Comparative study by molecular dynamics and smoothed particle hydrodynamics methods, Journal of Physics: Conference Series, vol.653
DOI : 10.1088/1742-6596/653/1/012043

URL : http://iopscience.iop.org/article/10.1088/1742-6596/653/1/012043/pdf

J. [. Ercolessi and . Adams, Interatomic potentials from rst-principles calculations: The force-matching method, Europhys. Lett
DOI : 10.1209/0295-5075/26/8/005

URL : http://arxiv.org/pdf/cond-mat/9306054v1.pdf

P. Español and M. Revenga, Smoothed dissipative particle dynamics, Physical Review E, vol.187, issue.2
DOI : 10.1016/0378-4371(92)90012-F

M. Serrano, I. Pagonabarraga, and I. Zuniga, Energy-conserving coarse-graining of complex molecules, Soft Matter

P. Español and P. Warren, Statistical Mechanics of Dissipative Particle Dynamics, Europhysics Letters (EPL), vol.30, issue.4
DOI : 10.1209/0295-5075/30/4/001

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, Handbook of Numerical Analysis
URL : https://hal.archives-ouvertes.fr/hal-00346077

G. Faure, R. Delgado-buscalioni, and P. Español, The entropy of a complex molecule, The Journal of Chemical Physics, vol.146, issue.22
DOI : 10.1039/c0cp02826f

G. Faure and J. Maillet, Simulation of detonation waves with smoothed dissipative particle dynamics

G. Faure, J. Maillet, J. Roussel, and G. Stoltz, Size consistency in smoothed dissipative particle dynamics, Physical Review E, vol.94, issue.4
DOI : 10.1016/0021-9991(83)90036-0

URL : https://hal.archives-ouvertes.fr/hal-01345009

G. Faure, J. Maillet, and G. Stoltz, Local density dependent potential for compressible mesoparticles, The Journal of Chemical Physics, vol.140, issue.11
DOI : 10.1016/j.jhazmat.2008.12.083

URL : https://hal.archives-ouvertes.fr/hal-00870895

G. Faure and G. Stoltz, Stable and accuracte schemes for smoothed dissipative particle dynamics
DOI : 10.1007/s10483-018-2256-8

URL : http://arxiv.org/pdf/1707.04232

J. Feldman and J. Bonet, Dynamic reenement and boundary contact forces in SPH with applications in uid ow problems, Int. J. Numer. Meth. Eng, p.:????
DOI : 10.1002/nme.2010

J. Ferziger and M. Peric, Computational Methods for Fluid Dynamics

. [. Franck, Mixed Eulerian-Lagrangian method, Methods in Computational Physics, p.pages ???

B. Frenkel and . Smit, Understanding Molecular Simulation, Computers in Physics, vol.11, issue.4
DOI : 10.1063/1.4822570

D. A. Fulk, A Numerical Analysis of Smoothed Particle Hydrodynamics

D. A. Fulk and D. W. Quinn, An Analysis of 1-D Smoothed Particle Hydrodynamics Kernels, Journal of Computational Physics, vol.126, issue.1
DOI : 10.1006/jcph.1996.0128

G. C. Ganzenmüller, S. Hiermaier, and M. O. Steinhauser, Energy-based coupling of smooth particle hydrodynamics and molecular dynamics with thermal uctuations, Eur. Phys. J. Spec. Top, p.???

N. A. Gatsonis, R. Potami, and J. Yang, A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries, Journal of Computational Physics, vol.256
DOI : 10.1016/j.jcp.2013.08.059

J. [. Germann, B. L. Hammerberg, and . Holian, Large-Scale Molecular Dynamics Simulations of Ejecta Formation in Copper, AIP Conference Proceedings, p.????
DOI : 10.1063/1.1780236

J. [. Gingold and . Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol.181, issue.3, p.:????
DOI : 10.1093/mnras/181.3.375

URL : https://academic.oup.com/mnras/article-pdf/181/3/375/3104055/mnras181-0375.pdf

P. [. Girault and . Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Series in Computational Mathematics
DOI : 10.1007/978-3-642-61623-5

J. N. Glosli, D. F. Richards, K. J. Caspersen, R. E. Rudd, J. A. Gunnels et al., Extending stability beyond CPU millennium, Proceedings of the 2007 ACM/IEEE conference on Supercomputing , SC '07, p.pages ???
DOI : 10.1145/1362622.1362700

M. S. Green, Markoo random processes and the statistical mechanics of time-dependent phenomena, J. Chem. Phys, p.????
DOI : 10.1063/1.1700722

M. Grmela and H. C. Öttinger, Dynamics and thermodynamics of complex uids. I. Development of a general formalism, Phys. Rev, p.????

E. Hairer, C. Lubich, and G. Wanner, Geometric numerical integration illustrated by the Störmer- Verlet method, Acta Numer, p.:????
DOI : 10.1017/s0962492902000144

N. [. Heim, T. C. Grønbech-jensen, B. L. Germann, E. M. Holian, and P. S. Kober, Inuence of interatomic bonding potentials on detonation properties General form of the mie-grüneisen equation of state, Phys. Rev. E CR Mecanique, issue.(

C. Hijón, P. Español, E. Vanden-eijnden, and R. Delgado-buscalioni, Mori???Zwanzig formalism as a practical computational tool, Faraday Discuss., vol.2, p.???; discussion ???, ???
DOI : 10.1007/s101890050013

T. C. Holian, J. Germann, C. T. Maillet, G. K. White, and . Straub, Atomistic mechanism for hot spot initiation Shock-wave structure via nonequilibrium molecular dynamics and navier-stokes continuum mechanics, Phys. Rev. Lett. Phys. Rev. A, p.:?????
DOI : 10.1103/physreva.22.2798

B. L. Holian, M. Mareschal, and R. Ravelo, Test of a new heat--ow equation for dense--uid shock waves, M. Mareschal, and E. Salomons. Modeling shock waves in an ideal gas: Going beyond the navier-stokes level. Phys
DOI : 10.1063/1.3486088

X. Hu and N. Adams, A multi-phase SPH method for macroscopic and mesoscopic ows, J. Comput. Phys
DOI : 10.1016/j.jcp.2005.09.001

S. Izvekov, P. W. Chung, and B. M. Rice, Particlebased multiscale coarse graining with densitydependent potentials: Application to molecular crystals (hexahydro--,,-trinitro-s-triazine) J
DOI : 10.1063/1.3607603

G. [. Izvekov and . Voth, Multiscale coarse graining of liquid-state systems, The Journal of Chemical Physics, vol.123, issue.13
DOI : 10.1063/1.555786

R. T. Jacobsen and R. B. Stewart, Thermodynamic properties of nitrogen including liquid and vapor phases from k to k with pressures to ,, bar, J. Phys. Chem. Ref. Data, p.:????
DOI : 10.1063/1.3253132

G. R. Johnson and S. R. Beissel, NORMALIZED SMOOTHING FUNCTIONS FOR SPH IMPACT COMPUTATIONS, International Journal for Numerical Methods in Engineering, vol.23, issue.16, p.????
DOI : 10.1002/nme.1620230313

[. K. Johnson, J. A. Zollweg, and K. E. Gubbins, The Lennard-Jones equation of state revisited, Molecular Physics, vol.139, issue.3, p.:????
DOI : 10.1016/0378-3812(91)87014-Z

M. E. Johnson, T. Head-gordon, and A. A. Louis, Representability problems for coarse-grained water potentials, The Journal of Chemical Physics, vol.126, issue.14
DOI : 10.1103/PhysRevE.73.066701

URL : http://arxiv.org/pdf/cond-mat/0702535

[. E. Jones, On the determination of molecular elds. ii. from the equation of state of a gas, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, p.???

K. Kadau, J. L. Barber, T. C. Germann, B. L. Holian, and B. J. Alder, Atomistic methods in uid simulation, p.????
DOI : 10.1098/rsta.2009.0218

C. [. Kadau, J. L. Rosenblatt, T. C. Barber, Z. Germann, P. Huang et al., The importance of uctuations in uid mixing

A. [. Kitsionas and . Whitworth, Smoothed Particle Hydrodynamics with particle splitting, applied to self-gravitating collapse, Monthly Notices of the Royal Astronomical Society, vol.296, issue.1, p.:????
DOI : 10.1046/j.1365-8711.1998.01479.x

URL : https://academic.oup.com/mnras/article-pdf/330/1/129/18411084/330-1-129.pdf

M. P. Kroonblawd, T. D. Sewell, and J. Maillet, Characteristics of energy exchange between interand intramolecular degrees of freedom in crystalline, trinitrobenzene (tatb) with implications for coarse-grained simulations of shock waves in polyatomic molecular crystals

L. Landau and E. Lifshits, Fluid Mechanics, volume of Course of Theroretical Physics

]. J. Larentzos, J. K. Brennan, J. D. Moore, M. Lísal, and W. D. Mattson, Parallel implementation of isothermal and isoenergetic Dissipative Particle Dynamics using Shardlow-like splitting algorithms, Computer Physics Communications, vol.185, issue.7
DOI : 10.1016/j.cpc.2014.03.029

]. E. Lee, H. C. Hornig, and J. W. Kury, Adiabatic Expansion Of High Explosive Detonation Products, CA (US)
DOI : 10.2172/4783904

URL : https://www.osti.gov/servlets/purl/4783904

C. Leforestier, Classical trajectories using the full ab initio potential energy surface
DOI : 10.1063/1.435520

H. Lei, C. J. Mundy, G. K. Schenter, and N. K. Voulgarakis, Modeling nanoscale hydrodynamics by smoothed dissipative particle dynamics, The Journal of Chemical Physics, vol.3, issue.19
DOI : 10.1021/jp0104029

URL : https://aip.scitation.org/doi/10.1063/1.4921222

T. Lelièvre, G. Stoltz, and M. Rousset, Free Energy Computations: A Mathematical Perspective
DOI : 10.1142/p579

G. Stoltz, Partial diierential equations and stochastic methods in molecular dynamics, Acta Numer, p.????

C. A. Lemarchand, M. Couty, and B. Rousseau, -polybutadiene: A bottom-up approach, The Journal of Chemical Physics, vol.146, issue.7
DOI : 10.1103/physrevb.31.5262

C. [. Lemons and . Lund, Thermodynamics of high temperature, Mie???Gruneisen solids, American Journal of Physics, vol.67, issue.12, p.????
DOI : 10.1119/1.19091

Z. Li, X. Bian, B. Caswell, and G. E. Karniadakis, Construction of dissipative particle dynamics models for complex uids via the mori-zwanzig formulation, Soft Matter, p.:?????
DOI : 10.1039/c4sm01387e

Z. Li, Z. Luo, Z. Liu, Y. Ye, Z. Li et al., High-speed microjet particles measurement using in-line pulsed holography, Journal of Applied Physics, vol.8, issue.11
DOI : 10.1088/0022-3735/7/10/001

B. L. Lin, T. C. Holian, A. Germann, and . Strachan, Mesodynamics with implicit degrees of freedom, The Journal of Chemical Physics, vol.141, issue.6
DOI : 10.1063/1.4793530

URL : http://arxiv.org/pdf/1403.7228

R. D. Lisio, E. Grenier, and M. Pulvirenti, The convergence of the SPH method, Computers & Mathematics with Applications, vol.35, issue.1-2
DOI : 10.1016/S0898-1221(97)00260-5

S. Litvinov, M. Ellero, X. Hu, and N. Adams, A splitting scheme for highly dissipative smoothed particle dynamics, Journal of Computational Physics, vol.229, issue.15
DOI : 10.1016/j.jcp.2010.03.040

S. Litvinov, M. Ellero, X. Hu, and N. A. Adams, Smoothed dissipative particle dynamics model for polymer molecules in suspension, Physical Review E, vol.139, issue.6
DOI : 10.1137/S1064827501392879

]. G. Liu and M. B. Liu, ?Smoothed particle hydrodynamics ? a meshfree method?, Computational Mechanics, vol.33, issue.6
DOI : 10.1007/s00466-004-0573-1

G. Liu and K. Lam, Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of Computational and Applied Mathematics, vol.155, issue.2
DOI : 10.1016/S0377-0427(02)00869-5

URL : https://doi.org/10.1016/s0377-0427(02)00869-5

]. W. Liu, S. Jun, and Y. F. Zhang, Reproducing kernel particle methods, International Journal for Numerical Methods in Fluids, vol.45, issue.8-9, p.????
DOI : 10.1137/1.9781611970104

M. Lísal, J. K. Brennan, and J. B. Avalos, Dissipative particle dynamics at isothermal, isobaric, isoenergetic, and isoenthalpic conditions using Shardlow-like splitting algorithms, The Journal of Chemical Physics, vol.135, issue.20
DOI : 10.1080/09500839008206493

E. [. Maillet, N. Bourasseau, G. Desbiens, G. Vallverdu, and . Stoltz, Mesoscopic simulations of shock-to-detonation transition in reactive liquid high explosive, EPL (Europhysics Letters), vol.96, issue.6
DOI : 10.1209/0295-5075/96/68007

URL : https://hal.archives-ouvertes.fr/hal-00676470

L. [. Maillet, G. Soulard, and . Stoltz, A reduced model for shock and detonation waves. II. The reactive case, Europhysics Letters (EPL), vol.78, issue.6
DOI : 10.1209/0295-5075/78/68001

URL : https://hal.archives-ouvertes.fr/hal-00125537

P. [. Mas-gallic and . Raviart, A particle method for rst-order symmetric systems, Numerische Mathematik, p.:????
DOI : 10.1007/bf01400118

]. R. Menikoo and M. S. Shaw, Modeling detonation waves in nitromethane, Combustion and Flame, issue.(

M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys

]. J. Moore, B. C. Barnes, S. Izvekov, M. Lisal, M. S. Sellers et al., A coarsegrain force eld for RDX: Density dependent and energy conserving Derivation of coarse-grained potentials via multistate iterative boltzmann inversion, ):::::::, . ¢ Cited on page

N. Moreno, P. Vignal, J. Li, and V. M. Calo, Multiscale modeling of blood ow: Coupling nite elements with smoothed dissipative particle dynamics, International Conference on Computational Science
DOI : 10.1016/j.procs.2013.05.442

URL : https://doi.org/10.1016/j.procs.2013.05.442

S. J. Numer-]-a, C. J. Niklasson, M. Tymczak, and . Challacombe, Time-reversible born-oppenheimer molecular dynamics CEL: a time-dependent, two-spacedimensional , coupled Eulerian-Lagrange code, Methods in Computational Physics, p.pages ????

]. W. Noid, J. Chu, G. S. Ayton, V. Krishna, S. Izvekov et al., The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models, ):::::::, . ¢ Cited on page
DOI : 10.1063/1.2714540

V. A. Ogorodnikov, A. L. Mikha?-ilov, V. V. Burtsev, S. A. Lobastov, S. V. Erunov et al., Detecting the ejection of particles from the free surface of a shock-loaded sample Hybrid molecular-continuum simulations using smoothed dissipative particle dynamics, J. Exp. Theor. Phys. J. Chem. Phys

L. G. Petsev, M. S. Leal, and . Shell, Multiscale simulation of ideal mixtures using smoothed dissipative particle dynamics, The Journal of Chemical Physics, vol.144, issue.8
DOI : 10.1063/1.2013208

URL : https://aip.scitation.org/doi/10.1063/1.4942499

]. R. Potestio, S. Fritsch, P. Español, R. Delgado-buscalioni, K. Kremer et al., Hamiltonian Adaptive Resolution Simulation for Molecular Liquids, Physical Review Letters, vol.110, issue.10
DOI : 10.1140/epje/i2008-10413-5

URL : https://link.aps.org/accepted/10.1103/PhysRevLett.110.108301

]. M. Praprotnik, L. D. Site, and K. Kremer, Adaptive resolution molecular-dynamics simulation: Changing the degrees of freedom on the fly, The Journal of Chemical Physics, vol.39, issue.22
DOI : 10.1103/PhysRevLett.85.3213

M. Pütz and F. Müller-plathe, Deriving eeective mesoscale potentials from atomistic simulations, J. Comput. Chem, p.????

W. Rice, J. Mattson, S. F. Grosh, and . Trevino, Molecular-dynamics study of detonation. I. A comparison with hydrodynamic predictions, Physical Review E, vol.70, issue.1
DOI : 10.1063/1.437577

C. Roland, T. De-rességuier, A. Sollier, E. Lescoute, D. Loison et al., Ejection of micronscale fragments from triangular grooves in laser shock-loaded copper samples, J. Dyn. Behavior Mater
DOI : 10.1007/s40870-016-0087-x

URL : https://hal.archives-ouvertes.fr/hal-01638852

C. Roland, T. De-rességuier, A. Sollier, E. Lescoute, L. Soulard et al., Hydrodynamic simulations of microjetting from shock-loaded grooves
DOI : 10.1063/1.4918537

URL : https://hal.archives-ouvertes.fr/hal-01518497

M. S. Shell, The relative entropy is fundamental to multiscale and inverse thermodynamic problems, The Journal of Chemical Physics, vol.129, issue.14
DOI : 10.1063/1.2336197

R. [. Sorenson, J. L. Minich, T. W. Romero, R. M. Tunnell, and . Malone, Ejecta particle size distributions for shock loaded Sn and Al metals, Journal of Applied Physics, vol.75, issue.10
DOI : 10.1016/S0378-4371(01)00158-3

URL : https://digital.library.unt.edu/ark:/67531/metadc716112/m2/1/high_res_d/783331.pdf

G. Stoltz, Stable schemes for dissipative particle dynamics with conserved energy, Journal of Computational Physics, vol.340
DOI : 10.1016/j.jcp.2017.03.059

URL : https://hal.archives-ouvertes.fr/hal-01416108

J. Swegle, D. Hicks, and S. Attaway, Smoothed Particle Hydrodynamics Stability Analysis, Journal of Computational Physics, vol.116, issue.1
DOI : 10.1006/jcph.1995.1010

M. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation. Oxford Graduate Texts

R. Vacondio, B. Rogers, P. Stansby, P. Mignosa, and J. Feldman, Variable resolution for SPH: A dynamic particle coalescing and splitting scheme, Computer Methods in Applied Mechanics and Engineering, vol.256
DOI : 10.1016/j.cma.2012.12.014

S. [. Van-duin, F. Dasgupta, W. A. Lorant, and . Goddard, Reaxx: A reactive force eld for hydrocarbons, J. Phys. Chem. A

M. Quesada, P. Ellero, and . Español, Consistent scaling of thermal uctuations in smoothed dissipative particle dynamics, J. Chem. Phys

H. Wang, C. Junghans, and K. Kremer, Comparative atomistic and coarse-grained study of water: What do we lose by coarse-graining?, The European Physical Journal E, vol.49, issue.2
DOI : 10.1002/(SICI)1521-4044(199802)49:2/3<61::AID-APOL61>3.0.CO;2-V

URL : https://link.springer.com/content/pdf/10.1140%2Fepje%2Fi2008-10413-5.pdf

D. Fu, X. Hu, and . Han, Feasibility analysis of SPH method in the simulation of condensed explosives detonation with ignition and growth model, Comput. Fluids