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,
141 6.2.2 Évolutions des rayons principaux et étude de convergence ,
148 6.3.1 Saut de viscosité à la membrane ,
152 6.4.3 Déformation de la membrane avec le temps ,
,
, J. Comput. Phys, p.155, 2008.
,
, Dans un premier temps, l'algorithme d'extension est évalué pour montrer son efficacité à partir d'un champ scalaire quelconque avec et sans la résolution en sous maille. Ensuite, le cas-test de la membrane bidimensionnelle étirée et pressurisée est présenté. L'évolution des rayons principaux ainsi que les distributions de pression et vitesse sont évaluées et comparées aux résultats de la littérature, Les différents modèles et méthodes numériques décrits dans le chapitre précédent sont évalués sur des castests de la littérature
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, Celui-ci contient une fine membrane hyperélastique d'une épaisseur de 0.2mm fixée à son diamètre, comme représentée sur la figure 7.1 à gauche. Ce nouveau réservoir va permettre d'obtenir des données inédites sur le ballottement dans les réservoirs à membrane. Les résultats nous permettront de choisir les modèles à implémenter au sein du code de calcul pour pouvoir approcher plus, phénomènes physiques pertinents, un nouveau réservoir sphérique va être envoyé début décembre 2018 à bord de l'ISS pour être intégré à l'expérience FLUIDICS
Parmi ceux-ci, un réservoir contenant une baffle antiballottement sera envoyé en même temps que le réservoir à membrane à bord de l'ISS. Cette baffle prend la forme d'un anneau circulaire rigide inséré dans le réservoir, comme représentée par transparence sur la figure 7.1 à droite. Ce dispositif est utilisé afin d'atténuer le ballottement en servant d'obstacle solide à l'intérieur du réservoir. L'expérimentation en micro-gravité permettra de connaître plus en détail l'effet d'une baffle sur l'amortissement des fluides lors d'une manoeuvre et apportera des données originales, FLUIDICS pour tester de nouvelles technologies de réservoir et de systèmes capillaires en micro-gravité ,
A partial differential equation approach to multidimensional extrapolation, J. Comput. Phys, vol.193, pp.349-355, 2004. ,
Capsule motion in flow: Deformation and membrane buckling, C. R. Physique, vol.10, pp.764-774, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00454462
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An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws, J. Comput. Phys, vol.227, pp.3191-3211, 2008. ,
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Black box multigrid, J. Comput. Phys, vol.48, pp.366-386, 1982. ,
Large deformation of red blood cell ghost in a simple shear flow, Phys. Fluids, vol.10, issue.8, pp.1834-1845, 1998. ,
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method), J. Comput. Phys, vol.152, pp.457-492, 1999. ,
Forms for the stored (strain) energy function for vulcanized rubber, J. of Polym. Sci, vol.28, pp.625-628, 1958. ,
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains, J. Comput. Phys, vol.176, pp.205-227, 2002. ,
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A numerical method for solving variable coefficient elliptic equation with interfaces, J. Comput. Phys, vol.202, pp.411-445, 2005. ,
A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves, J. Comput. Phys, vol.302, pp.439-468, 2015. ,
A full eulerian fluid-membrane coupling method with a smoothed volume-of-fluid approach, Commun Comput. Phys, vol.12, issue.2, pp.544-576, 2012. ,
A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput, vol.15, pp.323-360, 2000. ,
Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling, J. Fluid Mech, vol.516, pp.303-334, 2004. ,
On the computation of viscous terms for incompressible two-phase flows with Level Set/Ghost Fluid Method, J. Comput. Phys, vol.301, pp.289-307, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01308135
An immersed interface method for incompressible Navier-Stokes equations, J. Sci. Comput, vol.25, issue.3, pp.832-856, 2003. ,
On two-phase flow solvers in irregular domains with contact line, J. Comput. Phys, vol.321, pp.1217-1251, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01349346
The immersed interface method for elliptic equations with discontinuous coefficient and singular sources, SIAM J. Numer. Anal, vol.31, issue.4, pp.1019-1044, 1994. ,
Immersed interface methods for Stokes flow with elastic boundaries or surface tension, J. Sci. Comput, vol.18, issue.3, pp.709-735, 1997. ,
The immersed interface method for the Navier-Stokes equations with singular forces, J. Comput. Phys, vol.171, pp.822-842, 2001. ,
A boundary condition capturing method for Poisson's equation on irregular domain, J. Comput. Phys, vol.160, pp.151-178, 2000. ,
Fast and robust solvers for pressure-correction in bubbly flow problems, Journal of Computational Physics, vol.227, issue.23, pp.21-9991, 2008. ,
Fluid dynamic in space experiment, 68th International Astronautical Congress (IAC) ,
On reinitializing level set functions, J. Comput. Phys, vol.229, pp.2764-2772, 2010. ,
A second order accurate level set method on non-graded adaptive cartesian grids, J. Comput. Phys, vol.225, pp.300-321, 2007. ,
A theory of large elastic deformation, J. Appl. Phys, vol.11, pp.582-592, 1940. ,
An efficient fluid-solid coupling algorithm for single-phase flows, J. Comput. Phys, vol.228, pp.8807-8829, 2009. ,
Large deformation isotropic elasticity -On the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond, vol.326, pp.565-584, 1972. ,
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys, vol.79, pp.12-49, 1988. ,
Flow patterns around heart valves: a numerical method, J. Comput. Phys, vol.10, pp.252-271, 1972. ,
Numerical analysis of blood flow in the heart, J. Comput. Phys, vol.25, pp.220-252, 1977. ,
The immersed boundary method, Acta Numerica, vol.11, pp.479-517, 2002. ,
Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow, J. Fluid Mech, vol.297, pp.123-152, 1995. ,
Deformation of liquid capsule enclosed by elastic membranes in simple shear flow: large deformation and the effect of fluid viscosities, J. Fluid Mech, vol.361, pp.117-143, 1998. ,
A Ghost Fluid/Level Set Method for boiling flows and liquid evaporation: Application to the Leidenfrost effect, J. Comput. Phys, vol.316, pp.789-813, 2016. ,
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Direct Numerical Simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech, vol.31, pp.567-603, 1999. ,
A full Eulerian finite difference approach for solving fluid-structure coupling problems, Journal of Computational Physics, vol.230, pp.596-627, 2011. ,
A Level Set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys, vol.114, pp.146-159, 1994. ,
A sharp interface method for incompressible two-phase flows, J. Comput. Phys, vol.221, pp.469-505, 2007. ,
An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity accross a moving elastic membrane, J. Comput. Phys, vol.227, pp.9955-9983, 2008. ,
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Systematic derivation of jump conditions for the immersed interface method in three-dimensional flow simulation, J. Sci. Comput, vol.27, issue.6, pp.1948-1980, 2006. ,
Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates, Rubber Chemistry and Technology, vol.63, issue.5, pp.792-805, 1990. ,