Tesis sobre el tema "Estimation d’erreur"
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Allier, Pierre-Eric. "Contrôle d’erreur pour et par les modèles réduits PGD". Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLN063/document.
Many structural mechanics problems require the resolution of several similar numerical problems. An iterative model reduction approach, the Proper Generalized Decomposition (PGD), enables the control of the main solutions at once, by the introduction of additional parameters. However, a major drawback to its use in the industrial world is the absence of a robust error estimator to measure the quality of the solutions obtained.The approach used is based on the concept of constitutive relation error. This method consists in constructing admissible fields, thus ensuring the conservative and guaranteed aspect of the estimation of the error by reusing the maximum number of tools used in the finite elements framework. The ability to quantify the importance of the different sources of error (reduction and discretization) allows to control the main strategies of PGD resolution.Two strategies have been proposed in this work. The first was limited to post-processing a PGD solution to construct an estimate of the error committed, in a non-intrusively way for existing PGD codes. The second consists of a new PGD strategy providing an improved approximation associated with an estimate of the error committed. The various comparative studies are carried out in the context of linear thermal and elasticity problems.This work also allowed us to optimize the admissible fields construction methods by substituting the resolution of many similar problems by a PGD solution, exploited as a virtual chart
Loukkas, Nassim. "Synthèse d'observateurs ensemblistes pour l’estimation d’état basées sur la caractérisation explicite des bornes d’erreur d’estimation". Thesis, Université Grenoble Alpes (ComUE), 2018. http://www.theses.fr/2018GREAT040/document.
In This work, we propose two main new approaches for the set-membershipstate estimation problem based on explicit characterization of the estimation error bounds. These approaches can be seen as a combination between a punctual observer and a setmembership characterization of the observation error. The objective is to reduce the complexity of the on-line implimentation, reduce the on-line computation time and improve the accuracy of the estimated state enclosure.The first approach is a set-membership observer based on ellipsoidal invariant sets for linear discrete-time systems and also for Linear Parameter Varying systems. The proposed approach provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation error bounds. The important feature of the proposed approach is that does not require propagation of sets.The second approach is an interval version of the Luenberger state observer for uncertain discrete-time linear systems based on interval and invariant set computation. The setmembership state estimation problem is considered as a punctual state estimation issue coupled with an interval characterization of the estimation error
Mahamane, Amadou. "Analyse et estimation d’erreur en volumes finis. Application aux écoulements en milieu poreux et à l’adaptation de maillage". Paris 13, 2009. http://www.theses.fr/2009PA132008.
The First part of this thesis is devoted to the numerical simulation of two-phase flow in porous media and this has been done by an adaptative finite volume method. Using the global pressure approach proposed by G. Chavent this phenomenon is modeled by a set of elliptic equations in pressure coupled to a convection-diffusion equation in saturation. We use an upwind scheme to discretize a convection part and we approximate the diffusion part using the diamond scheme (VFdiamant). We prove the - stability of this discretization scheme in the pure convection case as well as in the pure diffusion case. The results obtained for some academic test cases on unstructured adaptive two-dimensional grids, are very similar to those contained in the literature. In the second part of the thesis, we study some finite volume schemes devoted to discretization of diffusion operators. Namely, we consider the following schemes: VFdiamant, DDFV developed by P. Omnes and K. Domelevo, VFmixte by J. Droniou and R. Eymard and CVFE developed by B. Amaziane and M. Afif. Thus, the convergence analysis of VFmixte applied to convection-diffusion-reaction equation has been conducted. It has shown the strong convergence of the numerical solution [. . . ] for all and the weak convergence of the discrete gradient [. . . ]. An a posteriori error analysis has also been conducted, for both DDFV and VFmixte, in the case of a diffusion equation. The implementation of error indicators for DDFV shows their efficiency in terms of localization of error. This study has been concluded by a numerical comparison of CVFE, DDFV and VFdiamant applied to theapproximate heat equation
Dabaghi, Jad. "Estimations d’erreur a posteriori pour des inégalités variationnelles : application à un écoulement diphasique en milieu poreux". Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS076.
In this thesis, we consider variational inequalities in the form of partial differential equations with complementarity constraints. We construct a posteriori error estimates for discretizations using the finite element method and the finite volume method, for inexact linearizations employing any semismooth Newton solver and any iterative linear algebraic solver. First, we consider the model problem of contact between two membranes, next we consider its extension into a parabolic variational inequality, and to finish we treat a two-phase compositional flow with phase transition as an industrial application. In the first chapter, we consider the stationnary problem of contact between two membranes. This problem belongs to the wide range of variational inequalities of the first kind. Our discretization is based on the finite element method with polynomials of order p ≥ 1, and we propose two discrete equivalent formulations: the first one as a variational inequality, and the second one as a saddle-point-type problem. We employ the Clarke differential so as to treat the nondifferentiable nonlinearities. It enables us to use semismooth Newton algorithms. Next, any iterative linear algebraic solver is used for the linear system stemming from the discretization. Employing the methodology of equilibrated flux reconstructions in the space H(div,Ω), we get an upper bound on the total error in the energy norm H01(Ω). This bound is fully computable at each semismooth Newton step and at each linear algebraic step. Our estimation distinguishes in particular the three components of the error, namely the discretization error (finite elements), the linearization error (semismooth Newton method), and the algebraic error (GMRES algorithm). We then formulate adaptive stopping criteria for our solvers to ultimately reduce the number of iterations. We also prove, in the inexact semismooth context, the local efficiency property of our estimators, up to a contact term that appears negligeable in numerics. Our numerical experiments illustrate the accuracy of our estimates and the reduction of the number of necessary iterations. They also show the performance of our adaptive inexacte semismooth Newton method. In the second chapter, we are interested in deriving a posteriori error estimates for a parabolic variational inequality and we consider the extension of the model of the first chapter to the unsteady case. We discretize our model using the finite element method of order p ≥ 1 in space and the backward Euler scheme in time. To treat the nonlinearities, we use again semismooth Newton algorithms, and we also employ an iterative algebraic solver for the linear system stemming from the discretization. Using the methodology of equilibrated flux reconstructions in the space H(div,Ω), we obtain, when p=1 and at convergence of the semismooth solver and the algebraic solver, an upper bound for the total error in the energy norm L²(0,T; H01(Ω)). Furthermore, we estimate in this case the time derivative error in a norm close to the energy norm L^2(0,T;H^{-1}(Ω)). In the case p ≥ 1, we present an a posteriori error estimate valid at each semismooth Newton step and at each linear algebraic step in the norm L²(0,T;H01(Ω)). We distinguish in this case the components of the total error, namely the discretization error, the linearization error, and the algebraic error. In particular, it enables us to devise adaptive stopping criteria for our solvers which reduces the number of iterations. In the third chapter, [...]
Yousef, Soleiman. "Etude d’estimations d’erreur a posteriori et d’adaptivité basée sur des critères d’arrêt et raffinement de maillages pour des problèmes d’écoulements multiphasiques et thermiques : Application aux procédés de récupération assistée d’huile". Paris 6, 2013. http://www.theses.fr/2013PA066616.
The goal of this thesis is the a posteriori error analysis and the conception of adaptive strategies based on stopping criteria and local mesh refinement. We treat a class of multi-dimensional degenerate parabolic equations which represent typical examples of industrial interest. The considered models are discretized by a finite volume scheme in space with the backward Euler temporal stepping. We prove un upper bound for a dual norm of the residual, augmented by a nonconformity evaluation term, by fully computable error estimators. These estimators include: an estimator associated to the linearization error, an estimator associated to the algebraic error, an estimator associated to the temporal error, and an estimator associated to the spatial error. Consequently, these estimators allow to formulate an adaptive resolution algorithm where the corresponding errors can be equilibrated. We also propose a strategy of local mesh reffinement. Finally, we prove the efficiency of our a posteriori estimates. A numerical test illustrates the efficiency of our estimates and the performance of the adaptive algorithm. In particular, a significant gain in terms of the number of mesh cells, the total number of the iterations of the linearization method, and the total number of algebraic solver iterations is achieved on several real-life reservoir engineering examples
Parret-Fréaud, Augustin. "Estimation d'erreur de discrétisation dans les calculs par décomposition de domaine". Thesis, Cachan, Ecole normale supérieure, 2011. http://www.theses.fr/2011DENS0022/document.
The control of the quality of mechanical computations arouses a growing interest in both design and certification processes. It relies on error estimators the use of which leads to often prohibitive additional numerical costs on large computations. The present work puts forward a new procedure enabling to obtain a guaranteed estimation of discretization error in the setting of linear elastic problems solved by domain decomposition approaches. The method relies on the extension of the constitutive relation error concept to the framework of non-overlapping domain decomposition through the recovery of admissible interface fields. Its development within the framework of the FETI and BDD approaches allows to obtain a relevant estimation of discretization error well before the convergence of the solver linked to the domain decomposition. An extension of the estimation procedure to heterogeneous problems is also proposed. The behaviour of the method is illustrated and assessed on several numerical examples in 2 dimension
Herrera, Milagros Estefania. "Estimations rigoureuses des erreurs dynamiques dans diverses applications de télédétection : concept, validation et réalisation dans l'algorithme GRASP". Electronic Thesis or Diss., Université de Lille (2022-....), 2022. http://www.theses.fr/2022ULILR012.
The understanding of the uncertainties in the retrieval of the aerosol and surface properties is very important for an adequate characterization of the processes that occur in the atmosphere. However, the reliable characterization of the error budget of the retrieval products is a very challenging aspect that currently remains not fully resolved in most remote sensing approaches. The level of uncertainties for the majority of the remote sensing products relies mostly on post-processing validations and inter comparisons with other data while the dynamic errors are rarely provided. This study describes, discusses and evaluates a concept realized in GRASP (Generalized Retrieval of Atmosphere and Surface Properties) algorithm for providing the dynamic estimates of uncertainties for retrieved parameters. The approach employs a rigorous concept of statistical optimization for estimating the effects of measurement uncertainties propagation to the retrieval results. The approach accounts for the effect of both random and systematic uncertainties in the initial data and provides error estimates both for directly retrieved parameters included in the retrieval state vector and for the characteristics derived from these parameters. The efficiency of the realized error estimation concept is extensively analyzed for GRASP applications for aerosol retrieval from ground-based observations by sun/sky photometer and lidar. The diverse aspects of the generations and evaluations of the error estimates are discussed and illustrated. The evaluation of the error estimates was realized using the series of comprehensive sensitivity tests when simulated sun/sky photometer measurements and lidar data are perturbed by random and systematic errors and inverted. The results of the retrievals and their error estimations obtained in the tests are analyzed and evaluated. The tests are conducted for the different observations of several types of aerosols including biomass burning, urban, dust and their mixtures. The study considers popular observations by AERONET sun/sky radiometer at 440, 675, 870 and 1020 nm and multi-wavelength elastic lidar at 355, 532 and 1064 nm. The sun/sky radiometer data are inverted aloneor together with lidar data. The analysis shows that the generated error estimates overall satisfactory of the uncertainties of different retrieved aerosol characteristics including aerosol size distribution, complex refractive index, single scattering albedo, lidar ratios, aerosol vertical profiles, etc. Also, the analysis shows that the main observed error dynamic agrees well with the errors tendencies commonly known fromthe retrieval experience. For example, the serious retrieval accuracy limitations for all aerosol types are associated with the situations with low optical depth. Also, for observations of multi-component aerosol mixtures, the reliable characterization of each component is possible only in limited situations, for example from radiometric data obtained for low solar zenith angle observations or from a combination of radiometricand lidar data. At the same time, total optical properties of aerosol mixtures tend to be always retrieved satisfactorily. In addition, the study includes the analysis of the detailed structure of correlation matrices for the retrieval errors of mono- and multi-component aerosols. The conducted analysis of error correlation appears to be a usefulapproach for optimizing observations schemes and retrieval setups. The illustration of the developed approach application to real data is provided for co-located observations of sun/sky photometer and lidar over Buenos Aires. Furthermore, the preliminary results for utilizing the error estimates for the retrieval of aerosol from satellite data are provided
Pled, Florent. "Vers une stratégie robuste et efficace pour le contrôle des calculs par éléments finis en ingénierie mécanique". Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2012. http://tel.archives-ouvertes.fr/tel-00776633.
Tirvaudey, Marie. "Couplage AIG/MEG pour l'analyse de détails structuraux par une approche non intrusive et certifiée". Thesis, Toulouse, INSA, 2019. http://www.theses.fr/2019ISAT0016/document.
In the current industrial context where the numerical simulation plays a major role, a large amount of tools are developed in order to perform accurate and effective simulations using as less numerical resources as possible. Among all these tools, the non-intrusive ones which do not modify the existing structure of commercial softwares but allowing the use of advanced solving methods, such as isogeometric analysis or multi-scale coupling, are the more attractive to the industry. The goal of these thesis works is thus the coupling of the Isogeometric Analysis (IGA) with the Finite Element Method (FEM) to analyse structural details with a non-intrusive and certified approach. First, we develop an approximate global link between the Lagrange functions, commonly used in the FEM, and the NURBS functions on which the IGA is based. It’s allowed the implementation of isogeometric analysis in an existing finite element industrial software considering as a black-box. Through linear and nonlinear examples implemented in the industrial software Code_Aster of EDF, we show the efficiency of the IGA\FEM bridge and all the industrial applications that can be made. This link is also a key to simplify the non-intrusive coupling between a global isogeometric problem and a local finite element problem. Then, as the non-intrusive coupling between both methods is possible, an adaptive process is introduced in order to certify this coupling regarding a quantity of interest. This adaptive strategy is based on a posteriori error estimation. A global estimator and indicators of iteration, model and discretization error sources are computed to control the definition of the coupled problem. Residual base methods are performed to estimated errors for linear cases, an extension to the concept of constitutive relation errors is also initiated for non-linear problems
Thai, Hoang phuong. "Sur l'utilisation de l'analyse isogéométrique en mécanique linéaire ou non-linéaire des structures : certification des calculs et couplage avec la réduction de modèle PGD". Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLN017/document.
The topic of the PhD thesis deals with the construction of advanced numerical approaches for the simulation and optimization of mechanical structures with complex geometry. It focuses on the Isogeometric Analysis (IGA) technology which has received much attention of the last decade due to its increased flexibility, accuracy, and robustness in many engineering simulations compared to classical Finite Element Analysis (FEA). In particular, IGA enables a direct link with CAD software (the same functions are used for both analysis and geometry) and facilitates meshing procedures.In this framework, and as a first part of the work, a verification method based on duality and the concept of Constitutive Relation Error (CRE) is proposed. It enables to derive guaranteed and fully computable a posteriori error estimates on the numerical solution provided by IGA. Such estimates, which are valid for a wide class of linear or nonlinear structural mechanics models, thus constitute performing and useful tools to quantitatively control the numerical accuracy and drive adaptive procedures. The focus here is on the construction of equilibrated flux fields, which is key ingredient of the CRE concept, and which was until now almost exclusively developed in the FEA framework alone. The extension to IGA requires to address some technical issues, due to the use of B-Spline/NURBS basis functions. The CRE concept is also implemented together with adjoint techniques in order to perform goal-oriented error estimation.In a second part, IGA is coupled with model reduction in order to get certified real-time solutions to problems with parameterized geometry. After defining the parametrization on the mapping from the IGA parametric space to the physical space, a reduced model based on the Proper Generalized Decomposition (PGD) is introduced to solve the multi-dimensional problem. From an offline/online strategy, the procedure then enables to describe the manifold of parametric solutions with reduced CPU cost, and to further perform shape optimization in real-time. Here again, a posteriori estimation of the various error sources inheriting from discretization and PGD model reduction is performed from the CRE concept. It enables to control the quality of the approximate PGD solution (globally or on outputs of interest), for any geometry configuration, and to feed a robust greedy algorithm that optimizes the computational effort for a prescribed error tolerance.The overall research work thus provides for reliable and practical tools in mechanical engineering simulation activities. Capabilities and performance of these tools are shown on several numerical experiments with academic and engineering problems, and with linear and nonlinear (damage) models
Essongue-Boussougou, Simon. "Méthode des éléments finis augmentés pour la rupture quasi-fragile : application aux composites tissés à matrice céramique". Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0018/document.
Computing the lifetime of woven Ceramic Matrix Composites (CMC) requires evaluating the crack density in the material (which can reach 10 mm-1). Numerical simulations at the mesoscopic scale are needed to precisely estimate it. Embedded Finite Element Methods (EFEM) seem to be the most appropriate to do so. They allow for a discrete representation of cracks with no additional degrees of freedom.We chose to work with an EFEM free from local iterations named the Augmented Finite Element Method (AFEM). Improvements over the original AFEM have been proposed. We also demonstrated that, under one hypothesis, the AFEM and the classical Finite Element Method (FEM) are fully equivalent. We then compare the accuracy of the AFEM and the classical FEM to represent weak and strong discontinuities. Finally, some examples of application of AFEM to CMC are given
Maknun, Imam Jauhari. "Évaluation numérique des éléments finis DKMQ pour les plaques et les coques". Thesis, La Rochelle, 2015. http://www.theses.fr/2015LAROS040/document.
In the linear case, the Mindlin-Reissner model for thick plates and the Naghdi model for thick shells are commonly used. The finite element discretization of these models leads to numerical locking phenomenon when the thickness approaches zero : shear locking for plates and both shear and membrane locking for shells. There are some finite elements that could reduce or even eliminate this phenomenon. DKMQ element for plates or DKMQ24 element for shells, are low-order elements, based on a mixed formulation, introduced a few years ago to prevent the numerical locking phenomenon. In this thesis, we concentrated on numerical evaluation of the performance of these elements. Besides the classical benchmark tests, we also focused on the analysis of discrete inf-sup condition for DKMQ element. We studied the s-norm test proposed by Bathe for DKMQ24 element. Finally, we performed a posteriori error estimation for DKMQ and DKMQ24 elements, using the error estimator Z2 (proposed by Zienkiewicz and Zhu), associated with the averaging, projection or SPR recovery methods. The results obtained have enabled us to quantify the performance of these two finite elements for locking problems, and to identify their limits. Two important applications of these elements DKMQ and DKMQ24 were then presented ; the first one concerns thin-walled beams with open cross-section and the second one composite plates
Fontana, Ilaria. "Interface problems for dam modeling". Thesis, Université de Montpellier (2022-….), 2022. http://www.theses.fr/2022UMONS020.
Engineering teams often use finite element numerical simulations for the design, study and analysis of the behavior of large hydraulic structures. For concrete structures, models of increasing complexity must be able to take into account the nonlinear behavior of discontinuities at the various interfaces located in the foundation, in the body of the dam or at the interface between structure and foundation. Besides representing the nonlinear mechanical behavior of these interfaces (rupture, sliding, contact), one should also be able to take into account the hydraulic flow through these openings.In this thesis, we first focus on the topic of interface behavior modeling, which we address through the Cohesive Zone Model (CZM). This model was introduced in various finite element codes (with the joint elements), and it is a relevant approach to describe the physics of cracking and friction problems at the geometrical discontinuities level. Although initially the CZM was introduced to take into account the phenomenon of rupture, we show in this thesis that it can be extended to sliding problems by possibly relying on the elasto-plastic formalism coupled to the damage. In addition, nonlinear hydro-mechanical constitutive relations can be introduced to model the notion of crack opening and the coupling with the laws of fluid flow. At the mechanical level, we work in the Standard Generalized Materials (SGM) framework, which provides a class of models automatically satisfying some thermodynamical principles, while having good mathematical and numerical properties that are useful for robust numerical modeling. We adapt the formalism of volumetric SGM to the interface zones description. In this first part of the thesis, we present our developpements under the hypothesis of SGM adapted to CZM, capable of reproducing the physical phenomena observed experimentally: rupture, friction, adhesion.In practice, nonlinearities of behavior of interface zones are dominated by the presence of contact, which generates significant numerical difficulties for the convergence of finite element computations. The development of efficient numerical methods for the contact problem is thus a key stage for achieving the goal of robust industrial numerical simulators. Recently, the weak enforcement of contact conditions à la Nitsche has been proposed as a mean to reduce numerical complexity. This technique displays several advantages, among which the most important for our work are: 1) it can handle a wide range of conditions (slip with or without friction, no interpenetration, etc.); 2) it lends itself for a rigorous a posteriori error analysis. This scheme based on the weak contact conditions represents in this work the starting point for the a posteriori error estimation via equilibrated stress reconstruction. This analysis is then used to estimate the different error components (e.g., spatial, nonlinear), and to develop an adaptive resolution algorithm, as well as stopping criteria for iterative solvers and the automatic tuning of possible numerical parameters.The main goal of this thesis is thus to make the finite element numerical simulation of structures with geometrical discontinuities robust. We address this question from two angles: on one side, we revisit the existing methods for the crack representation working on the mechanical constitutive relation for joints; on the other, we introduce a new a posteriori method for the contact problem and we propose its adaptation for the generic interface models
Giacomini, Matteo. "Quantitative a posteriori error estimators in Finite Element-based shape optimization". Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX070/document.
Gradient-based shape optimization strategies rely on the computation of the so-called shape gradient. In many applications, the objective functional depends both on the shape of the domain and on the solution of a PDE which can only be solved approximately (e.g. via the Finite Element Method). Hence, the direction computed using the discretized shape gradient may not be a genuine descent direction for the objective functional. This Ph.D. thesis is devoted to the construction of a certification procedure to validate the descent direction in gradient-based shape optimization methods using a posteriori estimators of the error due to the Finite Element approximation of the shape gradient.By means of a goal-oriented procedure, we derive a fully computable certified upper bound of the aforementioned error. The resulting Certified Descent Algorithm (CDA) for shape optimization is able to identify a genuine descent direction at each iteration and features a reliable stopping criterion basedon the norm of the shape gradient.Two main applications are tackled in the thesis. First, we consider the scalar inverse identification problem of Electrical Impedance Tomography and we investigate several a posteriori estimators. A first procedure is inspired by the complementary energy principle and involves the solution of additionalglobal problems. In order to reduce the computational cost of the certification step, an estimator which depends solely on local quantities is derived via an equilibrated fluxes approach. The estimators are validated for a two-dimensional case and some numerical simulations are presented to test the discussed methods. A second application focuses on the vectorial problem of optimal design of elastic structures. Within this framework, we derive the volumetric expression of the shape gradient of the compliance using both H 1 -based and dual mixed variational formulations of the linear elasticity equation. Some preliminary numerical tests are performed to minimize the compliance under a volume constraint in 2D using the Boundary Variation Algorithm and an a posteriori estimator of the error in the shape gradient is obtained via the complementary energy principle
Genchev, Svetoslav. "Localisation de robots mobiles dans des environnements inconnus a priori". Compiègne, 2011. http://www.theses.fr/2011COMP1961.
This work emphasizes on three utterly related subjects – resolving robot position by distance measurements to other robots, estimating the uncertainty of the computed position and planning the robot’s movement in order to minimize that uncertainty. The planning algorithm uses some of the robots as stationary beacons guiding the robots in motion, thus enabling long-term working in unstructured environments. The main purpose of the planning is not building collision-free paths, but maintaining the positioning accuracy during the motion. Two important optimality criteria are considered, related to specific aspects of the common motion – how to plan trajectories with good movement precision, how to choose which robots to use as beacons and how to position them, in order to form appropriate geometrical arrangements and thus maximize localization precision. To resolve the position, given the distance measurements, we introduce several novel methodologies – one real-time, low-computation technique and another two optimal, computation costly model. The methods and theirs statistical characteristics have been presented analytically, and compared numerically by graphical simulations. The uncertainty estimation is based on the Delta method for uncertainty propagation, which in our case produce very satisfying results, compared to numeric estimators. Good knowledge of the position’s uncertainty is important when combining it with information of other sources, when performing hybrid navigation. Furthermore, a fast and differentiable uncertainty estimator has been found, not depending on the number of beacons used. Maintaining minimal values for the position uncertainty is the first criterion for the optimal motion planning. As a second criterion, we developed a differentiable beacon configuration quality estimator that does not depend on the localized robot but only on the positions of the beacons used. The proposed solutions for the three tasks have been validated experimentally by computer simulation. A simulation platform has been implemented for this purpose. It has been programmed on C++, using the OpenGL graphic library
Liu, Hao. "Stratégie de raffinement automatique de maillage et méthodes multi-grilles locales pour le contact : application à l'interaction mécanique pastille-gaine". Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4720/document.
This Ph.D. work takes place within the framework of studies on Pellet-Cladding mechanical Interaction (PCI) which occurs in the fuel rods of pressurized water reactor. This manuscript focuses on automatic mesh refinement to simulate more accurately this phenomena while maintaining acceptable computational time and memory space for industrial calculations. An automatic mesh refinement strategy based on the combination of the Local Defect Correction multigrid method (LDC) with the Zienkiewicz and Zhu a posteriori error estimator is proposed. The estimated error is used to detect the zones to be refined, where the local subgrids of the LDC method are generated. Several stopping criteria are studied to end the refinement process when the solution is accurate enough or when the refinement does not improve the global solution accuracy anymore.Numerical results for elastic 2D test cases with pressure discontinuity shows the efficiency of the proposed strategy.The automatic mesh refinement in case of unilateral contact problems is then considered. The strategy previously introduced can be easily adapted to the multibody refinement by estimating solution error on each body separately. Post-processing is often necessary to ensure the conformity of the refined areas regarding the contact boundaries. A variety of numerical experiments with elastic contact (with or without friction, with or without an initial gap) confirms the efficiency and adaptability of the proposed strategy
Turbis, Pascal. "Modèles de flammelette en combustion turbulente avec extinction et réallumage : étude asymptotique et numérique, estimation d’erreur a posteriori et modélisation adaptative". Thèse, 2011. http://hdl.handle.net/1866/4916.
We are interested here in the modeling errors of subgrid flamelet models in nonpremixed turbulent combustion. The goal of this thesis is to develop an a posteriori error estimation strategy to determine the best model within a hierarchy, with a numerical cost at most that of using the models in the first place. Firstly, we develop and test a dual-weighted residual estimator strategy on a system of advection-diffusion-reaction equations. Secondly, we test that methodology on another system of equations, where quenching and ignition effects are added. In the absence of advection, a rigorous asymptotic analysis shows the existence of many combustion regimes already observed in numerical simulations. We obtain approximations of the quenching and ignition parameters, alongside the S-shaped curve, a plot of the maximal flame temperature as a function of the Damköhler number, consisting of three branches and two bends. When advection effects are added, we still obtain a S-shaped curve corresponding to the known combustion regimes. We compare the modeling errors of the asymptotic approximations in the two stable regimes and establish new model hierarchies for each combustion regime. These errors are compared with the estimations obtained by using the error estimation strategy. When only one stable combustion regime exists, the error estimator correctly identifies that regime; when two or more regimes are possible, it gives a systematic way of choosing one regime. For regimes where more than one model is appropriate, the error estimator’s predicted hierarchy is correct.