, Nous avons également produit quelques contributions notables pour la librairie. Plan de la thèse La thèse se compose de 10 chapitres, toutes les applications furent développées en utilisant Feel++
, Chapitre 1 : ? Notions d'analyse numérique, notamment sur les espaces de fonctions, ? Description de la méthode des éléments finis, La première partie est consacrée à la modélisation d'un problème aérothermie
, Chapitre 2 : ? Introduction des équation du problème ? Discrétisation utilisant la méthode des éléments finis 4. DETAILED AFFINE DECOMPOSITION FOR RB WITH STOKES FLOW 225
, ? Résolution non-linéaire et continuations
, Chapitre 3 : ? Méthode de Stabilisation de type Streamline Diffusion (SDM)
, Discussion sur le coefficient de stabilisation et l'évaluation de la longueur caractéristique d'une maille
, ? La méthode Reynolds Average Navier-Stokes (RANS)
, Allmaras ? Le modèle l ? ? SST La deuxième partie est consacré la réduction d'ordre
, Chapitre 5 : ? La méthode des bases réduites (RBM) pour les problèmes coercifs ? La méthode des bases réduites pour les problèmes de type point-selle Chapitre 6 : ? La méthode d
, ? EIM pour les opérateurs discrets d'ordre r ? Méthode de coconstruction EIM et RB (SER)
, Réduction d'un problème d'aerothermie ? Application OPUS : refroidissement de composants électroniques ? Application CHORUS : climatisation dans une cabine d'avion Bibliography, Chapitre
, A stable petrov-galerkin method for convection-dominated problems, Computer methods in applied mechanics and engineering, vol.140, issue.3-4, pp.291-304, 1997.
, Parametric families of reduced finite element models. theory and applications, Mechanical Systems and Signal Processing, vol.10, pp.381-394, 1996.
, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, pp.667-672, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00021702
, An introduction to fluid dynamics, 2000.
, On the existence, uniqueness and approximation of saddlepoint problems arising from lagrangian multipliers. Revue française d'automatique, informatique, recherche opérationnelle. Analyse numérique, vol.8, pp.129-151, 1974.
, Mixed and hybrid finite element methods, vol.15, 2012.
, Streamline-upwind/petrov-galerkin methods for advection dominated flows, 1980.
, Streamline upwind/petrovgalerkin formulations for convection dominated flows with particular emphasis on the incompressible navier-stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.32, issue.1, pp.199-259, 1982.
, A priori convergence of the greedy algorithm for the parametrized reduced basis, M2AN Math. Model. Numer. Anal, vol.46, pp.595-605, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00659314
, On a modification of gls stabilized fem for solving incompressible viscous flows, International Journal for Numerical Methods in Fluids, vol.51, pp.1001-1016, 2005.
, Continuous interior penalty finite element method for oseen's equations, SIAM Journal of Numerical Analysis, vol.44, pp.1248-1274, 2006.
, Nonlinear diffusion and discrete maximum principle for stabilized galerkin approximations of the convection-diffusionreaction equation, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.35, pp.3833-3855, 2002.
, Stabilized galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence, Mathematics of computation, vol.74, issue.252, pp.1637-1652, 2005.
, Time dependent simulation of the driven lid cavity at high reynolds number, 2008.
, Vers la simulation numérique des écoulements sanguins. Theses, 2013.
, Nonlinear model reduction via discrete empirical interpolation, SIAM Journal on Scientific Computing, vol.32, issue.5, pp.2737-2764, 2010.
, The finite element method for elliptic problems, 2002.
, A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation, Computer Methods in Applied Mechanics and Engineering, vol.110, issue.3-4, pp.325-342, 1993.
, Pseudotransient continuation and differential-algebraic equations, SIAM Journal on Scientific Computing, vol.25, issue.2, pp.553-569, 2003.
, Solution of high-reynolds incompressible flow with stabilized finite element and adaptive anisotropic meshing, Computer Methods in Applied Mechanics and Engineering, vol.267, pp.65-85, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00866734
, Certified realtime solution of parametrized partial differential equations, Handbook of materials modeling, pp.1529-1564, 2005.
, Simultaneous empirical interpolation and reduced basis method for non-linear problems, Comptes Rendus Mathématique, vol.353, issue.12, pp.1105-1109, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01219063
, A reduced basis framework: Application to large scale nonlinear multi-physics problems, ESAIM: Proceedings, vol.43, pp.225-254, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00786557
, Reduced basis method applied to large non-linear multi-physics problems : application to high field magnets design. Theses, 2016.
URL : https://hal.archives-ouvertes.fr/tel-01361722
, Natural convection of air in a square cavity: a benchmark solution, International Journal for Numerical Methods in Fluids, vol.3, pp.249-264, 1983.
, Reduced basis method for multi-parameterdependent steady navier-stokes equations: applications to natural convection in a cavity, Journal of Computational Physics, vol.228, issue.12, pp.4359-4378, 2009.
, Analyse théorique et numérique des conditions de glissement pour les fluides et les solides par la méthode de pénalisation, 2013.
, Feedback petrovgalerkin methods for convection-dominated problems, Computer methods in applied mechanics and engineering, vol.88, issue.1, pp.1-16, 1991.
, An absolutely stabilized finite element method for the stokes problem, Mathematics of computation, vol.52, issue.186, pp.495-508, 1989.
, Modélisation et simulation de systèmes multi-fluides. Applications aux écoulements sanguins, 2014.
, Fourth-order compact formulation of navierstokes equations and driven cavity flow at high reynolds numbers, International Journal for Numerical Methods in Fluids, vol.50, issue.4, pp.421-436, 2006.
, On the error behavior of the reduced basis technique for nonlinear finite element approximations, ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, vol.63, issue.1, pp.21-28, 1983.
, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13, pp.1785-1800, 2000.
, Reduced basis a posteriori error bounds for the stokes equations in parametrized domains: A penalty approach, Math. Models Methods Appl. Sci, vol.21, pp.2103-2134, 2011.
, Certified reduced basis methods for parametrized saddle point problems. SIAM, Journal of Scientific Computing, 2012.
DOI : 10.1137/110854084
URL : http://publications.rwth-aachen.de/record/82756/files/4312.pdf
, Supg reduced order models for convection-dominated convection-diffusion-reaction equations, Computer Methods in Applied Mechanics and Engineering, vol.289, pp.454-474, 2015.
, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.3, pp.575-605, 2007.
, Adaptive time-stepping for incompressible flow part i: scalar advection-diffusion, 2008.
DOI : 10.1137/070688018
URL : http://www.maths.dundee.ac.uk/%7Edfg/ggspartI.pdf
, Wall functions for general application CFD codes, pp.1112-1117, 1998.
, Stabilized finite element method for incompressible flows with high reynolds number, Journal of Computational Physics, vol.229, issue.23, pp.8643-8665, 2010.
DOI : 10.1016/j.jcp.2010.07.030
URL : https://hal.archives-ouvertes.fr/hal-00521881
, Analyse physique par simulation numérique et modélisation des écoulements décollés instationnaires autour de surfaces portantes, 2002.
, A new finite element formulation for computational fluid dynamics: V. circumventing the babuska-brezzi condition: a stable petrov-galerkin formulation of the stokes problem accommodating equal-order interpolations, Computer Methods in Applied Mechanics and Engineering, vol.59, issue.1, pp.85-99, 1986.
, A new finite element formulation for computational fluid dynamics: Viii. the galerkin/least-squares method for advective-diffusive equations, Computer Methods in Applied Mechanics and Engineering, vol.73, issue.2, pp.173-189, 1989.
, A new finite element formulation for computational fluid dynamics: Vi. convergence analysis of the generalized supg formulation for linear time-dependent multidimensional advective-diffusive systems, Computer Methods in Applied Mechanics and Engineering, vol.63, issue.1, pp.97-112, 1987.
, A new finite element formulation for computational fluid dynamics: Ii. beyond supg, Computer Methods in Applied Mechanics and Engineering, vol.54, issue.3, pp.341-355, 1986.
, A multidimensional upwind scheme with no crosswind diffusion. Finite Element Methods for Convection Dominated Flows, vol.34, pp.19-35, 1979.
, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup stability constants, Comptes Rendus Mathematique, vol.345, issue.8, pp.473-478, 2007.
, What are c and h?: Inequalities for the analysis and design of finite element methods, Computer Methods in Applied Mechanics and Engineering, vol.97, pp.157-192, 1992.
, A reduced-order method for simulation and control of fluid flows, Journal of computational physics, vol.143, issue.2, pp.403-425, 1998.
, Review of spalart-allmaras turbulence model and its modifications, 2010.
, On discontinuity-capturing methods for convection-diffusion equations. Numerical mathematics and advanced applications, pp.336-344, 2006.
, Crosswind smear and pointwise errors in streamline diffusion finite element methods. mathematics of computation, vol.49, pp.25-38, 1987.
, Finite element methods for linear hyperbolic problems, Computer methods in applied mechanics and engineering, vol.45, issue.1-3, pp.285-312, 1984.
DOI : 10.1016/0045-7825(84)90158-0
, Adaptive time-stepping for incompressible flow part ii: Navier-stokes equations, SIAM Journal on Scientific Computing, 2010.
, Convergence analysis of pseudotransient continuation, SIAM Journal on Numerical Analysis, vol.35, issue.2, pp.508-523, 1998.
, Reduced basis approximation and a posteriori error estimation for the parametrized unsteady boussinesq equations, Mathematical Models and Methods in Applied Sciences, 2010.
, The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers, Dokl. Akad. Nauk SSSR, vol.30, pp.299-303, 1941.
, Laminar flow behind a two-dimensional grid, Mathematical Proceedings of the Cambridge Philosophical Society, vol.44, pp.58-62, 1948.
DOI : 10.1017/s0305004100023999
, On the implementation of the ?-? turbulence model in incompressible flow solvers based on a finite element discretisation, International Journal of Computing Science and Mathematics, vol.1, issue.2-4, pp.193-206, 2007.
, Ix. parabolic equations. Contributions to the Theory of Partial Differential Equations.(AM-33), vol.33, p.167, 2016.
, Stabilized finite element methods:i. application to the advective-diffusive model, Computer Methods in Applied Mechanics and Engineering, vol.95, pp.253-276, 1992.
, Stabilized finite element methods:ii. the incompressible navier-stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.99, pp.209-233, 1992.
, Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics, vol.331, issue.2, pp.153-158, 2000.
, An online intrinsic stabilization strategy for the reduced basis approximation of parametrized advection-dominated problems, Comptes Rendus Mathematique, vol.354, issue.12, pp.1188-1194, 2016.
, A general, multipurpose interpolation procedure: the magic points. working paper or preprint, 2007.
DOI : 10.3934/cpaa.2009.8.383
URL : https://hal.archives-ouvertes.fr/hal-00174797
, A blackbox reduced-basis output bound method for noncoercive linear problems, Studies in Mathematics and Its Applications, vol.12, p.31, 2002.
, An explicit finite element algorithm for convection heat transfer problems, International Journal of Numerical Methods for Heat & Fluid Flow, vol.9, issue.8, pp.860-877, 1999.
DOI : 10.1108/09615539910297932
, An efficient computational framework for reduced basis approximation and a posteriori error estimation of parametrized navierstokes flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.4, pp.1199-1226, 2014.
, h-adaptive finite element solution of high rayleigh number thermally driven cavity problem, International Journal of Numerical Methods for Heat & Fluid Flow, vol.10, issue.6, pp.598-615, 2000.
, Zonal two equation kw turbulence models for aerodynamic flows, 23rd fluid dynamics, plasmadynamics, and lasers conference, p.2906, 1993.
DOI : 10.2514/6.1993-2906
, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA journal, vol.32, issue.8, pp.1598-1605, 1994.
, Ten years of industrial experience with the sst turbulence model. Turbulence, heat and mass transfer, vol.4, pp.625-632, 2003.
, On the performance of high aspect ratio elements for incompressible flows, Computer Methods in Applied Mechanics and Engineering, vol.188, issue.1-3, pp.269-287, 2000.
, A petrov-galerkin finite element method for convection-dominated flows: an accurate upwinding technique for satisfying the maximum principle, Computer Methods in Applied Mechanics and Engineering, vol.50, issue.2, pp.181-193, 1985.
, Efficient model reduction of parametrized systems by matrix discrete empirical interpolation, Journal of Computational Physics, vol.303, pp.431-454, 2015.
DOI : 10.1016/j.jcp.2015.09.046
URL : https://manuscript.elsevier.com/S0021999115006543/pdf/S0021999115006543.pdf
, Recent advances in reduction methods for nonlinear problems, Computers & Structures, vol.13, issue.1-3, pp.31-44, 1981.
, A driven cavity exploration
, The reduced basis method for incompressible viscous flow calculations, SIAM Journal on Scientific and Statistical Computing, vol.10, issue.4, pp.777-786, 1989.
, Finite element methods for fluids, 1989.
, Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, Journal of Fluids Engineering, vol.124, issue.1, pp.70-80, 2002.
, Reduced-basis output bounds for approximately parametrized elliptic coercive partial differential equations. Computing and Visualization in Science, vol.6, pp.147-162, 2004.
URL : https://hal.archives-ouvertes.fr/hal-01220801
, Numerical solution of parametrized navier-stokes equations by reduced basis methods, Numerical Methods for Partial Differential Equations: An International Journal, vol.23, issue.4, pp.923-948, 2007.
DOI : 10.1002/num.20249
, Certified reduced basis approximation for parametrized partial differential equations and applications, Journal of Mathematics in Industry, vol.1, issue.1, p.3, 2011.
DOI : 10.1186/2190-5983-1-3
URL : https://mathematicsinindustry.springeropen.com/track/pdf/10.1186/2190-5983-1-3
, On the theory and error estimation of the reduced basis method for multi-parameter problems, Nonlinear Analysis: Theory, Methods & Applications, vol.21, pp.849-858, 1993.
, Reduced-basis output bound methods for parametrized partial differential equations, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00798352
, Reduced-basis output bound methods for parametrized partial differential equations, 2003.
, Reduced basis approximation and a posteriori error estimation for stokes flows in parametrized geometries: roles of the inf-sup stability constants, Numerische Mathematik, vol.125, issue.1, pp.115-152, 2013.
, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives of Computational, Methods in Engineering, vol.15, issue.3, p.1, 2007.
DOI : 10.1007/s11831-008-9019-9
URL : https://hal.archives-ouvertes.fr/hal-01722593
, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Archives of Computational, Methods in Engineering, vol.15, issue.3, p.229, 2008.
DOI : 10.1007/s11831-008-9019-9
URL : https://hal.archives-ouvertes.fr/hal-01722593
, On the stability of the reduced basis method for stokes equations in parametrized domains, Computer methods in applied mechanics and engineering, vol.196, issue.7, pp.1244-1260, 2007.
, High Performance Computing for the Reduced Basis Method. Application to Natural Convection, ESAIM: Proceedings, pp.255-273, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00786560
, Fluid mechanics in the driven cavity, Annual Review of Fluid Mechanics, vol.32, issue.1, pp.93-136, 2000.
, Very high-order compact finite difference schemes on non-uniform grids for incompressible navier-stokes equations, Journal of Computational Physics, vol.224, issue.2, pp.1064-1094, 2007.
, Sensitization of the sst turbulence model to rotation and curvature by applying the spalart-shur correction term, Journal of Turbomachinery, vol.131, issue.4, p.41010, 2009.
, Effective inflow conditions for turbulence models in aerodynamic calculations, AIAA journal, vol.45, issue.10, pp.2544-2553, 2007.
, A one-equation turbulence model for aerodynamic flows, 30th aerospace sciences meeting and exhibit, p.439, 1992.
, Reduced-basis method (rbm) for non-affine elliptic parametrized pdes.(phd), 2012.
, Physical fluid dynamics, 2012.
, High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method, Journal of Computational Physics, vol.48, pp.387-411, 1982.
, Weak imposition of the slip boundary condition on curved boundaries for stokes flow, Journal of Computational Physics, vol.256, pp.748-767, 2014.
, A successive constraint method with minimal offline constraints for lower bounds of parametric coercivity constant, 2011.
, Certified real-time solution of the parametrized steady incompressible navier-stokes equations: Rigorous reduced-basis a posteriori error bounds, Int. J. Numer. Meth. Fluids, vol.47, pp.773-788, 2005.
, A posteriori error bounds for reduced-basis approximation of parametrized noncoercive and nonlinear elliptic partial differential equations, Proceedings of the 16th AIAA computational fluid dynamics conference, vol.3847, pp.23-26, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01219051
, A posteriori error estimation for reduced-basis approximation of parametrized elliptic coercive partial differential equations:"convex inverse" bound conditioners. ESAIM: Control, Optimisation and Calculus of Variations, vol.8, pp.1007-1028, 2002.
, A computational reduced basis framework : applications to nonlinears multiphysics problems. Theses, 2014.
URL : https://hal.archives-ouvertes.fr/tel-01079415
, A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution, Numerical Heat Transfer: Part B: Fundamentals, vol.40, issue.3, pp.199-228, 2001.
, Proper orthogonal decomposition closure models for turbulent flows: a numerical comparison, Computer Methods in Applied Mechanics and Engineering, vol.237, pp.10-26, 2012.
DOI : 10.1016/j.cma.2012.04.015
URL : http://arxiv.org/pdf/1106.3585
, Finite volume simulation of 2-d steady square lid driven cavity flow at high reynolds numbers, Brazilian Journal of Chemical Engineering, vol.30, issue.4, pp.923-937, 2013.
DOI : 10.1590/s0104-66322013000400023
URL : http://www.scielo.br/pdf/bjce/v30n4/a23v30n4.pdf
, Projection-based model order reduction methods for the estimation of vector-valued variables of interest, SIAM Journal on Scientific Computing, vol.39, issue.4, pp.1647-1674, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02140716