A comparison of the finite difference and finite element methods for heat transfer calculations

The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined

A review of nonlinear FFT-based computational homogenization methods

Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform

ALERT Doctoral School 2012: advanced experimental techniques in geomechanics

The twenty-second session of the European Graduate School 2012 (called usually ALERT Doctoral School) entitled Advanced experimental techniques in geomechanics is organized by Cino Viggiani, Steve Hall and Enrique Romero.Postprint (published version

Development of a Data Fusion-Based Multi-Sensor System for Hybrid Sheet Molding Compound

In den letzten Jahren ist die Produktion von faserverstärkten Kunststoffen stetig gestiegen. Ein Teil davon ist das glasfaser-verstärkte Sheet Molding Compound (SMC), welches sich durch seine günstigen Herstellkosten und einfache Verarbeitung auszeichnet. Allerdings weist dieses Material schlechte mechanische Eigenschaften auf, welche eine Anwendung für Strukturbauteile verhindert. Um diesem Nachteil entgegen zu wirken, wird das diskontinuierliche Glasfaser-SMC lokal mit kontinuierlichem Carbonfaser-SMC verstärkt. Dadurch können die Vorteile des günstigen und leicht zu verarbeitenden Glasfaser-SMC mit den sehr guten mechanischen Eigenschaften von Carbonfaser-SMC in Faserrichtung kombiniert werden. Die Kombination dieser beiden Werkstoffe kann bereits in einem frühen Produktionsschritt zu einer Vielzahl an möglichen Defekten wie beispielsweise Delamination, Falten oder Winkelabweichungen führen. Um keine weiteren wertschöpfenden Maßnahmen an defekten Bauteilen durchzuführen, muss die Qualitätssicherung bereits in einem frühen Prozessstadium durchgeführt werden. Die zu entdeckenden Fehler werden in außen- und innenliegende Defekte unterteilt. Da kein System verfügbar ist, um alle relevanten Defekte zu detektieren, wird pro Defektklasse ein Messsystem benötigt. Zudem erstreckt sich der Anwendungsbereich neben dem Halbzeug auch auf das ausgehärtete Bauteil. Das Laserlichtschnittsystem und die aktive Thermografie, in Form der Puls-Phasen-Thermografie, haben sich als geeignet erwiesen. Beide Systeme werden zunächst einzeln untersucht und für den vorliegenden Anwendungsfall angepasst. Dabei ist es möglich die Puls-Phasen-Thermografie methodisch zu einer Tiefenauswertung weiterzuentwickeln. Des Weiteren werden Fehler nicht nur detektiert, sondern auch definiert. Anschließen werden die beiden Systeme in einem Multisensorik-System zusammengeführt. Mit Hilfe der Datenfusion sind eine Auswertung von außen- und innenliegenden Defekten, sowie die Ermittlung von geometrischen Zusammenhängen zwischen einzelnen Defekten möglich. Durch den Aufbau eines Schichtmodells wird zusätzlich eine benutzerfreundliche Auswertung ermöglicht, welche dem Anwender schnell einzelne Schichten aufzeigen kann. Mit der Ermittlung der Messunsicherheit des Multisensorik-Systems wird die Güte aufgezeigt

A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering problems. The main contribution of the current work is to promote using the spatial gradient of the primary variable as an output from separated neural networks. Later on, the strong form which has a higher order of derivatives is applied to the spatial gradients of the primary variable as the physical constraint. In addition, the so-called energy form of the problem is applied to the primary variable as an additional constraint for training. The proposed approach only required up to first-order derivatives to construct the physical loss functions. We discuss why this point is beneficial through various comparisons between different models. The mixed formulation-based PINNs and FE methods share some similarities. While the former minimizes the PDE and its energy form at given collocation points utilizing a complex nonlinear interpolation through a neural network, the latter does the same at element nodes with the help of shape functions. We focus on heterogeneous solids to show the capability of deep learning for predicting the solution in a complex environment under different boundary conditions. The performance of the proposed PINN model is checked against the solution from FEM on two prototype problems: elasticity and the Poisson equation (steady-state diffusion problem). We concluded that by properly designing the network architecture in PINN, the deep learning model has the potential to solve the unknowns in a heterogeneous domain without any available initial data from other sources. Finally, discussions are provided on the combination of PINN and FEM for a fast and accurate design of composite materials in future developments

Spatial variability of aircraft-measured surface energy fluxes in permafrost landscapes

Arctic ecosystems are undergoing a very rapid change due to global warming and their response to climate change has important implications for the global energy budget. Therefore, it is crucial to understand how energy fluxes in the Arctic will respond to any changes in climate related parameters. However, attribution of these responses is challenging because measured fluxes are the sum of multiple processes that respond differently to environmental factors. Here, we present the potential of environmental response functions for quantitatively linking energy flux observations over high latitude permafrost wetlands to environmental drivers in the flux footprints. We used the research aircraft POLAR 5 equipped with a turbulence probe and fast temperature and humidity sensors to measure turbulent energy fluxes along flight tracks across the Alaskan North Slope with the aim to extrapolate the airborne eddy covariance flux measurements from their specific footprint to the entire North Slope. After thorough data pre-processing, wavelet transforms are used to improve spatial discretization of flux observations in order to relate them to biophysically relevant surface properties in the flux footprint. Boosted regression trees are then employed to extract and quantify the functional relationships between the energy fluxes and environmental drivers. Finally, the resulting environmental response functions are used to extrapolate the sensible heat and water vapor exchange over spatio-temporally explicit grids of the Alaskan North Slope. Additionally, simulations from the Weather Research and Forecasting (WRF) model were used to explore the dynamics of the atmospheric boundary layer and to examine results of our extrapolation

Theory, codes, and numerical simulation of heat transport in multicomponent systems

Heat transport is a topic that is fundamental in many fields, from materials engineering to planetary models. The calculation of the thermal transport coefficient with the Green-Kubo theory in multicomponent fluids, especially in ab-initio simulations, had a severe data analysis issue that this work solved. In this thesis, we derive the entire theory and data analysis framework for the multicomponent Green-Kubo. Then we show the computer codes we developed, allowing the user to apply the approach previously derived. We believe that in science, replicability and reproducibility are essential requirements. Every new technique must come with an open-source and reliable implementation. In the end, we demonstrate a significant application to superionic ammonia, fundamental to understanding the behavior of icy giant planets like Uranus and Neptune, providing an estimate for the thermal transport coefficient

Experimental and numerical analysis of wear flat generation and growth in alumina grinding wheels.

183 p.El proceso de rectificado supone entre un 20-25% del coste total de fabricación, suponiendo el consumo de muela un porcentaje muy elevado del coste total. De entre los diferentes tipos de desgaste, el wear flat es el más perjudicial para el proceso. Asimismo, nuevos generaciones de materiales abrasivos, como la alúmina microcristalina sinterizada, se van haciendo hueco en aplicaciones industriales. Sin embargo, su comportamiento ante el desgaste no está caracterizado. Es por ello, que este trabajo de investigación aborda la caracterización de la generación y evolución del wear flat en muelas de alúmina, analizando la influencia de la estructura cristalina de los granos abrasivos en el wear flat, desgaste de naturaleza triboquímica. Para ello, se realiza un análisis tanto experimental como numérico.Desde el punto de vista experimental, se realizan ensayos de rectificado en los que se aísla el desgaste de wear flat de los demás tipos de desgaste. Tras estos y debido a la importancia del contacto en el desgaste, se diseña un tribómetro pin-on-disk en el cual se controlan exhaustivamente las condiciones de contacto y se reproduce el ciclo térmico de los granos abrasivos para la cuantificación del desgaste triboquímico. Por último, desde un punto de vista numérico, se realiza un modelo térmico en FEM, para determinar la influencia de la temperatura en las propiedades de la alúmina y un modelo de desgaste en DEM, con el objetivo de simular el desgaste de un grano abrasivo, teniendo en cuenta su estructura cristalina. Como resultado se observan mayores valores de %A para la alúmina microcristalina durante el proceso de rectificado, ya que las altas temperaturas modifican la apariencia de la superficie desgastada de la muela. Sin embargo, las reacciones triboquímicas son más importantes en la alúmina WFA, como muestran los resultados tribológicos y numéricos

Model Predictive Control Strategies for Advanced Battery Management Systems

Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field.Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications where Lithium-ion (Li-ion) batteries are employed. From a manufacturer point of view, the optimal design and management of such electrochemical accumulators are important aspects for ensuring safe and profitable operations. The adoption of mathematical models can support the achievement of the best performance, while saving time and money. In the literature, all the models used to describe the behavior of a Li-ion battery belong to one of the two following families: (i) Equivalent Circuit Models (ECMs), and (ii) Electrochemical Models (EMs). While the former family represents the battery dynamics by means of electrical circuits, the latter resorts to first principles laws of modeling. As a first contribution, this Thesis provides a thorough investigation of the pseudo-two-dimensional (P2D) Li-ion battery EM. In particular, the objectives are to provide: (i) a detailed description of the model formulation, (ii) the Li-ION SIMulation BAttery (LIONSIMBA) toolbox as a finite volume Matlab implementation of the P2D model, for design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed tool with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, and a battery pack of series connected cells. The second contribution is related to the development of several charging strategies for Advanced Battery Management Systems (ABMSs), where predictive approaches are employed to attain optimal control. Model Predictive Control (MPC) refers to a particular family of control algorithms that, according to a mathematical model, predicts the future behavior of a plant, while considering inputs and outputs constraints. According to this paradigm, in this Thesis different ABMSs strategies have been developed, and their effectiveness shown through simulations. Due to the complexity of the P2D model, its inclusion within an MPC context could prevent the online application of the control algorithm. For this reason, different approximations of the P2D dynamics are proposed and their MPC formulations carefully explained. In particular, finite step response, autoregressive exogenous, piecewise affine, and linear time varying approximations are presented. For all the aforementioned reformulations, the closed-loop performance are evaluated considering the P2D implementation of LIONSIMBA as the real plant. The closed-loop simulations highlight the suitability of the MPC paradigm to be employed for the development of the future ABMSs. In fact, its ability to predict the future behavior of the cell while considering operating constraints can help in preventing possible safety issues and improving the charging performance. Finally, the reliability and efficiency of the proposed Matlab toolbox in simulating the P2D dynamics, support the idea that LIONSIMBA can significantly contribute in the advance of the battery field