Multilayer Saint-Venant Equations over movable beds. Accpeted for publication in Discrete Contin, Dyn. Syst. Ser. B, 2010. ,
DOI : 10.3934/dcdsb.2011.15.917
URL : https://hal.archives-ouvertes.fr/inria-00551486
Approximation of the hydrostatic navier-stokes system for density stratified flows by a multilayer model. kinetic interpretation and numerical validation, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00654642
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation, ESAIM: Mathematical Modelling and Numerical Analysis, vol.45, issue.1, p.2, 2010. ,
DOI : 10.1051/m2an/2010036
URL : https://hal.archives-ouvertes.fr/hal-00355730
A Multilayer Saint-Venant System with variable density for Shallow Water flows, J. Sci. Comp, 2010. ,
Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems, Discrete Contin. Dyn. Syst. Ser. B, vol.10, issue.4, pp.733-759, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00232824
Sainte-Marie, and I. Vignon-Clementel. A poroelastic model valid in large strains with applications to perfusion in cardiac modeling, Comp. Mech, vol.46, pp.2010-91 ,
Numerical simulations of a non-hydrostatic shallow water model, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00654634
A kinetic interpretation of the section-averaged Saint-Venant system for natural river hydraulics, International Journal for Numerical Methods in Fluids, vol.37, issue.2, 2010. ,
DOI : 10.1002/fld.2401
URL : https://hal.archives-ouvertes.fr/inria-00551487
Solutions to muscle fiber equations and their long time behaviour, Nonlinear Analysis: Real World Applications, vol.7, issue.4, pp.535-558, 2006. ,
DOI : 10.1016/j.nonrwa.2005.03.021
Vertically averaged models for the free surface Euler system. Derivation and kinetic interpretation. Accepted for publication in M3AS, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00551484
Modeling and estimation of the cardiac electromechanical activity, Computers & Structures, vol.84, issue.28, pp.1743-1759, 2006. ,
DOI : 10.1016/j.compstruc.2006.05.003
URL : https://hal.archives-ouvertes.fr/hal-00839206
Cardiac function estimation from MRI using a heart model and data assimilation: Advances and difficulties, Medical Image Analysis, vol.10, issue.4, pp.642-656, 2006. ,
DOI : 10.1016/j.media.2006.04.002
URL : https://hal.archives-ouvertes.fr/inria-00614997
Transport of pollutant in shallow water flows : A two time steps kinetic method, ESAIM: M2AN, pp.389-416, 2003. ,
A well-balanced positivity preserving ???second-order??? scheme for shallow water flows on unstructured meshes, Journal of Computational Physics, vol.206, issue.1, pp.311-333, 2005. ,
DOI : 10.1016/j.jcp.2004.12.016
URL : https://hal.archives-ouvertes.fr/inria-00070738
Back and forth nudging algorithm for data assimilation problems, C. R. Acad. Sci. Paris, Ser. I, vol.340, pp.873-878, 2005. ,
Finite-Volume Solvers for a Multilayer Saint-Venant System, International Journal of Applied Mathematics and Computer Science, vol.17, issue.3, pp.311-319, 2007. ,
DOI : 10.2478/v10006-007-0025-0
A nudging-based data assimilation method: the Back and Forth Nudging (BFN) algorithm, Nonlinear Processes in Geophysics, vol.15, issue.2, pp.305-319, 2008. ,
DOI : 10.5194/npg-15-305-2008
URL : https://hal.archives-ouvertes.fr/inria-00327422
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows, SIAM Journal on Scientific Computing, vol.25, issue.6 ,
DOI : 10.1137/S1064827503431090
Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model, International Journal for Numerical Methods in Fluids, vol.12, issue.3, pp.331-350, 2008. ,
DOI : 10.1002/fld.1534
Kinetic schemes for Saint-Venant equations with source terms on unstructured grids, 2000. ,
URL : https://hal.archives-ouvertes.fr/inria-00072657
Changes in regional myocardial volume during the cardiac cycle: implications for transmural blood flow and cardiac structure, AJP: Heart and Circulatory Physiology, vol.295, issue.2, pp.610-618, 2008. ,
DOI : 10.1152/ajpheart.00107.2008
Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable, Mathematics of Computation, vol.36, issue.153, pp.53-64, 1981. ,
DOI : 10.1090/S0025-5718-1981-0595041-4
Finite element formulations for hyperelastic transversely isotropic biphasic soft tissues, Computer Methods in Applied Mechanics and Engineering, vol.151, issue.3-4, pp.3-4513, 1998. ,
DOI : 10.1016/S0045-7825(97)82246-3
A multilayer Saint-Venant System : Derivation and Numerical Validation, Discrete Contin. Dyn. Syst. Ser. B, vol.5, issue.2, pp.189-214, 2005. ,
Nonlinear shallow water theories for coastal waves, pp.315-337, 2004. ,
A relaxation method for two-phase flow models with hydrodynamic closure law, Numer. Math, vol.99, issue.3, pp.411-440, 2005. ,
Fully nonlinear weakly dispersive modelling of wave transformation, breaking and runup, 2010. ,
Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Royal Soc. London Series A, vol.272, pp.47-78, 1972. ,
Boundary Conditions for the Shallow Water Equations solved by Kinetic Schemes, 2001. ,
URL : https://hal.archives-ouvertes.fr/inria-00072305
A biomechanical model of muscle contraction, In Lectures Notes in Computer ScienceJ. Niessen, M.A. Viergever, vol.2208, 2001. ,
A biomechanical model of muscle contraction, In Lectures Notes in Computer ScienceJ. Niessen & M.A. Viergever, vol.2208, 2001. ,
Boussinesq Equations and Other Systems for Small-Amplitude Long Waves in Nonlinear Dispersive Media. I: Derivation and Linear Theory, Journal of Nonlinear Science, vol.12, issue.4, pp.283-318, 2002. ,
DOI : 10.1007/s00332-002-0466-4
Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory, Nonlinearity, vol.17, issue.3, pp.925-952, 2004. ,
DOI : 10.1088/0951-7715/17/3/010
Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes, Comput. Meth. Appl. Mech. Eng, vol.155, issue.12, pp.49-72, 1998. ,
Barré de Saint-Venant. Théorie du mouvement non permanent des eaux avec applications aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Acad. Sci. Paris, vol.73, pp.147-154, 1871. ,
Un sch??ma simple pour les ??quations de Saint-Venant, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.326, issue.3, pp.386-390, 1998. ,
DOI : 10.1016/S0764-4442(97)83000-5
A sequel to a rough Godunov scheme: application to real gases, Computers & Fluids, vol.29, issue.7, pp.813-847, 2000. ,
DOI : 10.1016/S0045-7930(99)00026-2
Theory of propagation of elastic waves in a fluid-saturated porous solid. II higher frequency range, J. Acoust. Soc. Am, vol.28, 1956. ,
Theory of finite deformations of pourous solids, Indiana Univ. Math. J, vol.21, pp.597-620, 1972. ,
A central scheme for shallow water flows along channels with irregular geometry, ESAIM: M2AN, pp.333-351, 2009. ,
DOI : 10.1051/m2an:2008050
Cardiovascular Physiology, Annual Review of Physiology, vol.43, issue.1, 2001. ,
DOI : 10.1146/annurev.ph.43.030181.002041
A Positive Preserving High Order VFRoe Scheme for Shallow Water Equations: A Class of Relaxation Schemes, SIAM Journal on Scientific Computing, vol.30, issue.5, pp.2587-2612, 2008. ,
DOI : 10.1137/070686147
URL : https://hal.archives-ouvertes.fr/hal-00370486
A new model of Saint Venant and Savage???Hutter type for gravity driven shallow water flows, Comptes Rendus Mathematique, vol.336, issue.6, pp.531-536, 2003. ,
DOI : 10.1016/S1631-073X(03)00117-1
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment, M2AN Math. Model. Numer. Anal, vol.42, pp.683-698, 2008. ,
On the mechanical energy and effective stress in saturated and unsaturated porous continua, International Journal of Solids and Structures, vol.43, issue.6, pp.1764-1786, 2006. ,
Théorie de l'intumescence liquide appelée onde solitaire ou de translation se propageant dans un canal rectangulaire, C. R. Acad. Sci. Paris, vol.72, pp.755-759, 1871. ,
Théorie générale des mouvements qui sont propagés dans un canal rectangulaire horizontal, C. R. Acad. Sci. Paris, vol.73, pp.256-260, 1871. ,
Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl, vol.17, pp.55-108 ,
Construction of bgk models with a family of kinetic entropies for a given system of conservation laws, J. Stat. Phys, vol.95, pp.113-170, 1999. ,
Entropy satisfying flux vector splittings and kinetic bgk models, Numer. Math, vol.94, pp.623-672, 2003. ,
An introduction to finite volume methods for hyperbolic conservation laws, ESAIM Proc, vol.15, pp.107-127, 2004. ,
Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Birkhäuser, 2004. ,
A reduced stability condition for nonlinear relaxation to conservation laws, J. Hyperbolic Differ. Equ, vol.1, issue.1, pp.149-170, 2004. ,
Coupling Biot and Navier?Stokes equations for modelling fluid?poroelastic media interaction ,
Homogeneous hydrostatic flows with convex velocity profiles, Nonlinearity, vol.12, issue.3, pp.495-512, 1999. ,
Upwind methods for hyperbolic conservation laws with source terms, Computers & Fluids, vol.23, issue.8, pp.1049-1071, 1994. ,
DOI : 10.1016/0045-7930(94)90004-3
Gravity driven shallow water models for arbitrary topography, Communications in Mathematical Sciences, vol.2, issue.3, pp.359-389, 2004. ,
DOI : 10.4310/CMS.2004.v2.n3.a2
A robust well-balanced scheme for multi-layer shallow water equations, Discrete Contin. Dyn. Syst. Ser. B, vol.13, pp.739-758, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00538338
Contribution à l'étude des ondes de Favre Laboratoire National d'Hydraulique A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part I: Model development and analysis, Internat. J. Numer. Methods Fluids, issue.11, pp.511217-1253, 1968. ,
A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: Boundary conditions and validation, Int. J. Numer. Meth. Fluids, issue.9, pp.531423-1455, 2006. ,
Multiphysics model for blood flow and drug transport with application to patient-specific coronary artery flow, Computational Mechanics, vol.196, issue.29, pp.161-177, 2008. ,
DOI : 10.1007/s00466-008-0321-z
A Physiologically-Based Model for the Active Cardiac Muscle Contraction, In Lectures Notes in Computer Science Eds T. Katila, I.E. Magnin, P. Clarysse, J. Montagnat, J. Nenonen, vol.2230, 2001. ,
DOI : 10.1007/3-540-45572-8_18
Validation of a biomechanical heart model using animal data with acute myocardial infarction, CI2BM09 -MICCAI Workshop on Cardiovascular Interventional Imaging and Biophysical Modelling, 2009. ,
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods, Computers & Fluids, vol.37, issue.3, pp.299-316, 2008. ,
DOI : 10.1016/j.compfluid.2007.07.017
Some new Godunov and relaxation methods for two-phase flow problems, Godunov methods, pp.179-188, 1999. ,
Numerical simulation of two-layer shallow water flows through channels with irregular geometry Hyperbolic conservation laws with stiff relaxation terms and entropy, J. Comput. Phys. Comm. Pure Appl. Math, vol.195, issue.16, pp.202-235, 1994. ,
Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green???Naghdi Model, Journal of Scientific Computing, vol.37, issue.3, 2010. ,
DOI : 10.1007/s10915-010-9395-9
URL : https://hal.archives-ouvertes.fr/hal-00482561
ENERGY-PRESERVING MUSCLE TISSUE MODEL: FORMULATION AND COMPATIBLE DISCRETIZATIONS, International Journal for Multiscale Computational Engineering, vol.10, issue.2, 2011. ,
DOI : 10.1615/IntJMultCompEng.2011002360
URL : https://hal.archives-ouvertes.fr/hal-00678772
-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.1, pp.107-127, 2001. ,
DOI : 10.1051/m2an:2001108
URL : https://hal.archives-ouvertes.fr/hal-00908624
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.513-554, 2002. ,
DOI : 10.1051/cocv:2002050
Mechanics of porous continua, 1995. ,
Modelling heart tissue using a composite muscle model with blood perfusion, Computational Fluid and Solid Mechanics , 2nd MIT Conference, pp.1642-1646, 2003. ,
DOI : 10.1016/B978-008044046-0.50400-0
An entropy-correction free solver for non homogeneous shallow water equations, ESAIM: M2AN, pp.363-390, 2003. ,
A family of stable numerical solvers for the shallow water equations with source terms, Comput. Meth. Appl. Math. Eng, vol.192, pp.203-225, 2003. ,
Numerical simulation of wind-induced entrainment in a stably stratified water basin, Journal of Hydraulic Research, vol.61, issue.8, pp.21-41, 1997. ,
DOI : 10.1080/00221689709498642
ASYMPTOTIC DERIVATION OF THE SECTION-AVERAGED SHALLOW WATER EQUATIONS FOR NATURAL RIVER HYDRAULICS, Mathematical Models and Methods in Applied Sciences, vol.19, issue.03, pp.387-417, 2009. ,
DOI : 10.1142/S0218202509003474
URL : https://hal.archives-ouvertes.fr/hal-00275460
An accurate and efficient semi-implicit method for section averaged free surface flow modelling, 2007. ,
Sigma transformation and ALE formulation for three-dimensional free surface flows, International Journal for Numerical Methods in Fluids, vol.61, issue.6, pp.357-386, 2009. ,
DOI : 10.1029/2004JC002328
URL : https://hal.archives-ouvertes.fr/inria-00541170
Wave propagation over uneven bottoms, Advanced Series on Ocean Engineering -World Scientific, 1997. ,
Finite volume methods, VII, Handb. Numer. Anal., VII, pp.713-1020, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00346077
A well-balanced Runge-Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying, International Journal for Numerical Methods in Fluids, vol.107, issue.2, pp.1-25, 2008. ,
DOI : 10.1002/fld.1674
URL : https://hal.archives-ouvertes.fr/hal-00153788
Reducing numerical diffusion in interfacial gravity wave simulations, International Journal for Numerical Methods in Fluids, vol.32, issue.3, pp.301-329251, 2003. ,
DOI : 10.1002/fld.993
A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography, ESAIM: Mathematical Modelling and Numerical Analysis, vol.38, issue.2, pp.211-234, 2004. ,
DOI : 10.1051/m2an:2004010
Drug transport in artery walls: A sequential porohyperelastic-transport approach, Computer Methods in Biomechanics and Biomedical Engineering, vol.4, issue.3, pp.263-276, 2009. ,
DOI : 10.1115/1.2895529
Biomechanics: Mechanical Properties of Living Tissues, 1993. ,
Microvascular pressure distribution in skeletal muscle and the effect of vasodilation, Am J Physiol, vol.228, issue.3, pp.791-796, 1975. ,
Heterogeneities in regional volumes of distribution and flows in rabbit heart, Am J Physiol Heart Circ Physiol, vol.258, issue.4, pp.1012-1024, 1990. ,
Cardiac contraction affects deep myocardial vessels predominantly, Am J Physiol Heart Circ Physiol, issue.5, pp.261-1417, 1991. ,
Registration and interpretation of normal phasic inflow into a left coronary artery by an improved differential manometric method, Am J Physiol, vol.130, pp.114-125, 1940. ,
Some approximate Godunov schemes to compute shallow-water equations with topography, Computers & Fluids, vol.32, issue.4, pp.479-513, 2003. ,
DOI : 10.1016/S0045-7930(02)00011-7
A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996. ,
DOI : 10.1137/0733001
Conservative upwind difference schemes for open channel flows?theory and applications Relaxing the boussinesq approximation in ocean circulation models, Computers & Mathematics with Applications Journal of Atmospheric and Oceanic Technology, vol.50, issue.1211, pp.57-72, 2001. ,
A finite volume solver for 1D shallow-water equations applied to an actual river, International Journal for Numerical Methods in Fluids, vol.148, issue.1, pp.1-19, 2002. ,
DOI : 10.1002/fld.201
A derivation of equations for wave propagation in water of variable depth, Journal of Fluid Mechanics, vol.338, issue.02, pp.237-246, 1976. ,
DOI : 10.1017/S0022112076002425
Cardiac Perfusion and Pumping Engineering, World Scientific, 2007. ,
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms, Mat. Sb. Comput. Math. Appl, vol.39, issue.89, pp.47271-306135, 1959. ,
A well-balanced scheme using nonconservative products designed for hyperbolic systems of conservation laws with source terms, Math. Mod. Meth. Appl. Sci, vol.11, issue.2, pp.339-365, 2001. ,
Derivation of Viscous Saint-Venant System for Laminar Shallow Water; Numerical Validation, Discrete Contin. Dyn. Syst. Ser. B, vol.1, issue.1, pp.89-102, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-00691701
Numerical approximations of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996. ,
DOI : 10.1007/978-1-4612-0713-9
On the derivation of homogeneous hydrostatic equations, ESAIM: M2AN, pp.965-970, 1999. ,
Validation d'un schéma volumes finis pour les équations de Saint-Venant bidimensionnelles (in french), 1998. ,
Porous medium finite element model of the beating left ventricle, Am J Physiol Heart Circ Physiol, vol.262, issue.4, pp.1256-1267, 1992. ,
Gas-kinetic derivation of navier-stokes-like traffic equations, Phys. Rev. E, vol.53, pp.2366-2381, 1996. ,
Hydrodynamics of Free Surface Flows: Modelling with the finite element method, 2007. ,
The heat of shortening and the dynamic constants in muscle, Proc. Roy. Soc. London (B), vol.126, pp.136-195, 1938. ,
Modeling basin-scale internal waves in a stratified lake, Limnology and Oceanography, vol.45, issue.7, pp.1603-1620, 2000. ,
DOI : 10.4319/lo.2000.45.7.1603
The dynamics of avalanches of granular materials from initiation to runout, II. Experiments. Acta Mech, vol.109, pp.1-4127, 1995. ,
On upstream differencing and godunov-type schemes for hyperbolic conservation laws, SIAM Review, vol.25, issue.1, pp.35-61, 1983. ,
Computational electromechanics of the heart, Computational Biology of the Heart, pp.345-407, 1997. ,
Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.192, issue.Pt 2, pp.3445-3475, 2009. ,
DOI : 10.1016/0021-9290(87)90279-X
Wind Effects on the Water in a Narrow Two-Layered Lake, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.259, issue.1102, pp.391-430, 1966. ,
DOI : 10.1098/rsta.1966.0021
Continuum biomechanics of soft tissues, Proc. R. Soc. Lond. A, pp.3-46, 2002. ,
Muscle structure and theories of contraction, Progress in Biophysics and Biological Chemistry, pp.255-318, 1957. ,
Finite deformation theory of hierarchically arranged porous solids: I. balance of mass and momentum, Int. J. Engng Sci, vol.33, issue.13, pp.1861-1871, 1991. ,
Finite deformation theory of hierarchically arranged porous solids: Ii. constitutive behaviour, Int. J. Engng Sci, vol.33, issue.13, pp.1861-1871, 1991. ,
Improved regional myocardial perfusion measurement by means of an imaging cryomicrotome, 4th European Conference of the International Federation for Medical and Biological Engineering, pp.771-774, 2009. ,
DOI : 10.1007/978-3-540-89208-3_185
Physical Processes in Lakes and Oceans, 1998. ,
Physical Limnology, Adv. Applied Mech, vol.27, pp.303-475, 1990. ,
DOI : 10.1016/S0065-2156(08)70199-6
A non-hydrostatic model for free surface flows, Dissertation, JAP97b] F. Jülicher, A. Ajdari, and J. Prost. Modeling molecular motors, 1997. ,
A steady-state capturing method for hyperbolic systems with geometrical source terms, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.4, pp.631-645, 2001. ,
DOI : 10.1051/m2an:2001130
The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications on Pure and Applied Mathematics, vol.54, issue.3, pp.235-276, 1995. ,
DOI : 10.1002/cpa.3160480303
Multiphysics simulation of blood flow and LDL transport in a porohyperelastic arterial wall model, Journal of biomechanical engineering, vol.129, p.374, 2007. ,
Inverse finite element characterization of soft tissues with aspiration, 2001. ,
Central-Upwind Schemes for the Saint-Venant System, ESAIM: M2AN, pp.397-425, 2002. ,
DOI : 10.1051/m2an:2002019
A hemodynamic analysis of coronary capillary blood flow based on anatomic and distensibility data, Am J Physiol Heart Circ Physiol, vol.277, issue.6, pp.2158-2166, 1999. ,
Relaxation Models and Finite Element Schemes for the Shallow Water Equations, pp.621-631, 2003. ,
DOI : 10.1007/978-3-642-55711-8_58
Mixed-layer deepening in lakes after wind set-up, J. Hydraul. Div. ASCE, vol.111, pp.334-354, 1985. ,
New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection???Diffusion Equations, Journal of Computational Physics, vol.160, issue.1, pp.214-282, 2000. ,
DOI : 10.1006/jcph.2000.6459
Derivation of asymptotic two-dimensional timedependent equations for surface water wave propagation, Physics of Fluids, vol.21, issue.1, 2009. ,
Balancing Source Terms and Flux Gradients in High-Resolution Godunov Methods: The Quasi-Steady Wave-Propagation Algorithm, Journal of Computational Physics, vol.146, issue.1, pp.346-365, 1998. ,
DOI : 10.1006/jcph.1998.6058
Finite Volume Methods for Hyperbolic Problems, 2002. ,
Incompressible models, Mathematical Topics in Fluid Mechanics, vol.1, 1996. ,
A numerical scheme for the Green???Naghdi model, Journal of Computational Physics, vol.229, issue.6, pp.2034-2045, 2010. ,
DOI : 10.1016/j.jcp.2009.11.021
A Class of Approximate Riemann Solvers and Their Relation to Relaxation Schemes, Journal of Computational Physics, vol.172, issue.2, pp.572-591, 2001. ,
DOI : 10.1006/jcph.2001.6838
URL : https://hal.archives-ouvertes.fr/hal-01342280
Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates, Communications on Pure and Applied Mathematics, vol.4, issue.6, pp.599-638, 1996. ,
DOI : 10.1002/(SICI)1097-0312(199606)49:6<599::AID-CPA2>3.0.CO;2-5
A kinetic formulation of scalar multidimensional conservation laws, J. AMS, vol.7, pp.169-191, 1994. ,
Kinetic formulation of the isentropic gas dynamics and p-systems, Commun. Math. Physics, vol.163, pp.415-431, 1994. ,
Handbook of Numerical Analysis chapter Numerical Methods for Nonlinear Three-Dimensional Elasticity, pp.465-622, 1994. ,
A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus, J. Biomech. Eng, vol.120, issue.4, pp.504-517, 1998. ,
Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, European Journal of Mechanics - B/Fluids, vol.26, issue.1, pp.49-63, 2007. ,
DOI : 10.1016/j.euromechflu.2006.04.007
Comparisons of some steady state Saint-Venant solvers for some test problems with analytic solutions, 1995. ,
Steady open channel test problems with analytic solutions, 1995. ,
On Conservation Equations in Oceanography: How Accurate Are Boussinesq Ocean Models?, Journal of Physical Oceanography, vol.32, issue.5, pp.1574-1584, 2002. ,
DOI : 10.1175/1520-0485(2002)032<1574:OCEIOH>2.0.CO;2
Superposition of local zoom models and simultaneous calibration for 1D???2D shallow water flows, Mathematics and Computers in Simulation, vol.80, issue.3, pp.547-560, 2009. ,
DOI : 10.1016/j.matcom.2009.09.001
Short-term modelling of the controlled cardiovascular system, ESAIM: Proceedings, vol.12, pp.115-128, 2002. ,
DOI : 10.1051/proc:2002019
Evaluation of myocardial perfusion using three-dimensional myocardial contrast echocardiography, Nuclear Science Symposium Conference Record, pp.1691-1694, 2001. ,
Homogenization modeling for the mechanics of perfused myocardium, Progress in Biophysics and Molecular Biology, vol.69, issue.2-3, pp.463-481, 1998. ,
DOI : 10.1016/S0079-6107(98)00020-0
Wind-forced motions in stratified lakes and their effect on mixedlayer shear, Limnol. Oceanogr, vol.30, issue.4, pp.771-783, 1985. ,
An experimental study of the upwelling response of stratified reservoirs to surface shear stress, J. Fluid Mech, vol.171, pp.407-439, 1986. ,
Water movements in lakes during summer stratification; evidence from the distribution of temperature in Windermere, Phil. Trans. R. Soc. B, vol.236, pp.255-404, 1952. ,
Assessment of passive elastic stiffness for isolated heart muscle and the intact heart, Circul. Research, vol.33, pp.233-243, 1973. ,
Rough boundaries and wall laws, International Journal for Numerical Methods in Fluids, vol.318, issue.1-4, pp.1-4169, 1998. ,
DOI : 10.1002/(SICI)1097-0363(199801)27:1/4<169::AID-FLD657>3.0.CO;2-4
Mathematical modelling of the ischaemic heart, Nonlinear Analysis: Theory, Methods & Applications, vol.47, issue.1, pp.235-244, 2001. ,
DOI : 10.1016/S0362-546X(01)00172-9
Computational Mechanics of the Heart, Journal of Elasticity, vol.61, pp.113-141, 2000. ,
DOI : 10.1007/0-306-48389-0_4
McDonald's blood flow in arteries, 2005. ,
Non-oscillatory central differencing for hyperbolic conservation laws, Journal of Computational Physics, vol.87, issue.2, pp.408-463, 1990. ,
DOI : 10.1016/0021-9991(90)90260-8
Alternative form of Boussinesq equations for nearshore wave propagation, Journal of Waterway, Port, Coastal and Ocean Engineering ASCE, vol.119, issue.6, pp.618-638, 1993. ,
Horizontal transport induced by upwelling in a canyon-shaped reservoir, Hydrobiologia, vol.35, issue.2, pp.343-355, 2007. ,
DOI : 10.1007/s10750-007-0706-6
Two-layer shallow water models, Prikl. Mekh. Tekh. Fiz, vol.2, pp.3-14, 1979. ,
A Roe-type scheme for two-phase shallow granular flows over variable topography, ESAIM: M2AN, pp.851-885, 2008. ,
DOI : 10.1051/m2an:2008029
URL : https://hal.archives-ouvertes.fr/hal-01342261
Long waves on a beach, J. Fluid Mech, vol.27, pp.815-827, 1967. ,
An Introduction to Kinetic Schemes for Gas Dynamics., chapter An introduction to recent developments in theory and numerics for consevation laws, LNCS, 1999. ,
Kinetic formulation of conservation laws, 2002. ,
Non-linear viscoelastic laws for soft biological tissues, European Journal of Mechanics - A/Solids, vol.19, issue.5, pp.749-759, 2000. ,
DOI : 10.1016/S0997-7538(00)00202-3
Viscoelastic constitutive law in large deformations, Journal of Biomechanics, vol.31, issue.8, pp.753-757, 1998. ,
DOI : 10.1016/S0021-9290(98)00077-3
Adaptive finite element methods for Boussinesq equations, Numerical Methods for Partial Differential Equations, vol.39, issue.2, pp.214-236, 2000. ,
DOI : 10.1002/(SICI)1098-2426(200003)16:2<214::AID-NUM5>3.0.CO;2-9
A kinetic scheme for the Saint-Venant system??with a source term, Calcolo, vol.38, issue.4, pp.201-231, 2001. ,
DOI : 10.1007/s10092-001-8181-3
URL : https://hal.archives-ouvertes.fr/hal-00922664
A kinetic equation with kinetic entropy functions for scalar conservation laws, Communications in Mathematical Physics, vol.81, issue.3, pp.501-517, 1991. ,
DOI : 10.1007/BF02099071
Sensitivity analysis and material identification for activated smooth muscle, Computer Assisted Mechanics and Engineering Science, vol.9, pp.519-541, 2002. ,
3-D Multiple-level simulation of free surface flows, Journal of Hydraulic Research, vol.113, issue.4, pp.413-423, 2002. ,
DOI : 10.1175/1520-0469(1957)014<0184:ACSHSS>2.0.CO;2
Approximate riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys, vol.135, issue.2, pp.250-258, 1997. ,
Multilevel finite-difference model for three-dimensional hydrodynamic circulation, Ocean Engineering, vol.24, issue.9, pp.785-816, 1997. ,
DOI : 10.1016/S0029-8018(96)00036-4
Undular bores and secondary waves -Experiments and hybrid finite-volume modelling, Journal of Hydraulic Research, vol.31, issue.1, pp.33-431, 1991. ,
DOI : 10.1080/00221689409498738
Structure and function of the diastolic heart: Material properties of passive myocardium, Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, 1991. ,
The initial response of a stratified lake to a surface shear stress, Journal of Fluid Mechanics, vol.286, issue.-1, pp.39-66, 1996. ,
DOI : 10.1146/annurev.fl.10.010178.001411
Analysis of coronary blood flow interaction with myocardial mechanics based on anatomical models, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.359, issue.1783, pp.1251-1262, 2001. ,
DOI : 10.1098/rsta.2001.0829
Coronary structure and perfusion in health and disease, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.72, issue.1, pp.3137-3153, 1878. ,
DOI : 10.1152/physrev.00029.2005
A computational study of the interaction between coronary blood flow and myocardial mechanics, Physiological Measurement, vol.25, issue.4, pp.863-877, 2004. ,
Simulation model of a mesotrophic reservoir (Lac de Pareloup, France): melodia, an ecosystem reservoir management model, Ecological Modelling, vol.84, issue.1-3, pp.163-187, 1996. ,
DOI : 10.1016/0304-3800(94)00141-3
Water Waves: The Mathematical Theory with Applications, 1958. ,
Total arterial inertance as the fourth element of the windkessel model, Am. J. Physiol, vol.276, pp.81-88, 1999. ,
Theoretical Soil Mechanics, 1943. ,
On standing internal waves of finite amplitude, J. Fluid Mech, vol.32, pp.299-319, 1968. ,
Response of a numerical model of a stratified lake to wind stress, Second International Symposium on Stratified Flows, pp.562-570, 1980. ,
The non-linear field theories of mechanics, 1992. ,
Undular bores (favre waves) in open channels -experimental studies, J. Hydr. Research, vol.32, issue.3, pp.355-370, 1994. ,
A FINITE ELEMENT MIXTURE MODEL FOR HIERARCHICAL POROUS MEDIA, International Journal for Numerical Methods in Engineering, vol.96, issue.2, pp.193-210169, 1979. ,
DOI : 10.1002/(SICI)1097-0207(19970130)40:2<193::AID-NME55>3.0.CO;2-9
Mechanical characterization of skin???Finite deformations, Journal of Biomechanics, vol.3, issue.1, pp.114-124, 1970. ,
DOI : 10.1016/0021-9290(70)90055-2
A numerical Method for Extended Boussinesq Shallow-Water Wave Equations, 1999. ,
Analog studies of the human systemic arterial tree, Journal of Biomechanics, vol.2, issue.2, pp.121-143, 1969. ,
DOI : 10.1016/0021-9290(69)90024-4
Cross-Talk Between Cardiac Muscle and Coronary Vasculature, Physiological Reviews, vol.86, issue.4, pp.1263-1308, 2006. ,
DOI : 10.1152/physrev.00029.2005
Temperature observations in Loch Earn, with a further contribution to the hydrodynamical theory of the temperature seiche, Trans. R. Soc. Edin, vol.48, pp.629-695, 1912. ,
Modelling concentric contraction of muscle using an improved cross-bridge model, Journal of Biomechanics, vol.32, issue.8, pp.837-848, 1999. ,
DOI : 10.1016/S0021-9290(99)00057-3
Upwind Conservative Scheme for the Saint Venant Equations, Journal of Hydraulic Engineering, vol.130, issue.10, pp.977-987, 2004. ,
DOI : 10.1061/(ASCE)0733-9429(2004)130:10(977)
Dynamic finite element modeling of poroviscoelastic soft tissue, Computer Methods in Biomechanics and Biomedical Engineering, vol.102, issue.1, pp.7-16, 2006. ,
DOI : 10.1002/nme.1620320704
A distribution moment approximation for kinetic theories of muscular contraction, Mathematical Biosciences, vol.55, pp.89-114, 1981. ,
An integrated model of LV muscle mechanics , coronary flow, and fluid and mass transport, Am J Physiol Heart Circ Physiol, vol.268, issue.2, pp.633-645, 1995. ,