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Computer simulation is acknowledged as the third branch of Science. From the seminal work of Turner et al. (1956) [on Finite Elements, impressive improvements have been made in terms of software and hardware, so that, nowadays, there is no engineering device (in the broad sense of the word) that is not subjected to any kind of simulation. However, in the same way as there is a gap between theory and practice, at an industrial level there are still problems where, at the moment, numerical simulations are not used and instead, a hand-craft approach is applied. The mitigation of distortion in large aluminium forgings is one of these problems. Post-machining distortion is an open problem that affects every single large thickwalled aluminium forging assembled on an aircraft. The origin of distortion is the presence of residual stresses (RS) developed along the manufacturing chain, especially after the heat treatment of quenching. When machining takes places, it causes a redistribution at an internal level as the previous equilibrium state is broken by the material removal action. At a theoretical level, if the RS in a part are known in advance, a proper machining sequence could be planned with the aim to mitigate or counteract a warped geometry. This strategy is already implemented for parts machined from rolled plates, where RS can be considered as constant along the longitudinal direction. However, for forgings, RS are a function of the geometry and, as a result, a complex three-dimensional stress field is present. Important research efforts are done in order to predict RS numerically for forgings but still, the deterministic nature of numerical simulations are not able to capture the variable behaviour of distortions. At the moment, the current research direction looks at the distortion problem as something to avoid upwards in the manufacturing chain, it means, focusing the efforts in the steps before or during machining at latest. In the present thesis, we opted to follow the opposite direction, which means, how to proceed and handle distortion once it has arisen. To perform this task, the problem was first studied by conventional Finite Element Method (FEM), and then, by applying a non-intrusive Model Order Reduction (ROM) technique called Sparse Subspace Learning (SSL). The content of this thesis is structured as follows. In chapter 1 we introduce the distortion problem, followed by the definition and interconnection of the three main actors: residual stresses, distortion and reshaping. Then, a review of the available reshaping techniques is provided and finally, the challenges and perspectives for reshaping simulation are discussed. Chapter 2 presents two numerical models devoted to determine the residual stresses after quenching and plastic bending, respectively as the heat treatment is considered as the main source of residual stresses in aluminium forgings and the latter corresponds to the selected reshaping operation to be studied in this thesis. After its validation, both models are applied in the following chapters and they provide the reference solution to our problem. In chapter 3, we introduce the reshaping diagrams as a tool to assist the bending straightening operation. In addition, the residual stress free hypothesis is presented as an alternative to study the reshaping problem. This approach uses the distorted geometry as the main input to simulate the reshaping step by considering the part without residual stresses. Then, in chapter 4, a multiparametric study of bending straightening is provided with the aid of the SSL, so that the reshaping diagrams can be generalized for a previously defined set of parameters. Finally, as reshaping is an iterative and sequential procedure, in chapter 5, two consecutive bending straightening operations are simulated. Different reshaping strategies are studied and a methodology is provided to tackle in a more systematic way the open problem of reshaping. Las distorsiones después del mecanizado de grandes piezas de aluminio son un problema recurrente para la industria aeronáutica. Estas desviaciones de la geometría de diseño se deben a la presencia de tensiones residuales, que se desarrollan a lo largo de la cadena de fabricación, especialmente después del tratamiento térmico de temple. Para restablecer la geometría nominal, es necesario realizar una serie de operaciones de remodelación muy manuales y que requieren mucho tiempo. El presente trabajo de investigación se centra en el desarrollo de herramientas eficaces de simulación numérica para ayudar a los operadores en el enderezamiento por flexión, que es una de las operaciones de remodelación más comunes. Para ello, se desarrolla un modelo de simulación de elementos finitos representativo de la cadena de fabricación, incluyendo el temple, el mecanizado y la remodelación, que permite predecir las tensiones y distorsiones residuales en piezas forjadas de aluminio de paredes gruesas. El modelo se valida con los datos experimentales que se encuentran en la literatura. A continuación, se introduce el concepto de diagramas de remodelación, una herramienta que permite seleccionar una carga de flexión casi óptima para minimizar la distorsión. Se muestra que el diagrama de remodelación no necesita tener en cuenta el campo de tensión residual, ya que su único efecto es desfasar horizontalmente el diagrama de remodelación por una cierta distancia. Por lo tanto, el comportamiento general que incluye un campo de tensión residual tridimensional real en una pieza forjada puede recuperarse desplazando el diagrama de remodelación libre de tensión residual por el desfase apropiado. Por último, se propone una estrategia para identificar el desfase sobre la marcha durante la operación de remodelación utilizando medidas sencillas de fuerza-desplazamiento. A continuación, se explora el uso de nuevas técnicas numéricas, especialmente la reducción del orden del modelo (MOR), con un doble propósito: i) acelerar el cálculo de los diagramas de remodelación; y ii) tener en cuenta varios parámetros del proceso, como la distorsión inicial o la configuración de la remodelación. Para ello, nos basamos en el método de Sparse Subspace Learning (SSL), un método MOR no intrusivo que permite reconstruir el espacio de solución directamente a partir de los resultados del modelo de elementos finitos. Con la solución paramétrica a mano, se puede encontrar la configuración óptima de remodelación en tiempo real, para minimizar la distorsión antes de lanzar la operación de remodelación real. Por último, se propone los primeros pasos hacia la ampliación de la metodología anterior, que combina los diagramas de remodelación y los métodos MOR, a un entorno multietapa en el que se realizan varias operaciones de corrección de la forma de manera secuencial. La simulation numérique est reconnue comme étant la troisième branche de la science. À partir des travaux fondateurs de Turner et al. (1956) sur les éléments finis, des améliorations impressionnantes ont été apportées en termes de software et de hardware, de sorte qu’aujourd’hui, il n’existe plus aucun dispositif d’ingénierie (au sens large du terme) qui ne soit pas transcrit par une quelconque simulation.Cependant, tout comme il existe un fossé entre théorie et pratique, il existe encore des problèmes au niveau industriel où, pour le moment, les simulations numériques n’ont pas encore pris la place des approches artisanales. L’atténuation de la distorsion dans les grandes pièces forgées en aluminium est l’un des exemples.La distorsion post-usinage est un problème ouvert qui affecte chaque grande pièce forgée en aluminium à paroi épaisse assemblée sur un avion. Cette distorsion provient de la présence de contraintes résiduelles (RS) développées tout au long de la chaine de fabrication, en particulier après traitement thermique par trempe.Lorsque l’usinage a lieu, il provoque une redistribution à un niveau interne car l´état d’équilibre précédent est rompu par l’action d’enlèvement de matière. Au niveau théorique, si les RS d’une pièce sont connues à l’avance, une séquence d’usinage appropriée pourrait être planifiée dans le but d’atténuer ou de contrecarrer une géométrie déformée. Cette stratégie est déjà mise en œuvre pour les pièces usinées à partir de tôles laminées, où la RS peut être considérée comme constante dans la direction longitudinale. Cependant, pour les pièces forgées, les RS sont fonction de la géométrie et, par conséquent, un champ de contrainte tridimensionnel complexe est présent. D’importants efforts de recherche sont réalisés afin de prédire numériquement les RS pour les pièces forgées, mais la nature déterministe des simulations numériques ne permet toujours pas de saisir le comportement variable des déformations. Pour l’instant, l’orientation actuelle de la recherche considère le problème des distorsions comme quelque chose à éviter depuis le début de la chaine de fabrication, c’est-à-dire en concentrant les efforts dans les étapes précédentes, où au plus tard pendant l’usinage. Dans la présente thèse, nous avons choisi de suivre la direction opposée, c’est-à-dire comment procéder et gérer la distorsion une fois qu’elle est apparue. Pour réaliser cette tâche, le problème a d’abord été étudié par la méthode classique des éléments finis (FEM), et par la suite en appliquant une technique non intrusive de réduction de l’ordre des modèles (ROM) appelée ”Sparse Subspace Learning” (SSL).Le contenu de cette thèse est structuré comme suit. Dans le chapitre 1 le problème de la distorsion sera introduit, suivi de la définition et de l’interconnexion des trois acteurs principaux : les contraintes résiduelles, la distorsion et le redressage. Les techniques de redressage seront ensuite passées en revue pour finalement examiner les défis et les perspectives de la simulation du redressage. Le chapitre 2 présente deux modèles numériques consacres à la détermination des contraintes résiduelles après la trempe et le pliage plastique, le traitement thermique étant considéré comme la principale source de contraintes résiduelles dans les pièces forgées en aluminium. C’est dans ce cadre (origine majoritairement thermique des contraintes résiduelles) que sera étudiée l’opération de redressage sélectionnée dans cette thèse.Après leurs validations, les deux modèles sont appliqués dans les chapitres suivants où ils constitueront la solution de référence du problème. Dans le chapitre 3, les diagrammes de mise en forme sont présentés comme un outil d’aide à l’opération de redressement par flexion. En outre, l’hypothèse reste sans contrainte résiduelle est présentée comme une alternative pour étudier le problème de redressage. Cette approche utilise la géométrie déformée comme entrée principale permettant de simuler l’étape de redressage en considérant la pièce sans contraintes résiduelles. Le chapitre 4 montrera une étude multiparamétrique du redressement par flexion à l’aide du SSL.Les diagrammes de redressage seront généralisés pour un ensemble de paramètres préalablement définis. Le redressage étant une procédure itérative et séquentielle, le chapitre 5 explicitera la simulation de deux opérations consécutives de redressement par flexion. Différentes stratégies de redressage seront étudiées, et une méthodologie sera fournie pour aborder de manière plus systématique le problème ouvert du redressage. Erasmus Mundus en simulació en enginyeria i desenvolupament de l'emprenedoria

This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10915-019-00917-2 Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed.

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

International audience; We discuss the use of hierarchical collocation to approximate the numerical solution of parametric models. With respect to traditional projection-based reduced order modeling, the use of a collocation enables non-intrusive approach based on sparse adaptive sampling of the parametric space. This allows to recover the low-dimensional structure of the parametric solution subspace while also learning the functional dependency from the parameters in explicit form. A sparse low-rank approximate tensor representation of the parametric solution can be built through an incremental strategy that only needs to have access to the output of a determin-istic solver. Non-intrusiveness makes this approach straightforwardly applicable to challenging problems characterized by nonlinearity or non affine weak forms. As we show in the various examples presented in the paper, the method can be interfaced with no particular effort to existing third party simulation software making the proposed approach particularly appealing and adapted to practical engineering problems of industrial interest.

PurposeThe purpose of this paper is to present a reduced order computational strategy for a multi-physics simulation involving a fluid flow, electromagnetism and heat transfer in a hot-wall chemical vapour deposition reactor. The main goal is to produce a multi-parametric solution for fast exploration of the design space to perform numerical prototyping and process optimisation.Design/methodology/approachDifferent reduced order techniques are applied. In particular, proper generalized decomposition is used to solve the parameterised heat transfer equation in a five-dimensional space.FindingsThe solution of the state problem is provided in a compact separated-variable format allowing a fast evaluation of the process-specific quantities of interest that are involved in the optimisation algorithm. This is completely decoupled from the solution of the underlying state problem. Therefore, once the whole parameterised solution is known, the evaluation of the objective function is done on-the-fly.Originality/valueReduced order modelling is applied to solve a multi-parametric multi-physics problem and generate a fast estimator needed for preliminary process optimisation. Different order reduction techniques are combined to treat the flow, heat transfer and electromagnetism problems in the framework of separated-variable representations.

International audience; Mesh adaptation has proven to be very efficient for simulating transient multiphase computational fluid dynamics applications. In this work, we present a new parallel anisotropic mesh adaptation technique relying on an edge based error estimator. It provides a high level of accuracy while substantially reducing the computational effort. This technique enables a good capture of physical phenomena, boundary layers, interfaces, free surfaces and even multiphase turbulent flows, and has a great potential to simulate a large variety of applications. Current investigations explore the performance of the new algorithm on massively parallel resources. In this paper, we show that the developed adaptive meshing works very well in a parallel environment involving topological mesh modifications and dynamic repartitioning of parallel slots. It is also shown that the proposed methodology provides an additional gain in terms of computational cost due the production of a non-uniform mesh size distribution. Runs performed on national and European supercomputers will show the scalability and pertinence of our developments.

International audience; Offshore wind turbines are currently increasing the potential of wind energy, and numerical simulation is a way to help this industry to reach maturity. In the context of floating wind energy, predicting the loads applied on structures and their response is essential. Those data will enable an optimization of floaters dimensioning, necessary for CAPEX reduction. As the simulation of floating wind turbines requires the representation of both complex geometries and phenomena, several alternative techniques have been developed. The wake generated by the rotor can be modeled using methodologies inherited from onshore wind turbines simulation, and coupled with a hydrodynamic code. However those simplified methods have been primarily developed for wake study, and thus have varying precision for loads estimation. This work proposes a methodology for the simulation of a single or several turbines with an exact representation of the geometries involved, targeting an accurate evaluation of loads. The software library used is ICI-tech, developed at the High Performance Computing Institute (ICI) of Centrale Nantes. A monolithic approach is applied on a single computational mesh, where all the different phases are defined through level-set functions. The Navier-Stokes (NS) equations are solved in the Variational MultiScale (VMS) formalism using stabilized finite elements. This approach, coupled with an automatic and anisotropic adaptation procedure, guarantees the good representation of the geometries immersed. The automatic adaptation refines the mesh only in interest zones, allowing the simulation of phenomena with very different orders of magnitude, e.g. aerodynamics around blades and waves propagation. The reduction of the number of points in the mesh and the massive parallelization of the code are also necessary for wind turbine simulation.

Part of the Lecture Notes in Computer Science book series (LNCS, volume 10759)Also part of the Lecture Notes in Artificial Intelligence book sub series (LNAI, volume 10759); International audience; Learning from interpretation transition (LFIT) automatically constructs a model of the dynamics of a system from the observation of its state transitions. So far, the systems that LFIT handles are restricted to discrete variables or suppose a discretization of continuous data. However, when working with real data, the discretization choices are critical for the quality of the model learned by LFIT. In this paper, we focus on a method that learns the dynamics of the system directly from continuous time-series data. For this purpose, we propose a modelling of continuous dynamics by logic programs composed of rules whose conditions and conclusions represent continuums of values.

International audience; An overview of various numerical methods developed for speeding-up computations is presented in the field of the bulk material forming under solid state, which is characterized by complex and evolving geometries requiring frequent remeshings and numerous time increments. These methods are oriented around the axis that constitutes the meshing problem. The multi-mesh method allows to optimally solve several physics involved on the same domain, according to its finite element discretization with several different meshes, for example in the cogging or cold pilgering processes. For quasi steady-state problems and problems with quite pronounced localization of deformation, such as Friction Stir Welding (FSW) or High Speed Machining, an Arbitrary Lagrangian or Eulerian formulation (ALE) with mesh adaptation shows to be imperative. When the problem is perfectly steady, as for the rolling of long products, the direct search for the stationary state allows huge accelerations. In the general case, where no process specificity can be used to solve the implicit equations, the multigrid method makes it possible to construct a much more efficient iterative solver, which is especially characterized by an almost linear asymptotic cost.

This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linear models to be solved. In the context of developing "Smart Grids" with the distributed generation of power, real time analysis of complex systems such as these needs fast, reliable and accurate models. In the current study we propose model order reduction methods both a-priori and a-posteriori suitable for dynamic models of power grids. The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model; this method combines POD with multiple linear approximations. For the transmission lines, a distributed parameters model in frequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines., Cette these présente l'étude de la réduction de modeles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modeles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modeles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systemes complexes tels que ceux-ci nécessite des modeles rapides, fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modeles a la fois a priori et a posteriori, adaptées aux modeles dynamiques des réseaux électriques. Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modele oscillant non­linéaire et complexe. La non-linéarité de ce modele nécessite une attention particuliere pour bénéficier du maximum d'avantages des techniques de réduction de modeles. lnitialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succes divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modeles la mieux adaptée pour le modele dynamique oscillant. Pour les lignes de transmission, un modele de parametres distribués en domaine fréquentiel est utilisé. Des modeles réduits de type PGD sont proposés pour le modele DP des lignes de transmission. Un probleme multidimensionnel entierement paramétrique a été formulé, avec les parametres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modele des lignes de transmission pour laquelle les parametres dépendent de la fréquence., Esta tesis presenta un estudio de la reducción de modelos (MOR) para redes de transmisión y distribución de electricidad. El enfoque principal utilizado ha sido la dinámica transitoria y para la reducción de modelos se ha adoptado un punto de vista matemático. Las redes eléctricas son complejas y tienen un tamaño importante. Por lo tanto, el análisis y diseño de este tipo de redes mediante la simulación numérica, requiere la resolución de modelos no-lineales complejos. En el contexto del desarrollo de redes inteligentes, el objetivo es un análisis en tiempo real de sistemas complejos, por lo que son necesarios modelos rápidos, fiables y precisos. En el presente estudio se proponen diferentes métodos de reducción de modelos, tanto a priori como a posteriori, adecuados para modelos dinámicos de redes eléctricas. La dinámica transitoria de redes eléctricas, se describe mediante modelos dinámicos oscilatorios no-lineales. Esta no-linearidad del modelo necesita ser bien tratada para obtener el máximo beneficio de las técnicas de reducción de modelos. Métodos como la POD y la LATIN han sido inicialmente utilizados en esta problemática con diferentes grados de éxito. El método de TPWL, que combina la POD con múltiples aproximaciones lineales, ha resultado ser el mas adecuado para sistemas dinámicos oscilatorios. En el caso de las redes de transmisión eléctrica, se utiliza un modelo de parámetros distribuidos en el dominio de la frecuencia. Se propone reducir este modelo basándose en la PGD, donde los parámetros eléctricos de la red de transmisión son incluidos como coordenadas de la representación separada del modelo paramétrico. Este método es ampliado para representar la solución de modelos con parámetros dependientes de la frecuencia para las redes de transmisión eléctrica

International audience; The properties of short fibre-reinforced polymer composites depend on the distribution and the orientation of fibres which drastically changes during the forming of composites. During this stage, these materials behave as fibre suspensions and usually flow in confined geometries. To analyse their flow-induced fibrous microstructures, we previously conducted 3D real-time in situ observations of the compression of non-Newtonian dilute fibre suspensions using fast X-ray microtomography [T. Laurencin et al., Compos Sci Technol 134 (2016)]. Here, we successfully simulated these experiments with a multi-domain Finite Element code and compared them with the predictions of Jeffery's model. Often, the Jeffery's equations agree with the experimental and numerical data. However, for fibres closed to compression platens, important deviations were observed with faster simulated and experimental fibre rotation. Adopting the dumbbell approach and revisiting the recent work of Perez et al. [J non-Newtonian Fluid Mech 233 (2016)], an extension of the Jeffery's model is proposed to account both for the non-Newtonian rheology of the suspending fluid and confinement effects. Despite its simplicity, the new model allows a good description of simulation and experimental results.

International audience; Le préconditionnement d’un algorithme itératif de résolution à l’aide d’une méthode multigrille (MG) permet d’approcher le comportement asymptotique en O(N) recherché pour les très grands problèmes. La méthode MG retenue est hybride : algébrique pour la construction des systèmes linéaires des grilles grossières et géométrique pour celle de s opérateurs de passage. Adaptée à une formulation mixte en vitesse et pression, compatible avec le calcul parallèle et avec les nombreux remaillages inhérents à la mise en forme, elle accélère les calculs par un facteur compris entre 1,5 et 2.

International audience; In this paper, a new methodology to build automatically 3D adapted meshes, ready for numerical simulations and directly from images, is proposed. It is based on the Immersed Image Method, which interpolates the image information on an initial mesh and combines it with parallel automatic anisotropic mesh adaptation with a control of the number of mesh nodes. Simultaneously, a smooth redistancing technique, based on the resolution of a Hamilton–Jacobi equation, is developed to produce phase functions for the objects to be detected in the image. The proposed methodology is applied on mesh generation and in multiphase flow computations based on 2D and 3D images.

International audience