Une large classe de méthodes volumes finis sur maillage non-structuré, à laquelle appartient la méthode multipente proposée ,
, Condition limite dédiée : Les fortes singularités rencontrées sur l'axe de symétrie ne permettent pas l'utilisation d'une méthodologie usuelle et demandent la mise en place d'un traitement spécifique de la limite comme proposé Section
Les modèles et méthodes ont été intégrés dans le code SIERRA, parallélisé pour l'occasion en mémoire partagée comme décrit Section 8.2 et intégrant les dernières normes FORTRAN ,
, Comme présenté dans les derniers chapitres, l'ensemble de ces apports permet aujourd'hui la conduite de simulations d'écoulements diphasiques polydispersés en taille et en vitesse en configurations industrielles. Cela ouvre la voie à des simulations à la prédictibilité accrue pour l'étude notamment des performances et de la stabilité des moteurs-fusées à propergol solide
Fourth order Chebyshev methods with recurrence relation, SIAM Journal on Scientific Computing, vol.23, issue.6, pp.2041-2054, 2002. ,
Droplet vaporization model for spray combustion calculations, International journal of heat and mass transfer, vol.32, issue.9, pp.1605-1618, 1989. ,
The History of Large Solid Rocket Motor Development in the United States, 30th AIAA AIAA/ASME/SAE/ASEE Joint Propulsion Conference, pp.94-3057, 1994. ,
The Gaussian-BGK model of Boltzmann equation with small Prandtl number, European Journal of Mechanics-B/Fluids, vol.19, issue.6, pp.813-830, 2000. ,
URL : https://hal.archives-ouvertes.fr/inria-00072951
Experimental and numerical study of aeroacoustic phenomena in large solid propellant boosters, 2000. ,
Coupled level-set/volume-of-fluid method for simulation of injector atomization, Journal of Propulsion and Power, vol.29, issue.1, pp.147-157, 2012. ,
Coalescence and separation in binary collisions of liquid drops, Journal of Fluid Mechanics, vol.221, pp.183-204, 1990. ,
A two-phase mixture theory for the deflagration-todetonation transition (DDT) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986. ,
Assessment on analysis and prediction method applied on thrust oscillations of Ariane 5 solid rocket motor, 2003. ,
Agglomeration of aluminized solid rocket propellants, 2009. ,
Développement de schémas numériques adaptés à l'hydrodynamique. Une méthode numérique à pas fractionnaires. Application aux calculs d'écoulements hypersoniques réactifs non visqueux. Formulation du schéma MUSCL de van Leer pour une configuration axisymétrique, 1991. ,
Rocket propulsion, 1960. ,
An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid: with an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops, 1883. ,
, 1888. A treatise on hydrodynamics: with numerous examples, vol.2
On the choice of wavespeeds for the HLLC Riemann solver, SIAM Journal on Scientific Computing, vol.18, issue.6, pp.1553-1570, 1997. ,
Aluminium Combustion". In Internal aerodynamics in solid rocket propulsion. RTO AVT/VKI Special Course, 2002. ,
Modeling of combustion and ignition of solid-propellant ingredients, Progress in Energy and Combustion Science, vol.33, issue.6, pp.497-551, 2007. ,
Analysis of injection induced flows in porous walled duct with application to aerochemistry of solid propellant motor, 1981. ,
Computational methods in Lagrangian and Eulerian hydrocodes, Computer methods in Applied mechanics and Engineering, vol.99, issue.2-3, pp.235-394, 1992. ,
Adaptive mesh refinement for hyperbolic partial differential equations, Journal of computational Physics, vol.53, issue.3, pp.484-512, 1984. ,
Analysis of slope limiters on irregular grids, 2005. ,
A low diffusive lagrange-remap scheme for the simulation of violent air-water free-surface flows, Journal of Computational Physics, vol.274, pp.19-49, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00798783
Numerical approximations of the 10-moment Gaussian closure, Communications in Mathematical Sciences, vol.3, issue.2, pp.1809-1831, 2005. ,
DOI : 10.1090/s0025-5718-06-01860-6
URL : https://www.ams.org/mcom/2006-75-256/S0025-5718-06-01860-6/S0025-5718-06-01860-6.pdf
, Why the MUSCL-Hancock Scheme is L1-stable, Numerische Mathematik, vol.104, issue.1, pp.27-46
Asymptotic preserving HLL schemes, Numerical methods for partial differential equations, vol.27, issue.6, pp.1396-1422, 2011. ,
DOI : 10.1002/num.20586
Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes, Applied Numerical Mathematics, vol.16, issue.4, pp.417-438, 1995. ,
DOI : 10.1016/0168-9274(95)00007-h
A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Physical review, vol.94, issue.3, p.511, 1954. ,
Modélisation et simulation du rayonnement dans les jets de moteurs à propergol solide à haute altitude, 2018. ,
Direct simulation and the Boltzmann equation, The Physics of Fluids, vol.13, issue.11, pp.2676-2681, 1970. ,
DOI : 10.1063/1.1692849
Lessons learned in solid rocket combustion instability, AIAA Paper, vol.5803, 2007. ,
DOI : 10.2514/6.2007-5803
Modeling and numerical scheme of two-size moment Eulerian multi-fluid model describing statistical trajectory crossing, International Journal on Multiphase Flow, IJMF, 2017. ,
Two-size moment Eulerian multi-fluid method describing the statistical trajectory crossing: modeling and numerical scheme, 9th International Conference on Multiphase Flow, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01543507
Geometric structures for three-dimensional shape representation, ACM Transactions on Graphics (TOG), vol.3, issue.4, pp.266-286, 1984. ,
DOI : 10.1145/357346.357349
On the prediction of gas-solid flows with two-way coupling using large eddy simulation, Physics of Fluids, vol.12, issue.8, pp.2080-2090, 2000. ,
Flux-corrected transport, Journal of Computational Physics, vol.135, issue.2, pp.172-186, 1997. ,
On zero pressure gas dynamics, Advances in kinetic theory and computing, 1994. ,
Duality solutions for pressureless gases, monotone scalar conservation laws, and uniqueness, Communications in partial differential equations, vol.24, pp.2173-2189, 1999. ,
Numerical approximations of pressureless and isothermal gas dynamics, SIAM Journal on Numerical Analysis, vol.41, issue.1, pp.135-158, 2003. ,
Sur la résistance qu'oppose un liquide indéfini en repos, CR Acad. Sci, vol.100, pp.935-937, 1885. ,
Sticky particles and scalar conservation laws, SIAM journal on numerical analysis, vol.35, issue.6, pp.2317-2328, 1998. ,
DOI : 10.1137/s0036142997317353
Vortex shedding as a source of acoustic energy in segmented solid rockets, Journal of Spacecraft and Rockets, vol.18, issue.4, pp.312-319, 1981. ,
Approximate Riemann solvers for moment models of dilute gases, 1996. ,
Response of a burning heterogeneous propellant to small pressure disturbances, Proceedings of the Combustion Institute, vol.30, pp.2079-2086, 2005. ,
Monoslope and multislope MUSCL methods for unstructured meshes, Journal of Computational Physics, vol.229, issue.10, pp.3745-3776, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00323691
A Monte carlo radiation model for simulating rarefied multiphase plume flows, 38th AIAA Thermophysics Conference, 2005. ,
An Euler-Lagrange strategy for simulating particleladen flows, Journal of Computational Physics, issue.238, pp.1-31, 2013. ,
Strongly coupled fluid-particle flows in vertical channels. II. Turbulence modeling, Physics of Fluids, vol.28, issue.3, p.33306, 2016. ,
Spatial instability of planar channel flow with fluid injection through porous walls, Physics of Fluids, vol.10, issue.10, pp.2558-2568, 1998. ,
High resolution finite volume schemes and computational aerodynamics, Nonlinear Hyperbolic Equations-Theory, Computation Methods, and Applications, pp.63-74, 1989. ,
Ultrasonic method applied to full-scale solid rocket motors, Journal of Propulsion and Power, vol.16, issue.3, pp.523-528, 2000. ,
The Boltzmann equation, The Boltzmann Equation and Its Applications, pp.40-103, 1988. ,
Etude et modélisation de l'écoulement diphasique à l'intérieur des propulseurs à poudre, 1997. ,
Polydisperse evaporating spray turbulent dispersion: Eulerian model and numerical simulation, 2009. ,
Pulsated free jets with spray injection : Eulerian Multi-Fluid modelling and simulation versus experimental measurements, Proceedings of the International Conference on Multiphase Flows, vol.07, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00191015
Multivariate Gaussian extended quadrature method of moments for turbulent disperse multiphase flow, SIAM Multiscale Modeling & Simulation, vol.15, issue.4, pp.1553-1583, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01358390
An all-regime Lagrange-Projection like scheme for the gas dynamics equations on unstructured meshes, Communications in Computational Physics, vol.20, issue.1, pp.188-233, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01007622
Beyond pressureless gas dynamics : Quadraturebased velocity moment models, Communications in Mathematical Sciences, vol.10, issue.4, pp.1241-1272, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00535782
A compressible model for separated twophase flows computations, ASME 2002 Joint US-European Fluids Engineering Division Conference, pp.809-816, 2002. ,
The mathematical theory of non-uniform gases: an account of the kinetic theory of viscosity, thermal conduction and diffusion in gases, 1970. ,
, Firearms: a global history to 1700, vol.37, 2003.
Expanded analogy between Boltzmann kinetic theory of fluids and turbulence, Journal of Fluid Mechanics, vol.519, pp.301-314, 2004. ,
Status of Gel Propulsion in the Year 2010 with a Special View on the German Activities, 2010. ,
L ? stability of the MUSCL methods, Numerische Mathematik, vol.116, issue.1, pp.31-64, 2010. ,
DOI : 10.1007/s00211-010-0299-2
URL : https://hal.archives-ouvertes.fr/hal-00329588
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 high-order finite volume method for systems of conservation laws-Multi-dimensional Optimal Order Detection (MOOD), Journal of Computational Physics, vol.230, issue.10, pp.4028-4050, 2011. ,
Analyse de schémas d'ordre élevé pour les écoulements compressibles, 2008. ,
Etude analytique de l'amortissement des ondes acoustiques longitudinales dans une chambre avec injection pariétale, programme ASSM 5 axe stabilité de fonctionnement, 1996. ,
The development of discontinuous Galerkin methods, Discontinuous Galerkin Methods, pp.3-50, 2000. ,
Adaptive multiresolution for finite volume solutions of gas dynamics, Computers & fluids, vol.32, issue.1, pp.31-38, 2003. ,
DOI : 10.1016/s0045-7930(01)00096-2
The piecewise parabolic method (PPM) for gasdynamical simulations, Journal of Computational Physics, vol.54, issue.1, pp.174-201, 1984. ,
DOI : 10.1016/0021-9991(84)90143-8
URL : https://cloudfront.escholarship.org/dist/prd/content/qt5sr307f1/qt5sr307f1.pdf?t=p0i4wh
Development of high-order Taylor-Galerkin schemes for LES, Journal of Computational Physics, vol.162, issue.2, pp.338-371, 2000. ,
DOI : 10.1006/jcph.2000.6538
Study of combustion instabilities in liquid-propellant rocket engines: diffuse interface model and kinetic model coupling for primary atomization simulations, Polytechnique. REFERENCES, vol.319, 2019. ,
Very high-order accurate finite volume scheme on curved boundaries for the two-dimensional steady-state convection-diffusion equation with Dirichlet condition, Applied Mathematical Modelling, vol.54, pp.752-767, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01914596
High order semi-Lagrangian particle methods for transport equations: numerical analysis and implementation issues, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.4, pp.1029-1060, 2014. ,
DOI : 10.1051/m2an/2014009
URL : https://hal.archives-ouvertes.fr/hal-00991150
Über die partiellen Differenzengleichungen der mathematischen Physik, Mathematische annalen, vol.100, issue.1, pp.32-74, 1928. ,
DOI : 10.1007/978-1-4612-5385-3_7
Multiphase flow handbook, vol.59, 2005. ,
, Multiphase flows with droplets and particles, 2011.
DOI : 10.1201/b11103
Turbulent diffusion of heavy particles in the atmosphere, Journal of the Atmospheric Sciences, vol.20, issue.3, pp.201-208, 1963. ,
Prediction of the stability of unsteady motions in solidpropellant rocket motors, Nonsteady Burning and Combustion Stability of Solid Propellants, vol.143, pp.719-779, 1992. ,
Rotational axisymmetric mean flow and damping of acoustic waves in a solid propellant rocket, AIAA Journal, vol.4, issue.8, pp.1462-1464, 1966. ,
Eulerian approach for unsteady two-phase solid rocket flows with aluminum particles, J. of Propulsion and Power, vol.16, issue.2, pp.309-317, 2000. ,
DOI : 10.2514/2.5570
A comparison between centered and upwind schemes for two-phase compressible flows, AIAA/SAE/ASME/ASEE, Joint Propulsion Conference and Exhibit, vol.29, pp.269-280, 1993. ,
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations, Journal of computational physics, vol.193, issue.2, pp.563-594, 2004. ,
History of the development of solid rocket propellant in France, Journal of Propulsion and Power, vol.11, issue.2, pp.285-291, 1995. ,
A rotationally biased upwind difference scheme for the Euler equations, Journal of Computational Physics, vol.56, issue.1, pp.65-92, 1984. ,
, TVD finite difference schemes and artificial viscosity, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.3, pp.445-473
Arbitrary high-order schemes for the linear advection and wave equations: application to hydrodynamics and aeroacoustics, Comptes Rendus Mathematique, vol.342, issue.6, pp.441-446, 2006. ,
Some issues related to the modeling of interfacial areas in gasliquid flows I. The conceptual issues, Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics, vol.329, issue.5, pp.397-410, 2001. ,
Jump conditions and entropy sources in two-phase systems. Local instant formulation, International Journal of Multiphase Flow, vol.1, issue.3, pp.395-409, 1974. ,
Analysis of Godunov type schemes applied to the compressible Euler system at low Mach number, Journal of Computational Physics, vol.229, issue.4, pp.978-1016, 2010. ,
Highlights of solid rocket propulsion history, Chemical Rocket Propulsion, pp.1015-1032, 2017. ,
Microstructure effects in aluminized solid rocket propellants, Journal of propulsion and power, vol.26, issue.4, pp.724-733, 2010. ,
Operator splitting methods with error estimator and adaptive time-stepping. Application to the simulation of combustion phenomena, Splitting Methods in Communication, Imaging, Science, and Engineering, pp.627-641, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01183745
Operator splitting for nonlinear reaction-diffusion systems with an entropic structure: singular perturbation and order reduction, Numer. Math, vol.97, issue.4, pp.29-599, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00188449
A quadrature-based moment method for dilute fluid-particle flows, Journal of Computational Physics, vol.227, issue.4, pp.2514-2539, 2008. ,
The theory of canonical moments with applications in statistics, probability, and analysis, vol.338, 1997. ,
Modeling and simulation of polydisperse moderately dense coalescing spray flows with nanometric-to-inertial droplets: application to Solid Rocket Motors, 2013. ,
URL : https://hal.archives-ouvertes.fr/tel-01009896
On Multi-Fluid models for spray-resolved LES of reacting jets, Proceedings of the Combustion Institute, vol.36, pp.2441-2450, 2017. ,
A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows, Journal of Computational Physics, vol.329, pp.48-72, 2017. ,
Eulerian MultiFluid models for the simulation of dynamics and coalescence of particles in solid propellant combustion, Journal of Computational Physics, vol.234, pp.230-262, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00618806
Numerical strategy for unsteady two-way coupled polydisperse sprays: application to solid-rocket instabilities, Journal of Propulsion and Power, vol.30, issue.3, pp.727-748, 2014. ,
A Taylor-Galerkin method for convective transport problems, International Journal for Numerical Methods in Engineering, vol.20, issue.1, pp.101-119, 1984. ,
Finite element methods for flow problems, 2003. ,
A family of embedded Runge-Kutta formulae, Journal of Computational and Applied Mathematics, vol.6, issue.1, pp.19-26, 1980. ,
, Theory of multicomponent fluids, vol.135, 2006.
Eulerian modeling and simulations of separated and disperse two-phase flows: development of a unified modeling approach and associated numerical methods for highly parallel computations, 2017. ,
URL : https://hal.archives-ouvertes.fr/tel-01618320
Concentration waves and flow modification in a particle-laden circular vortex, Physics of Fluids, vol.6, issue.10, pp.3276-3284, 1994. ,
, On the two-way interaction in two-dimensional particle-laden flows: the accumulation of particles and flow modification, Journal of Fluid Mechanics, vol.297, pp.49-76, 1995.
Adaptive numerical methods in time and space for the simulation of multiscale reaction fronts, 2011. ,
URL : https://hal.archives-ouvertes.fr/tel-00667857
New resolution strategy for multiscale reaction waves using time operator splitting, space adaptive multiresolution, and dedicated high order implicit/explicit time integrators, SIAM Journal on Scientific Computing, vol.34, issue.1, pp.76-104, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00457731
High-order dimensionally split Lagrange-remap schemes for compressible hydrodynamics, Comptes Rendus Mathematique, vol.348, issue.1-2, pp.105-110, 2010. ,
Modélisation Multi-Fluide eulérienne pour les écoulements diphasiques à inclusions dispersées, 2005. ,
A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems, Journal of Computational Physics, vol.304, pp.275-319, 2016. ,
Contribution à l'étude du rôle de la phase condensée dans la stabilité d'un propulseur à propergol solide pour lanceur spatial, 1996. ,
Some Aspects of Two-Phase Flows in Solid-Propellant Rocket Motors, Solid Propellant Chemistry, Combustion, and Motor Interior Ballistics, vol.185, pp.859-883, 2000. ,
Inert condensed phase driving effect of combustion instabilities in solid rocket motor, th International Spacecraft Propulsion Conference, 2008. ,
Steady and unsteady reactive two-phase computations in solid rocket motors with Eulerian and Lagrangian approaches, 37th Joint Propulsion Conference and Exhibit, 2001. ,
Accurate and robust numerical strategy for axisymmetric Eulerian modeling of particles laden flows of moderate inertia, Journal of Computational Mathematics, 2018. ,
Eulerian models and related numerical schemes and parallel implementation for the simulation of polydisperse two-phase flows in solid rocket motors, SimRace, International conference on numerical methods and High Performance Computing for industrial fluid flows, 2015. ,
On the influence of the numerical strategy on the predictive character of an EulerEuler model for two-phase flow simulations in solid rocket motor instabilities, 3rd International Conference on Numerical Methods in Multiphase Flows, ICNMMF-III, 2015. ,
Etude par simulations numériques instationnaires de l'écoulement dans les moteurs à propergol solide, 2012. ,
Transferts radiatifs dans les chambres de combustions de propulseurs à propergol solide aluminisé, 2002. ,
On Godunov-type methods for gas dynamics, SIAM Journal on Numerical Analysis, vol.25, issue.2, pp.294-318, 1988. ,
On Godunov-type methods near low densities, Journal of Computational Physics, vol.92, issue.2, pp.273-295, 1991. ,
On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification, Physics of Fluids A: Fluid Dynamics, vol.5, issue.7, pp.1790-1801, 1993. ,
Modeling of spray polydispersion with two-way turbulent interactions for high pressure direct injection in engines, 2014. ,
URL : https://hal.archives-ouvertes.fr/tel-01089937
Eulerian moment methods for automotive sprays, Atomization and Sprays, vol.25, issue.3, pp.189-254, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01097531
Considérations sur les résultats d'un allégement indéfini des moteurs, Journal de physique theorique et appliquee, vol.3, issue.1, pp.218-230, 1913. ,
Contribution to a unified Eulerian modeling of fuel injection: from dense liquid to polydisperse evaporating spray, 2018. ,
High order moment model for polydisperse evaporating sprays towards interfacial geometry description, SIAM Applied Mathematics, pp.1-42, 2016. ,
Statistical modeling of the gas-liquid interface using geometrical variables: toward a unified description of the disperse and separated phase flows, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01615076
Combustion of aluminum particles in solid rocket motors, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2003. ,
, Recent Advances in Research on Solid Rocket Propulsion". AerospaceLab, vol.1, issue.11, p.15, 2016.
Convergence analysis for a class of high-order semi-Lagrangian advection schemes, SIAM Journal on Numerical Analysis, vol.35, issue.3, pp.909-940, 1998. ,
Monte-Carlo simulation of colliding particles or coalescing droplets transported by a turbulent flow in the framework of a joint fluid-particle pdf approach, International Journal of Multiphase Flow, vol.74, pp.165-183, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01362106
A fast Eulerian method for disperse two-phase flow, International Journal of Multiphase Flow, vol.27, issue.7, pp.1199-1226, 2001. ,
, Equilibrium expansion for the Eulerian velocity of small particles, Powder Technology, vol.125, issue.2-3, pp.131-139, 2002.
, Equilibrium Eulerian approach for predicting the thermal field of a dispersion of small particles, International Journal of Heat and Mass Transfer, vol.48, issue.3-4, pp.681-689, 2005.
Computational methods for fluid dynamics, 2012. ,
Partitioning of particle velocities in a gassolid turbulent flow into a continuous field and a spatially-uncorrelated random distribution : theoretical formalism and numerical study, J. Fluid Mech, vol.533, pp.1-46, 2005. ,
A moment matrix approach to multivariable cubature, Integral Equations and Operator Theory, vol.52, issue.1, pp.85-124, 2005. ,
Binary water droplet collision study in presence of solid aerosols in air, 7th International Conference on Multiphase Flow, 2010. ,
Generation of finite difference formulas on arbitrarily spaced grids, Mathematics of computation, vol.51, pp.699-706, 1988. ,
A quadrature-based third-order moment method for dilute gas-particle flow, Journal of Computational Physics, vol.227, issue.12, pp.6313-6350, 2008. ,
, Optimal moment sets for multivariate direct quadrature method of moments, Industrial & Engineering Chemistry Research, vol.48, issue.21, pp.9686-9696
Numerical simulation of spray coalescence in an Eulerian framework : direct quadrature method of moments and Multi-Fluid method, Journal of Computational Physics, vol.227, issue.6, pp.2215-2222, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00157269
Method of moments with interpolative closure, Chemical Engineering Science, vol.57, issue.12, pp.2229-2239, 2002. ,
Aerosol dynamics modeling using the method of moments, Journal of colloid and interface science, vol.118, issue.1, pp.252-261, 1987. ,
Aluminum combustion driven instabilities in solid rocket motors, Journal of Propulsion and Power, vol.25, issue.2, pp.509-521, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01871428
Computational study of turbulence in a subscale solid rocket motor, AIAA Paper, vol.4052, 2004. ,
Aluminum combustion driven instabilities in solid rocket motors, Journal of propulsion and power, vol.25, issue.2, p.509, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01871428
Analysis of the parareal time-parallel time-integration method, SIAM Journal on Scientific Computing, vol.29, issue.2, pp.556-578, 2007. ,
Internal ballistics considerations of nozzleless rocket motors, J. Propul. Power, vol.15, issue.6, pp.866-873, 1999. ,
Tensorial algebra and analysis for continuum mechanics, Lecture, 2016. ,
URL : https://hal.archives-ouvertes.fr/cel-00679923
Orthogonal polynomials: computation and approximation, 2004. ,
Droplet breakup phenomena in flows with velocity lag, Progress in energy and combustion science, vol.22, issue.3, pp.201-265, 1996. ,
Thermoacoustic instabilities in solid propellant motor, 2018. ,
A Numerical analysis of the aluminium combustion driven instability in solid rocket motors, 7th European Conference for Aeronautics and Space Sciences, 2017. ,
Asymptotic stability of equilibrium states for multicomponent reactive flows, Math. Models Methods Appl. Sci, vol.8, issue.2, pp.218-2025, 1998. ,
A method of reaching extreme altitudes, Nature, vol.105, issue.2, pp.809-811, 1920. ,
Unsteady eulerian two-phase flow analysis of solid rocket motor slag, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 1997. ,
Numerical Approximation of Hyperbolic Systems of Conservation Laws, vol.118, 1996. ,
An interesting class of quasilinear systems, Dokl. Akad. Nauk SSSR, vol.139, pp.521-523, 1961. ,
Reminiscences about Difference Schemes, Journal of Computational Physics, vol.153, issue.1, pp.6-25, 1999. ,
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Matematicheskii Sbornik, vol.89, issue.3, pp.271-306, 1959. ,
Computer program for calculation of complex chemical equilibrium compositions and applications, National Aeronautics / Space Administration, vol.1, 1994. ,
Solid Propellant Combustion and Internal Ballistics of Motors in Solid Rocket Propulsion Technology, 1993. ,
Assessment of Riemann solvers for unsteady onedimensional inviscid flows of perfect gases, Journal of Computational Physics, vol.78, issue.2, pp.437-458, 1988. ,
On high order strong stability preserving Runge-Kutta and multi step time discretizations, Journal of Scientific Computing, vol.25, issue.1, pp.105-128, 2005. ,
Strong stability preserving Runge-Kutta and multistep time discretizations, 2011. ,
Strong stability-preserving high-order time discretization methods, SIAM review, vol.43, issue.1, pp.89-112, 2001. ,
Un schema de volumes-finis décentré pour la résolution des équations d'Euler en axisymétrique, 1989. ,
On the kinetic theory of rarefied gases, Communications on pure and applied mathematics, vol.2, issue.4, pp.331-407, 1949. ,
Kinetic Theory of Plasmas : Translational Energy, Mathematical Models and Methods in Applied Sciences, vol.19, issue.04, pp.527-599, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00185109
Instabilité pariétale et accrochage aéro-acoustique dans les conduits à parois débitantes simulant les moteurs à propergol solide d'Ariane 5, 2001. ,
On the nonparallel stability of the injection-induced twodimensional Taylor flow, Phys. Fluids, vol.13, issue.6, pp.1635-1644, 2001. ,
Spatial instability of flow in a semi-infinite cylinder with fluid injection through its porous walls, Eur. J. of Mech. B-Fluids, vol.19, pp.69-87, 2000. ,
Multiscale equilibrium and nonequilibrium thermodynamics in chemical engineering, Advances in Chemical Engineering, vol.39, pp.75-129, 2010. ,
Towards physically realizable and hyperbolic moment closures for kinetic theory, Continuum Mechanics and Thermodynamics, vol.21, issue.6, p.467, 2009. ,
Finite element/volume solution to axisymmetric conservation laws, Journal of Computational Physics, vol.224, issue.2, pp.489-518, 2007. ,
Solid propulsion for space applications: An updated roadmap, Acta Astronautica, vol.66, issue.1, pp.201-219, 2010. ,
On the behavior of upwind schemes in the low Mach number limit: II. Godunov type schemes, Computers & fluids, vol.33, issue.4, pp.655-675, 2004. ,
URL : https://hal.archives-ouvertes.fr/inria-00072433
On the Behaviour of Upwind Schemes in the Low Mach Number Limit: A Review, Handbook of Numerical Analysis, vol.18, pp.203-231, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01534938
Discrétisation en maillage non structuré général et applications LES, 2009. ,
Parallel implementation of kexact finite volume reconstruction on unstructured grids, High Order Nonlinear numerical schemes for evolutionary PDEs, p.325, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01283662
Stability analysis of the cell centered finitevolume M uscl method on unstructured grids, Numerische Mathematik, vol.113, issue.4, pp.555-600, 2009. ,
Solving ordinary differential equations. I. xv+528. Nonstiff problems, second revised edition, 1993. ,
Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Series in Computational Mathematics, vol.8, 1993. ,
Solving ordinary differential equations. II. xv+614. Stiff and differential-algebraic problems, second revised edition, vol.isbn, pp.3-540, 1996. ,
, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, vol.14, 1996.
High resolution schemes for hyperbolic conservation laws, Journal of Computational Physics, vol.49, issue.3, pp.357-393, 1983. ,
, Adaptive multiresolution schemes for shock computations, Journal of Computational Physics, vol.115, issue.2, pp.319-338, 1994.
Uniformly high order accurate essentially non-oscillatory schemes, III". In Upwind and high-resolution schemes, pp.218-290, 1987. ,
Self adjusting grid methods for one-dimensional hyperbolic conservation laws, Journal of Computational Physics, vol.50, issue.2, pp.235-269, 1983. ,
On upstream differencing and Godunov-type scheme for hyperbolic conservation laws, SIAM review, vol.25, issue.1, pp.35-61, 1983. ,
Drag coefficients of spheres in continuum and rarefied flows, AIAA, vol.14, issue.6, pp.707-708, 1976. ,
A parallel Eulerian interface tracking/Lagrangian point particle multiscale coupling procedure, Journal of Computational Physics, vol.229, issue.3, pp.745-759, 2010. ,
Nodal discontinuous Galerkin methods: algorithms, analysis, and applications, 2007. ,
Mechanics and thermodynamics of propulsion, pp.764-765, 1992. ,
Numerical Computation of Internal and External Flows: Fundamentals of Numerical Discretization, 1990. ,
, Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics, 2007.
Analytical model for the prediction of pulsations in a cold-gas scale-model of a Solid Rocket Motor, Journal of Sound and Vibration, vol.419, pp.452-468, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01737077
An arbitrary Lagrangian-Eulerian computing method for all flow speeds, Journal of Computational Physics, vol.14, issue.3, pp.227-253, 1974. ,
Computational fluid dynamics for dense gas-solid fluidized beds: a multi-scale modeling strategy, Chemical Engineering Science, vol.59, pp.5157-5165, 2004. ,
The Koren upwind scheme for variable gridsize, Applied numerical mathematics, vol.37, issue.4, pp.459-487, 2001. ,
New statistical models for kinetic theory: methods of construction, The Physics of Fluids, vol.9, issue.9, pp.1658-1673, 1966. ,
New simple correlation formula for the drag coefficient of non-spherical particles, Powder Technology, vol.184, issue.3, pp.361-365, 2008. ,
Drop properties after secondary breakup, International Journal of Multiphase Flow, vol.19, issue.5, pp.721-735, 1993. ,
Drop deformation and breakup due to shock wave and steady disturbances, International Journal of Multiphase Flow, vol.21, issue.4, pp.545-560, 1995. ,
Numerical Solution of Time-Dependent AdvectionDiffusion-Reaction Equations, 2003. ,
Modélisation cinétique et simulation numérique d'un brouillard dense de gouttelettes. Application aux propulseurs à poudre, 1999. ,
Thermo-fluid dynamics of two-phase flow, 2010. ,
Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE Journal, vol.25, issue.5, pp.843-855, 1979. ,
Various levels of models for aerosols, Mathematical Models and Methods in Applied Sciences, vol.12, issue.7, pp.903-919, 2002. ,
An equation set for non-equilibrium two phase flow, and an analysis of some aspects of choking, acoustic propagation, and losses in low pressure wet steam, International journal of multiphase flow, vol.9, issue.5, pp.491-510, 1983. ,
Diffusion regulation for Euler solvers, Journal of Computational Physics, vol.221, issue.2, pp.577-599, 2007. ,
Analysis and design of numerical schemes for gas dynamics, 1: artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence, International Journal of Computational Fluid Dynamics, vol.4, issue.3-4, pp.171-218, 1995. ,
, Positive schemes and shock modelling for compressible flows, International Journal for Numerical Methods in Fluids, vol.20, issue.8-9, pp.743-776
Numerical solution of the Euler equations for complex configurations, AIAA 6th Computational Fluid Dynamics Conference, pp.83-1929, 1983. ,
Some Recent Developments in Numerical Methods for Transonic Flow, Computer Methods in Applied Mechanics and Engineering, vol.51, pp.467-493, 1985. ,
Numerical solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes, 1981. ,
Efficient implementation of weighted ENO schemes, Journal of computational physics, vol.126, issue.1, pp.202-228, 1996. ,
Gaussian-moment relaxation closures for verifiable numerical simulation of fast magnetic reconnection in plasma, 2011. ,
Calculus of finite differences, 1965. ,
Domain of definition of Levermore's five-moment system, Journal of Statistical Physics, vol.93, issue.5-6, pp.1143-1167, 1998. ,
Maximum entropy moment systems and Galilean invariance, Continuum Mechanics and Thermodynamics, vol.14, issue.6, pp.563-576, 2002. ,
Taking into account polydispersity for the modeling of liquid fuel injection in internal combustion engines, 2010. ,
URL : https://hal.archives-ouvertes.fr/tel-00618786
High order moment method for polydisperse evaporating sprays with mesh movement: application to internal combustion engines, International Journal of Multiphase Flow, vol.71, pp.38-65, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00941796
A high order moment method simulating evaporation and advection of a polydisperse liquid spray, Journal of Computational Physics, issue.2, pp.394-422, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00536512
Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence, Journal of Computational Physics, vol.227, issue.13, pp.6448-6472, 2008. ,
Schaum's Outline of Tensor Calculus, 1988. ,
Multivariate distributions and the moment problem, Journal of Multivariate Analysis, vol.113, pp.7-18, 2013. ,
Thermo-fluid dynamics of separated two-phase flow, 1971. ,
A robust upwind discretization method for advection, diffusion and source terms. Centrum voor Wiskunde en Informatica Amsterdam, 1993. ,
Computation of vortex shedding in solid rocket motors using time-dependant turbulence model, Journal of Propulsion and Power, vol.15, issue.3, pp.390-400, 1999. ,
Contractivity of Runge-Kutta methods, BIT Numerical Mathematics, vol.31, issue.3, pp.482-528, 1991. ,
The inhomogeneous MUSIG model for the simulation of polydispersed flows, Nuclear Engineering and Design, vol.238, issue.7, pp.1690-1702, 2008. ,
Contribution à l'étude des pertes d'impulsion specifique dans les fusees a propergol solide, La Recherche Aérospatiale, vol.5, pp.341-351, 1973. ,
Gravity settling in liquid/liquid dispersions, The Canadian Journal of Chemical Engineering, vol.63, issue.3, pp.368-376, 1985. ,
Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique, Chemical Engineering Science, vol.61, issue.10, pp.3327-3342, 2006. ,
On the solution of population balance equations by discretization-I. A fixed pivot technique, Chemical Engineering Science, vol.51, issue.8, pp.1311-1332, 1996. ,
, On the solution of population balance equations by discretization-II. A moving pivot technique, Chemical Engineering Science, vol.51, issue.8, pp.1333-1342
Explicit and implicit FEM-FCT algorithms with flux linearization, Journal of Computational Physics, vol.228, issue.7, pp.2517-2534, 2009. ,
Space mission analysis and design. Microcosm, 1992. ,
Multi-fluid modeling of laminar poly-dispersed spray flames: origin, assumptions and comparison of the sectional and sampling methods, Comb. Theory and Modelling, vol.5, issue.4, pp.537-572, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00185799
Eulerian Multi-Fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays, Journal of Computational Physics, vol.194, issue.2, pp.505-543, 2004. ,
URL : https://hal.archives-ouvertes.fr/hal-00187619
Two-size moment multi-fluid model: a robust and high-fidelity description of polydisperse moderately dense evaporating sprays, Communications in Computational Physics, vol.20, issue.4, pp.902-943, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01169730
Systems of Conservation, Communications on pure and applied mathematics, vol.13, pp.217-237, 1960. ,
Shock waves and entropy, Contributions to nonlinear functional analysis, pp.603-634, 1971. ,
Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on Pure and Applied Mathematics, vol.7, issue.1, pp.159-193, 1954. ,
Couplage entre modèles diphasiques à «phases séparées» et à «phase dispersée» pour la simulation de l'atomisation primaire en combustion cryotechnique, 2015. ,
Multislope MUSCL method for general unstructured meshes, Journal of Computational Physics, vol.284, pp.389-418, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00939475
Coupling vaporization model with the Eulerian-Lagrangian Spray Atomization (ELSA) model in Diesel engine conditions, Tech. rep. SAE Technical Paper, 2005. ,
Numerical simulation of primary break-up and atomization: DNS and modelling study, International Journal of Multiphase Flow, vol.35, issue.3, pp.247-260, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00649748
A thermodynamic description of thermodiffusion in suspensions of rigid particles, The European Physical Journal-Special Topics, vol.146, issue.1, pp.3-12, 2007. ,
Towards the ultimate conservative difference scheme IV. A new approach to numerical convection, Journal of Computational Physics, vol.23, pp.276-299, 1977. ,
, 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.
Sur le calcul de solutions faibles des systèmes hyperboliques de lois de conservation à l'aide de schémas aux différences. Office national d'études et de recherches aérospatiales, 1981. ,
Propriétés dispersives et dissipatives d'une classe de schémas aux différences pour les systèmes hyperboliques non linéaires, La Recherche Aérospatiale, vol.2, pp.61-79, 1975. ,
Experimental demonstration of the vacuum specific impulse of a hybrid rocket engine, Journal of Spacecraft and Rockets, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01558999
Numerical methods for conservation laws. Second. x+214. Basel: Birkhäuser Verlag, vol.isbn, pp.3-7643, 1992. ,
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems, Finite volume methods for hyperbolic problems. xx+558. Cambridge Texts in Applied Mathematics, vol.98, 2002. ,
Moment closure hierarchies for kinetic theories, Journal of statistical Physics, vol.83, issue.5-6, pp.1021-1065, 1996. ,
The Gaussian moment closure for gas dynamics, 1998. ,
, SIAM J. Appl. Math, vol.59, issue.1, pp.72-96
Rocket Propulsion: A Résumé of Theory with an Account of the Practical Experiments made to Date, Aircraft Engineering and Aerospace Technology, vol.7, issue.9, pp.227-231, 1935. ,
The moment calculation of polyhedra, Pattern Recognition, vol.26, issue.8, pp.1229-1233, 1993. ,
Multiscale simulation of atomization with small droplets represented by a Lagrangian point-particle model, International Journal of Multiphase Flow, vol.76, pp.122-143, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01196361
Résolution d'EDP par un schéma en temps «pararéel», Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, vol.332, issue.7, pp.661-668, 2001. ,
Incompressible limit for a viscous compressible fluid, Journal de mathématiques pures et appliquées, vol.77, issue.6, pp.585-627, 1998. ,
An introduction to meshfree methods and their programming, 2005. ,
Weighted essentially non-oscillatory schemes, Journal of Computational Physics, vol.115, issue.1, pp.200-212, 1994. ,
Finite element flux-corrected transport (FEM-FCT) for the euler and Navier-Stokes equations, International Journal for Numerical Methods in Fluids, vol.7, issue.10, pp.1093-1109, 1987. ,
Full Numerical Unsteady computations Of Vortx Shedding Phenomenon". Tech. rep. RT n°10/6133 EY. ONERA.-. 1992a, 30th Aerospace and Sciences Meeting and Exhibit, 1991. ,
Simulation numérique bidimensionnelle des écoulements instationnaires dans les propulseurs à propergol solide, La Recherche Aérospatiale, issue.2, pp.21-41, 1992. ,
Parietal vortex shedding as a cause of instability for long solid propellant motors-Numerical simulations and comparisons with firing tests, 34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp.96-0761, 1993. ,
Numerical simulations of the unsteady flow inside Ariane 5 P230 SRM booster with burning aluminum particles, 2 nd European Conference on Launcher Technology, 2000. ,
The effect of viscosity in hypervelocity impact cratering, Journal of spacecraft and rockets, vol.40, issue.5, pp.757-763, 1969. ,
Theoretical analysis of hydrides in solid and hybrid rocket propulsion, international journal of hydrogen energy, vol.37, issue.2, pp.1760-1769, 2012. ,
On steady rotational high speed flows: the compressible Taylor-Culick profile, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.463, pp.131-162, 2007. ,
Laminar cold-flow model for the internal gas dynamics of a slab rocket motor, Aerospace science and technology, vol.5, issue.3, pp.193-207, 2001. ,
Higher mean-flow approximation for a solid rocket motor with radially regressing walls, 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 2001. ,
The Rocket Pioneers, Engineering and Science, vol.31, issue.5, pp.9-32, 1968. ,
Kinetic flux vector splitting for Euler equations, 1994. ,
Dynamics of dusty gases, Ann. Rev. Fluid Mech, vol.2, pp.397-446, 1970. ,
Acoustic disturbance from gas non-uniformities convected through a nozzle, Journal of Sound and Vibration, vol.55, issue.2, pp.225-243, 1977. ,
Some application of splitting-up methods to the solution of mathematical physics problems, Aplikace matematiky, vol.13, issue.2, pp.103-132, 1968. ,
, Splitting and alternating direction methods, Handbook of numerical analysis, vol.1, pp.197-462, 1990.
Dispersion and polydispersity of droplets in stationary isotropic turbulence, International journal of multiphase flow, vol.23, issue.2, pp.337-355, 1997. ,
Étude théorique et numérique de la modélisation instationnaire des écoulements turbulents anisothermes gaz-particules par une approche Euler-Euler, 2010. ,
The mesoscopic Eulerian approach for evaporating droplets interacting with turbulent flows, Flow, Turbulence and Combustion, vol.86, issue.3, pp.563-583, 2011. ,
An algebraic-closure-based momentmethod for unsteady Eulerian modeling of non-isothermal particle-laden turbulent flows in very dilute regime and high Stokes number, ICHMT DIGITAL LIBRARY ONLINE, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00915061
Ecoulements Compressibles et Supersoniques, ECP, 2014. ,
A robust moment method for evaluation of the disappearance rate of evaporating sprays, SIAM J. Appl. Math, vol.70, issue.8, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00332423
The motion of small spherical particles in a cellular flow field". The Physics of fluids, vol.30, pp.1915-1928, 1987. ,
Numerical modeling of micron-scale flows using the Gaussian moment closure, AIAA Paper, vol.5035, 2005. ,
Affordable robust moment closures for CFD based on the maximum-entropy hierarchy, Journal of Computational Physics, vol.251, pp.500-523, 2013. ,
Description of aerosol dynamics by the quadrature method of moments, Aerosol Science and Technology, vol.27, pp.255-265, 1997. ,
Large eddy simulation of disperse phase flows with inverse coupling, 2018. ,
Matrix and tensor calculus, 1947. ,
Two-phase flow analysis of instabilities driven by vortexshedding in solid rocket motors, 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 1995. ,
A method for solving algebraic equations using an automatic computer, Mathematical Tables and Other Aids to Computation, vol.10, issue.56, pp.208-215, 1956. ,
Basics of statistical physics, 2013. ,
The extension of incompressible flow solvers to the weakly compressible regime, Computers & Fluids, vol.32, issue.2, pp.173-196, 2003. ,
Numerical Modeling of Dispersed Two-Phase Flows". Available at www.aerospacelab-journal.org/al2, Aerospace Lab, vol.2, pp.1-13, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-01181241
Rockets in Mysore and Britain, 1750-1850 AD, 1985. ,
Rocket propulsion with gelled propellants for sounding rockets, Proceedings of the 20th symposium on European rocket and balloon programmes and related research, 2011. ,
Solution of population balance equations in applications with fine particles: mathematical modeling and numerical schemes, Journal of Computational Physics, vol.325, pp.129-156, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01247390
Closing the hierarchy of moment equations in nonlinear dynamical systems, Physical Review E, vol.58, issue.4, p.4391, 1998. ,
Tools for Triangulations and Tetrahedrizations, Scientific Visualization, pp.429-525, 1994. ,
Parallel methods for integrating ordinary differential equations, Communications of the ACM, vol.7, issue.12, pp.731-733, 1964. ,
Dynamics of multiphase media, vol.2, 1990. ,
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers, Journal of Computational Physics, vol.227, issue.4, pp.2560-2581, 2008. ,
Die Rakete zu den Planetenräumen, 1923. ,
On the construction of kinetic schemes, Journal of Computational Physics, vol.177, issue.1, pp.156-175, 2002. ,
Theoretical and practical aspects of some initial boundary value problems in fluid dynamics, SIAM Journal on Applied Mathematics, vol.35, issue.3, pp.419-446, 1978. ,
Collective drop effects on vaporizing liquid sprays, 1981. ,
Neure methoden und ergebnisse in der hydrodynamik, 1927. ,
Upwind schemes and boundary conditions with applications to Euler equations in general geometries, Journal of Computational Physics, vol.50, issue.3, pp.447-481, 1983. ,
General projection operator formalism for the dynamics and thermodynamics of complex fluids, Journal of Rheology, vol.57, issue.2, pp.1285-1304, 1998. ,
The mathematical procedure of coarse graining: From Grad's ten-moment equations to hydrodynamics, Multiscale Modeling & Simulation, vol.6, issue.1, pp.53-69, 2007. ,
Two-way coupled stochastic model for dispersion of inertial particles in turbulence, Journal of Fluid Mechanics, vol.700, pp.29-62, 2012. ,
On the dissipation mechanism of Godunov-type schemes, Journal of Computational Physics, vol.188, issue.2, pp.524-542, 2003. ,
Preconditioned HLLE method for flows at all Mach numbers, AIAA journal, vol.44, issue.11, pp.2645-2653, 2006. ,
Generalized Basset-Boussinesq-Oseen equation for unsteady forces on a sphere in a compressible flow, Physical review letters, vol.106, issue.8, p.84501, 2011. ,
A hyperbolic model for viscous Newtonian flows, Continuum Mechanics and Thermodynamics, vol.28, issue.1-2, pp.85-104, 2016. ,
Numerical solution of hyperbolic systems. Application to gas dynamics, p.30524, 1979. ,
Simulating compressible gas bubbles with a smooth volume tracking 1-fluid method, International Journal of Multiphase Flow, vol.36, issue.4, pp.273-283, 2010. ,
Comparison of diesel spray combustion in different high-temperature, high-pressure facilities, SAE International Journal of Engines, vol.3, pp.156-181, 2010. ,
Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop, International journal of multiphase flow, vol.13, issue.6, pp.741-757, 1987. ,
Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, vol.101, issue.1, pp.104-129, 1992. ,
Physique statistique hors d'équilibre-Processus irréversibles linéaires, 2007. ,
Experimental observations of combustion instability, Fundamentals of Solid-Propellant Combustion, vol.90, pp.733-790, 1984. ,
Regimes of coalescence and separation in droplet collision, Journal of Fluid Mechanics, vol.331, pp.59-80, 1997. ,
Study of coalescence in spray headers: application to the spray system of PWRs, 2009. ,
Aerodynamic shattering of liquid drops, AIAA Journal, vol.7, issue.2, pp.285-290, 1968. ,
Evaporation from drops, Chem. Eng. Prog, vol.48, issue.3, pp.141-146, 1952. ,
A numerical model for temperature gradient and particle effects on Rijke burner oscillations, Combustion and flame, vol.94, issue.1-2, pp.1-24, 1993. ,
A mixed finite element method for 2-nd order elliptic problems, Mathematical aspects of finite element methods, pp.292-315, 1977. ,
The finite element method in heat transfer and fluid dynamics, 2010. ,
, CEDRE software". Available at www.aerospacelab-journal.org/al2, vol.2, pp.1-10, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01182463
Cold flow tests for flow field and deformation characteristics of the PTF membrane from the PODX, 6th European Conference for Aeronautics and Space Sciences, 2015. ,
Analysis of weakly turbulent diluted-spray flames and spray combustion regimes, J. Fluid Mech, vol.537, pp.317-347, 2005. ,
An introduction to the calculus of finite differences, 1954. ,
LXXI. Notice of a new method of causing a vibration of the air contained in a tube open at both ends". The London, Edinburgh, and Dublin Philosophical Magazine and, Journal of Science, vol.17, issue.116, pp.419-422 ,
Diffusion experiments with numerically intergrated isotropic turbulence, Physics of Fluids, vol.17, pp.292-297, 1974. ,
Approximate Riemann solvers, parameter vectors and difference schemes, Journal of Computational Physics, vol.43, pp.84-53, 1981. ,
Efficient construction and utilisation of approximate Riemann solutions, Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI, pp.499-518, 1985. ,
Eigenvalues and eigenvectors of the Euler equations in general geometries, 15th AIAA Computational Fluid Dynamics Conference, 2001. ,
Stability of operator splitting methods for systems with indefinite operators: Advection-diffusion-reaction systems, Journal of Computational REFERENCES, vol.333, 2009. ,
The calculation of the interaction of non-stationary shock waves with barriers, Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, vol.1, issue.2, pp.267-279, 1961. ,
The effect of voidage on the drag force on particles, droplets and bubbles in dispersed two-phase flow, Japanese European Two-Phase Flow Meeting, 2000. ,
Eulerian models and realizable numerical schemes for the description of lowto-medium inertia polydisperse sprays in turbulent two-phase flows, 2016. ,
On the development of high order realizable schemes for the Eulerian simulation of disperse phase flows: a convex-state preserving Discontinuous Galerkin method, The Journal of Computational Multiphase Flows, vol.6, issue.3, pp.247-270, 2014. ,
Statistical description of turbulent particleladen flows in the very dilute regime using the Anisotropic Gaussian Moment Method, International Journal of Multiphase Flow, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01886835
Numerical simulation of distributed combustion in solid rocket motors with metalized propellant, Journal of Propulsion and Power, vol.19, issue.1, pp.48-55, 2003. ,
A parallel solution-adaptive scheme for multi-phase core flows in solid propellant rocket motors, International Journal of Computational Fluid Dynamics, vol.19, issue.2, pp.159-177, 2005. ,
, Numerical solution scheme for inert, disperse, and dilute gas-particle flows, International journal of multiphase flow, vol.33, issue.3, pp.282-299, 2007.
Shock Waves & Explosions, 2016. ,
On the stability of laminar flow of a dusty gas, J. Fluid Mech, vol.13, issue.1, pp.120-128, 1962. ,
Two-phase flows-Second-order schemes and boundary conditions, AIAA journal, vol.32, issue.6, pp.1214-1221, 1994. ,
A drag coefficient correlation, V.D.I Zeitung, vol.77, pp.318-320, 1935. ,
The Riemann problem for the transportation equations in gas dynamics, vol.654, 1999. ,
Explicit formulae for polyhedra moments, Pattern Recognition Letters, vol.22, issue.10, pp.1103-1109, 2001. ,
Deformation and breakup of drops by aerodynamic forces, Atomization and Sprays, vol.6, issue.6, 1996. ,
Efficient implementation of essentially non-oscillatory shockcapturing schemes, Journal of Computational Physics, vol.77, pp.439-471, 1988. ,
, Efficient implementation of essentially non-oscillatory shock-capturing schemes, II, Upwind and High-Resolution Schemes, pp.328-374, 1989.
Modélisation et étude de l'évaporation et de la combustion de gouttes dans les moteurs à propergol solide par une approche eulérienne Multi-Fluide, 2015. ,
Simulation of reactive polydisperse sprays strongly coupled to unsteady flows in solid rocket motors: Efficient strategy using Eulerian multi-fluid methods, Journal of Computational Physics, vol.339, pp.210-246, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01063816
Modélisation eulérienne de la phase dispersée dans les moteurs à propergol solide, avec prise en compte de la pression particulaire, 2003. ,
On the spatial distribution of heavy-particle velocities in turbulent flow : from continuous field to particulate chaos, Journal of Turbulence, vol.40, 2002. ,
A general approach to moment calculation for polygons and line segments, Pattern Recognition, vol.26, issue.7, pp.1019-1028, 1993. ,
Fluid Dynamics and Transport of Droplets and Sprays. xvii+311. Cambridge: Cambridge Univ, Pr. isbn, pp.0-521, 1999. ,
, Fluid dynamics and transport of droplets and sprays, 2010.
General circulation experiments with the primitive equations, Monthly Weather Review, vol.91, issue.3, pp.99-164, 1963. ,
Numerical solution of partial differential equations: finite difference methods, 1985. ,
Some measurements of particle velocity autocorrelation functions in a turbulent flow, Journal of Fluid Mechanics, vol.48, issue.1, pp.41-71, 1971. ,
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of Computational Physics, vol.27, issue.1, pp.1-31, 1978. ,
URL : https://hal.archives-ouvertes.fr/hal-01635155
A new class of optimal high-order strong-stabilitypreserving time discretization methods, SIAM Journal on Numerical Analysis, vol.40, issue.2, pp.469-491, 2002. ,
Preferential concentration of particles by turbulence, Physics of Fluids, vol.3, issue.5, pp.1169-1178, 1991. ,
Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence, J. Fluids Mech, vol.226, pp.1-35, 1991. ,
Report on recent researches in hydrodynamics, Brit. Ass. Rep, vol.1, pp.1-20, 1846. ,
Accurate partial difference methods I: Linear Cauchy problems, Archive for Rational Mechanics and Analysis, vol.12, issue.1, pp.392-402, 1963. ,
, On the construction and comparison of difference schemes, SIAM Journal on Numerical Analysis, vol.5, issue.3, pp.506-517, 1968.
Statistical modeling of sprays using the droplet distribution function, Physics of Fluids, vol.13, issue.3, pp.624-642, 2001. ,
On central-difference and upwind schemes, Journal of computational physics, vol.101, pp.292-306, 1991. ,
High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM journal on numerical analysis, vol.21, issue.5, pp.995-1011, 1984. ,
A sectional model for evaporation and combustion of sprays of liquid fuel, Isr. J. Technol, vol.18, pp.47-56, 1980. ,
Fluid flow in regions bounded by porous surfaces, In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol.234, pp.456-475, 1199. ,
Attenuation and dispersion of sound by particulaterelaxation processes, The Journal of the Acoustical Society of America, vol.40, issue.2, pp.317-324, 1966. ,
Galerkin finite element methods for parabolic problems, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical REFERENCES, vol.1054, 1984. ,
Restoration of the contact surface in the HLLRiemann solver, Shock waves, vol.4, issue.1, pp.25-34, 1994. ,
Ultrasonic measurements of solid propellant burning rates in nozzleless rocket motors, Journal of Propulsion and Power, vol.2, issue.3, pp.215-222, 1986. ,
A subscale test program to assess the vortex shedding driven instabilities in segmented solid rocket motors, 33 rd Joint Propulsion Conference, 1997. ,
On the product of semi-groups of operators, Proc. Am. Math. Soc, vol.10, pp.545-551, 1959. ,
Preconditioned methods for solving the incompressible and low speed compressible equations, Journal of Computational Physics, vol.72, issue.2, pp.277-298, 1987. ,
, Review of preconditioning methods for fluid dynamics, Applied Numerical Mathematics, vol.12, issue.1-3, pp.257-284, 1993.
Computation of volume and surface body moments, Pattern Recognition, vol.36, issue.11, pp.2521-2529, 2003. ,
Stability and acoustic resonance of internal flows generated by side injection, Solid Propellant Chemistry, Combustion and Motor Interior Ballistics, AIAA Progress in Astronautics and Aeronautics Series, vol.185, pp.823-836, 2000. ,
Modélisation eulerienne de l'atomisation d'un jet liquide, 1999. ,
, Comptes Rendus de l'Académie des Sciences-Series IIB-Mechanics-Physics-Astronomy, vol.327, issue.10, pp.1015-1020
Towards the ultimate conservative difference scheme III. Upstream-centered finitedifference schemes for ideal compressible flow, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, vol.23, pp.263-275, 1973. ,
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.90019-90028, 1974. ,
Flow stability in a channel with porous walls, Fluid Dynamics, vol.4, issue.5, pp.60-62, 1969. ,
A second-order Rosenbrock method applied to photochemical dispersion problems, SIAM Journal on Scientific Computing, vol.20, issue.4, pp.1456-1480, 1999. ,
A comparison of stiff ODE solvers for atmospheric chemistry problems, Atmospheric environment, vol.30, issue.1, pp.49-58, 1996. ,
Interaction des structures pariétales sur le développement instationnaire d'écoulements cisaillés en milieu confiné-Rôle de l'injection différentielle, 2001. ,
On the Anisotropic Gaussian closure for the prediction of inertial-particle laden flows, Communications in Computational Physics, vol.17, issue.1, pp.1-46, 2015. ,
Size-velocity correlations in high order moment methods for polydisperse evaporating sprays: modeling and numerical issues, Journal of Computational Physics, vol.237, pp.177-210, 2013. ,
On the Direct Numerical Simulation of moderate-Stokes-number turbulent particulate flows using Algebraic-Closure-Based and REFERENCES Kinetic-Based Moment Methods, Proceedings of the summer program, pp.355-364, 2012. ,
Slag accumulation in solid propellant rocket motors with a submerged nozzle, 2000. ,
Numerical modelling of bore propagation and run-up on sloping beaches using a MacCormack TVD scheme, Journal of hydraulic research, vol.39, issue.1, pp.41-49, 2001. ,
Vortex-shedding phenomena in solid rocket motors, J. Propulsion and Power, vol.11, issue.4, pp.626-639, 1995. ,
2D Navier-Stokes computations for solid rocket motors : rotationnal combustion and two-phase flow effects, 33rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, pp.97-3326, 1997. ,
Combustion and turbulent flow effects in 2D unsteady Navier-Stokes simulations of oscillatory solid rocket motors-First applications, 34th Aerospace Sciences Meeting and Exhibit, 1996. ,
Some HPC challenges for multi-physics extended CFD computations, The 16th IEEE International Conference on High Performance Computing and Communications, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01102182
Stability prediction for large segmented solid propellant rocket motors, AAAF: 5ème Symposium International sur la propulsion dans les Transports Spatiaux, 1996. ,
A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation, Journal of Statistical Physics, vol.66, issue.3, pp.1011-1044, 1992. ,
Upwind second-order difference schemes and applications in aerodynamic flows, AIAA Journal, vol.14, issue.9, pp.1241-1249, 1976. ,
The modified equation approach to the stability and accuracy analysis of finite-difference methods", Journal of Computational Physics, vol.14, issue.2, pp.159-179, 1974. ,
Fundamental simulation of aluminum droplet combustion, 46th AIAA Joint Propulsion Conference, vol.6677, pp.1-15, 2010. ,
Design principles for bounded higher-order convection schemes-a unified approach, Journal of Computational Physics, vol.224, issue.1, pp.182-207, 2007. ,
An experimental study of forced convective heat transfer from smooth, solid spheres, International Journal of Heat and Mass Transfer, vol.109, pp.1059-1067, 2017. ,
Combustion Theory (Combustion Science and Engineering Series), Phys. Fluids, vol.1, pp.541-545, 1958. ,
Fundamental aspects of solid propellant rockets, 1969. ,
Green Solid Propellants for Launchers, Space Propulsion conference, pp.2-06, 2016. ,
The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of Computational Physics, vol.54, issue.1, pp.115-173, 1984. ,
A semi-Lagrangian high-order method for Navier-Stokes equations, Journal of Computational Physics, vol.172, issue.2, pp.658-684, 2001. ,
The method of fractional steps, 1971. ,
Construction of explicit and implicit symmetric TVD schemes and their applications, Journal of Computational Physics, vol.68, issue.1, pp.151-179, 1987. ,
Conditional quadrature method of moments for kinetic equations, Journal of Computational Physics, vol.230, issue.22, pp.8216-8246, 2011. ,
An extended quadrature method of moments for population balance equations, Journal of Aerosol Science, vol.51, pp.1-23, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00726736
Particles in turbulent flows, 2008. ,
Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence, Physics of Fluids, vol.15, issue.10, pp.2995-3005, 2003. ,
An Eulerian approach for large eddy simulation of particle transport in turbulent flows, Journal of Turbulence, issue.10, p.4, 2009. ,
Radiation induces turbulence in particle-laden fluids, Physics of Fluids, vol.26, issue.7, p.71701, 2014. ,
On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, Journal of Computational Physics, vol.229, issue.23, pp.8918-8934, 2010. ,
Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes, Journal of Scientific Computing, vol.50, issue.1, pp.29-62, 2012. ,
On maximum-principle-satisfying high order schemes for scalar conservation laws, Journal of Computational Physics, vol.229, issue.9, pp.3091-3120, 2010. ,
Issledovaniye mirovykh prostranstv reaktivnymi priborami (Study of outer space by reaction devices), 1903. ,