.. Numerical-resolution, 181 5.6 Comparison with a silicone oil dome experiment, p.186

. [. Bibliographie, M. Audusse, B. Bristeau, J. Perthame, ]. C. Sainte-marieaca09 et al., A multilayer Saint-Venant system with mass exchanges for Shallow Water flows. Derivation and numerical validation The dam-break problem for Herschel- Bulkley viscoplastic fluids down steep flumes The dam-break problem for viscous fluids in the high-capillary-number limit, ESAIM : Math. Model. Num. Anal. J. Non-Newt. Fluid Mech. J. Fluid Mech, vol.45, issue.624, pp.169-20018, 2009.

]. C. Anc01 and . Ancey, Snow avalanches, Geomorphological Fluid Mechanics, pp.319-338, 2001.

]. C. Anc07 and . Ancey, Plasticity and geophysical flows : a review, J. Non-Newt

E. [. Acary-robert, G. Fernández-nieto, P. Narbona-reina, . J. Vigneaux-]-n, R. V. Balmforth et al., A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model A consistent thin-layer theory for Bingham plastics, J. Sci. Comput. J. Non-Newt. Fluid Mech, vol.53, issue.133, pp.608-641, 1999.

L. [. Boutounet, P. Chupin, J. Noble, and . Vila, Shallow water viscous flows for arbitrary topopgraphy, Communications in Mathematical Sciences, vol.6, issue.1, pp.29-55, 2008.
DOI : 10.4310/CMS.2008.v6.n1.a2

. J. Bcp-+-07-]-n, R. V. Balmforth, P. Craster, A. C. Perona, R. Rust et al., Viscoplastic dam breaks and the Bostwick consistometer Viscoplastic flow over an inclined surface, J. Non- Newt. Fluid Mech. J. Non-Newt. Fluid Mech, vol.142, issue.164, pp.63-78, 2006.

B. J. Balmforth, R. V. Craster, and R. Sassi, Dynamics of cooling viscoplastic domes, Journal of Fluid Mechanics, vol.499, issue.168, pp.149-182, 2004.
DOI : 10.1017/S0022112003006840

B. [. Bresch and . Desjardins, On the construction of approximate solutions for the 2D viscous shallow water model and for compressible Navier???Stokes models, Journal de Math??matiques Pures et Appliqu??es, vol.86, issue.4, pp.362-368, 2006.
DOI : 10.1016/j.matpur.2006.06.005

URL : https://hal.archives-ouvertes.fr/hal-00385847

M. [. Bercovier and . Engelman, A finite-element method for incompressible non-Newtonian flows, Journal of Computational Physics, vol.36, issue.3, pp.313-326, 1980.
DOI : 10.1016/0021-9991(80)90163-1

. Bgh-+-97-]-h, P. L. Borouchaki, F. George, P. Hecht, E. Laug et al., Delaunay mesh generation governed by metric specifications. Part I. Algorithms. Finite elements in analysis and design, pp.61-83, 1997.

I. [. Bouchut, A. Ionescu, and . Mangeney, A shallow model including static-flowing transition for viscoplastic Drucker-Prager materials. submitted, p.20, 2014.

]. E. Bin22, ]. Bingham, J. Bercovici, and . Lin, Fluidity and plasticity A gravity current model of cooling mantle plume heads with temperature-dependent buoyancy and viscosity, p.165, 1922.

]. S. Bla90 and . Blake, Viscoplastic models of lava domes, Lava flows and domes, pp.3291-3309, 1990.

J. [. Brady, . Morrisbmmr97-]-k, Y. Boukir, B. Maday, E. Metivet et al., Microstructure of strongly sheared suspensions and its impact on rheology and diffusion A highorder characteristic/finite element method for the incompressible navier-stokes equations Numerical modeling of non-newtonian viscoplastic flows : part II. Viscoplastic fluids and general tridimensional topographies, BSS14] N. Bernabeu, P. Saramito, and C. Smutek. A new shallow approximation for tridimensional non-isothermal viscoplastic lava flows. submitted, pp.103-139, 1997.

C. [. Coussot, . Anceyca09-]-s, C. Cochard, G. C. Ancey, E. Georgiou et al., Rheophysical classification of concentrated suspensions and granular pastes Experimental investigation of the spreading of viscoplastic fluids on inclined planes Cessation of Couette and Poiseuille flows of a Bingham plastic and finite stopping times, Phys. Rev. E J. Non-Newt. Fluid Mech. J. Non-Newt. Fluid Mech, vol.59, issue.1293, pp.4445-445773, 1999.

]. B. Cha90, . W. Chapmancisl95-]-a, J. H. Chow, S. W. Iwayima, D. T. Sinton et al., Shear-induced migration phenomena in concentrated suspensions Particle migration of non-Brownian, concentrated suspensions in a truncated cone-and-plate Conduction of heat in solids Numerical simulation of lava flows based on depth-averaged equations, In Society of Rheology Meeting Geophys. Res. Lett, vol.32, issue.20, pp.102-174, 1946.

C. , A. W. Chow, S. W. Sinton, J. H. Iwamiya, T. S. Stephenscspn99-]-k et al., Shear-induced particle migration in Couette and parallel-plate viscometers : NMR imaging and stress measurements Cooling and crystallization of lava in open channels, and the transition of p¯ ahoehoe lava to'a'¯ a Global linear convergence of an augmented lagrangian algorithm to solve convex quadratic optimization problems, Magmatic fragmentation. Encyclopedia of Volcanology, pp.535-559, 1994.

M. L. Damiani, G. Groppelli, G. Norini, E. Bertino, A. Gigliuto et al., A lava flow simulation model for the development of volcanic hazard maps for Mount Etna (Italy), Computers & Geosciences, vol.32, issue.4, pp.512-526, 2006.
DOI : 10.1016/j.cageo.2005.08.011

R. [. Drever and . Johnston, Synopsis, Transactions of the Royal Society of Edinburgh, vol.12, issue.03, pp.459-499, 1958.
DOI : 10.1080/08120095409414129

R. [. Drever and . Johnston, Picritic minor intrusions. Ultramafic and related rocks, pp.71-82, 1967.

J. [. Duvaut, J. L. Duvaut, . D. Lions-]-d, S. Santos, M. F. Frey et al., Inequalities in mechanics and physics A dynamical model of lava flows cooling by radiation Numerical approximations for flow of viscoplastic fluids in a lid-driven cavity, Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leurs lits. C. R. Acad. Sci, pp.93-110, 1972.

]. J. Fay94, F. Fay-fortin, and . Brezzi, Introduction to fluid mechanics Mixed and hybrid finite element methods, pp.28-53, 1991.

O. Féménias, H. Diot, T. Berza, A. Gauffriau, and D. Demaiffe, Asymmetrical to symmetrical magnetic fabric of dikes : Paleo-flow orientations and paleo-stresses recorded on feeder-bodies from the Motru Dike Swarm (Romania), J. Struct. Geol, issue.8, pp.261401-1418, 2004.

R. [. Fortin and . Glowinski, Augmented Lagrangian methods : applications to the numerical solution of boundary-value problems, pp.44-51, 1983.

R. [. Fink and . Griffiths, Morphology, eruption rates, and rheology of lava domes: Insights from laboratory models, Journal of Geophysical Research: Solid Earth, vol.26, issue.E4, pp.527-545, 1969.
DOI : 10.1029/97JB02838

A. A. Fang, J. F. Mammoli, M. S. Brady, L. A. Ingber, A. L. Mondy et al., Flow-aligned tensor models for suspension flows, [FN05] I. A. Frigaard and C. Nouar. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Non-Newt, pp.137-166, 2002.
DOI : 10.1016/S0301-9322(01)00055-6

S. [. Fourestey, . J. Pipernofptz00-]-x, N. Fan, R. Phan-thien, . Zhenggar12-]-f et al., A second-order time-accurate ALE Lagrange???Galerkin method applied to wind engineering and control of bridge profiles, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.39-41, pp.4117-4137, 1968.
DOI : 10.1016/j.cma.2003.12.060

URL : https://hal.archives-ouvertes.fr/hal-00607735

]. R. Glo84, . Glowinski-]-r, J. Glowinski, R. Lions, and . Trémolières, Numerical methods for nonlinear variational problems, Analyse numérique des inéquations variationnelles. Méthodes mathématiques de l'informatique, pp.46-63, 1976.

P. [. Glowinski and . Tallec, Augmented Lagrangian and operator splitting methods in nonlinear mechanics Effects of demixing on suspension rheometry, SIAM Rheol. Acta, vol.17, issue.18, pp.52139-150, 1987.

[. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water ; numerical validation. Discrete and continuous dynamical systems -serie B, pp.89-102, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00691701

P. [. Girault and . Raviart, Finite element methods for Navier-Stokes equations : theory and algorithms, p.58, 1986.
DOI : 10.1007/978-3-642-61623-5

]. R. Gri00 and . Griffiths, The dynamics of lava flows, Ann. Rev. Fluid Mech, vol.32, pp.477-518, 2000.

A. [. Glowinski, . H. Wachs-]-w, R. Herschel, and . Bulkley, On the numerical simulation of viscoplastic fluid flow Numerical Methods for Non-Newtonian Fluids, volume 16 of Handbook of Numerical Analysis Measurement of consistency as applied to rubber-benzene solutions, Proceedings of the American Society for Testing and Material, pp.483-717, 1926.

K. [. Hoover, M. Cashman, . R. Mangahes69-]-m, M. Huang, . Garcia-]-m et al., The yield strength of subliquidus basalts?experimental results BAMG : bidimensional anisotropic mesh generator Multiplier and gradient methods A Herschel-Bulkley model for mud flow down a slope VTFS project : development of the lava flow simulation code LavaSIM with a model for three-dimensional convection, spreading, and solidification The effects of hydraulic resistance on dam-break and other shallow inertial flows, Hohenemser and W. Prager. Über die ansätze der mechanik isotroper kontinua, pp.1-18, 1932.

S. [. Harris and . Rowland, FLOWGO: a kinematic thermo-rheological model for lava flowing in a channel, Bulletin of Volcanology, vol.63, issue.1, pp.20-44, 2001.
DOI : 10.1007/s004450000120

]. G. Hul74 and . Hulme, The interpretation of lava flow morphology, Geophys. J. Int, vol.39, issue.14, pp.361-383, 1974.

]. H. Hup82 and . Huppert, The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface, Ion13] I. R. Ionescu. Viscoplastic shallow flow equations with topography, pp.43-58, 1982.

J. Non-newt, ]. G. Fluid-mechjou13, and . Jouvet, A multilayer model for ice flow. preprint, 2013 Mechanics of growth of some laccolithic intrusions in the Henry mountains, Utah, I : field observations , Gilbert's model, physical properties and flow of the magma, Tectonophysics, vol.193, issue.183, pp.116-128, 1973.

]. G. Krishnan, S. Beimfohr, D. T. Leightonkd59-]-i, T. J. Krieger, . M. Doughertyklk08-]-j et al., Shear-induced radial segregation in bidisperse suspensions A mechanism for non-Newtonian flow in suspensions of rigid spheres Numerical simulations of particle migration in suspension flows : frame-invariant formulation of curvature-induced migration Flow differentiation in igneous dikes and sills : profiles of velocity and phenocryst concentration, Nagoya Math. J. J. Fluid. Mech. Trans. Soc. Rheol. J. Non-Newt. Fluid Mech. America Bulletin America Bulletin, vol.128, issue.834, pp.1-14, 1959.

]. A. Kri72, . Krieger, ]. D. Colloidla87, A. Leighton, ]. Acrivos et al., The shear-induced migration of particles in concentrated suspensions Numerical modeling of mudflows Drop impact of yield-stress fluids, Interface Sci J. Fluid Mech. J. Hydr. Engrg. J. Fluid Mech, vol.3, issue.632, pp.111-36415, 1972.

C. [. Liu, . F. Meilm90-]-k, C. C. Liu, and . Mei, Slow spreading of a sheet of Bingham fluid on an inclined plane, Journal of Fluid Mechanics, vol.7, issue.-1, pp.505-529, 1989.
DOI : 10.1063/1.1706737

]. F. Mar07, M. Marche, J. Manga, K. V. Castro, M. Cashman et al., Ecole Nationale des Ponts et Chaussées Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects Rheology of bubble-bearing magmas, Christelle Lusso. Modélisation numérique des écoulements gravitaires viscoplastiques avec transition fluide, pp.1949-63, 1998.

A. [. Matson, . P. Hoggmm65-]-p, V. P. Mossolov, and . Miasnikov, Two-dimensional dam break flows of Herschel-Bulkley fluids : The approach to the arrested state Variational methods in the theory of the fluidity of a viscous plastic medium On stagnant flow regions of a viscous-plastic medium in pipes, J. Non-Newt. Fluid Mech. J. Mech. Appl. Math. J. Mech. Appl. Math, vol.142, issue.304, pp.79-94, 1965.

A. Rev, ]. Manga, and H. A. Stone, Interactions between bubbles in magmas and lavas : effects of bubble deformation, Earth Planet. Sci. J. Volcanol. Geotherm. Res, vol.12, issue.13, pp.337-357, 1984.

]. L. Mur14, . C. Muravleva-]-c, M. Mei, and . Yuhi, Uzawa-like methods for numerical modeling of unsteady viscoplastic Bingham medium flows Slow flow of a Bingham fluid in a shallow channel of finite width, Appl. Num. Math. J. Fluid Mech, vol.59, issue.146, pp.74-01135, 2001.

T. [. Mitsoulis, . D. Zisis-]-k, M. A. Nikitin, K. M. Olshanskii, Y. V. Terekhov et al., Flow of Bingham plastics in a lid-driven square cavity, Mathematical Proceedings of the Cambridge Philosophical Society, pp.173-180, 0200.
DOI : 10.1016/S0377-0257(01)00147-1

. J. Pab-+-92-]-r, R. C. Phillips, R. A. Armstrong, A. L. Brown, J. R. Graham et al., A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration Flows of materials with yield, Phys. Fluids A J. Rheol, vol.4, issue.1275, pp.30-41, 1987.

]. R. Per05, ]. Peronapia96, and . Piau, Bostwick degree and rheological properties : an up-todate viewpoint Flow of a yield stress fluid in a long domain. Application to flow on an inclined plane, Appl. Rheol. J. Rheol, vol.15, issue.37, pp.218-229, 1988.

P. [. Park, -. Pinkerton, G. J. Nortonpow69-]-m, and . Powell, Oscillatory pipe flows of a yield-stress fluid Rheological properties of basaltic lavas at sub-liquidus temperatures : laboratory and field measurements on lavas from mount Etna A method for nonlinear constraints in minimization problems, J. Fluid Mech. J. Volcanol. Geotherm. Res, vol.658, issue.684, pp.211-228, 1969.

]. W. Pra54, . Pragerps78-]-h, R. S. Pinkerton, . Sparksps92-]-h, R. J. Pinkerton et al., Academic Press Field measurements of the rheology of lava Methods of determining the rheological properties of magmas at sub-liquidus temperatures Adaptive remeshing for compressible flow computations Estimations d'erreur pour un fluide viscoplastique par éléments finis P k et maillages adaptés The viscosity of suspensions of rigid spheres, Nature J. Volcanol. Geotherm. Res. J. Comp. Phys. C. R. Acad. Sci, serie I, Math, vol.276, issue.3317, pp.17383-385, 1954.

. App, G. Phys, A. Roult, B. Peltier, T. Taisne et al., A new comprehensive classification of the Piton de la Fournaise activity spanning the 1985?2010 period Search and analysis of short-term precursors from a broad-band seismological station An adaptive finite element method for Bingham fluid flows around a cylinder The latest release of the lava flows simulation model SCIARA : first application to mt Etna (Italy) and solution of the anisotropic flow direction problem on an ideal surface A new constitutive equation for elastoviscoplastic fluid flows, J. Volcanol. Geotherm. Res. Comput. Appl. Meth. Mech. Engrg. Procedia Computer Science J. Non Newtonian Fluid Mech. J. Non Newtonian Fluid Mech, vol.3, issue.158, pp.267-1678, 1952.

]. P. Sar13a, ]. Saramitosb01, J. F. Sierou, ]. A. Bradysga14, G. C. Syrakos et al., Méthodes numériques en fluides complexes : théorie et algorithmes Accelerated Stokesian dynamics simulations Performance of the finite volume method in solving regularised Bingham flows : Inertia effects in the lid-driven cavity flow Rheology of basalt in the melting range The picritic sills of northwest Trotternish Isle of Skye, Sim67] T. Simkin. Flow differentiation in the picritic sills of north skye. Ultramafic and related rocksSIM + 98] S. R. Subia, M. S. Ingber, L. A. Mondy, S. A. Altobelli, and A. L, pp.181-59115, 1966.

]. P. Grahamsr01, N. Saramito, and . Roquet, An adaptive finite element method for viscoplastic fluid flows in pipes Numerical modeling of shallow non-Newtonian flows : Part I. the 1D horizontal dam break problem revisited, J. Fluid. Mech. Comput. Meth. Applied Mech. Engng Int. J. Numer. Anal. Model., Series B, vol.373, issue.43, pp.193-219, 1998.

T. [. Shaw, D. L. Wright, R. Peck, . J. Okamurasyk82-]-f, D. A. Spera et al., The viscosity of basaltic magma ; an analysis of field measurements in Makaopuhi lava lake, Hawaii Thermal boundary layer convection in silicic magma chambers : Effects of temperaturedependent rheology and implications for thermogravitational chemical fractionation, Am. J. Sci. J. Geophys. Res. Solid Earth, vol.266, issue.87B10, pp.225-264, 1968.

M. [. Tarquini, A. L. Favalli, M. S. Graham, S. R. Ingber, L. A. Subia et al., Mapping and DOWNFLOW simulation of recent lava flow fields at Mount Etna, Journal of Volcanology and Geothermal Research, vol.204, issue.1-4, pp.27-39307, 1998.
DOI : 10.1016/j.jvolgeores.2011.05.001

A. Vicari, H. Alexis, C. Del-negro, M. Coltelli, M. Marsella et al., Modeling of the 2001 lava flow at Etna volcano by a Cellular Automata approach, [VBL03] D. Vola, L. Boscardin, and J. C. Latché. Laminar unsteady flows of Bingham fluids : a numerical strategy and some benchmark results, pp.1465-1471, 1990.
DOI : 10.1016/j.envsoft.2006.10.005

N. Villeneuve, D. R. Neuville, P. Boivin, P. Bachélery, and P. Richet, Magma crystallization and viscosity: A study of molten basalts from the Piton de la Fournaise volcano (La R??union island), Chemical Geology, vol.256, issue.3-4, pp.242-251, 2008.
DOI : 10.1016/j.chemgeo.2008.06.039

]. T. Vu10, G. Vu, A. Vinay, J. Wachs, C. R. Agassant et al., Numerical simulation of nonisothermal viscoplastic waxy crude oil flows A new interpretation of viscosity and yield stress in dense slurries : coal and other irregular particles Slow spreading of fluid mud over a conical surface, Rhéologie des suspensions non newtoniennesZha10] J. Zhang. An augmented Lagrangian approach to Bingham fluid flows in a lid-driven square cavity with piecewise linear equal-order finite elements. Comp. Meths. Appl. Mech, pp.120144-16275, 1985.

P. [. Zhou, F. T. Uhlherr, and . Luo, Yield stress and maximum packing fraction of concentrated suspensions, Rheologica Acta, vol.24, issue.6, pp.544-561, 1995.
DOI : 10.1007/BF00712315