In dieser Arbeit verwende ich den Formalismus der endoreversiblen Thermodynamik um ein hydraulisches Rekuperationssystem für Nutzfahrzeuge zu modellieren und zu untersuchen. Dafür führe ich verlustbehaftete Übergänge extensiver Größen zwischen Teilsystemen eines Systems ein. Diese können einerseits der Modellierung von Leckagen und Reibungsverlusten, welche als Partikel- oder Drehmomentverluste dargestellt würden, dienen. Andererseits ermöglichen sie die Modellierung einer endoreversiblen Maschine, welche – durch Definition eines solchen verlustbehafteten, internen Überganges – ein gegebenes Wirkungsgradkennfeld und daraus resultierende Entropieproduktion inne hat. Diese wird infolge zur Modellierung der Hydraulikeinheit des Rekuperationssystems verwendet. Desweiteren basiert die Beschreibung des Rekuperationssystems auf der Modellierung der Hydraulikflüssigkeit als Van-der-Waals-Fluid, sodass Druckverluste im endoreversiblen Sinne konsistent berücksichtigt werden können. Von gegebenen Materialparamtern werden die dafür notwendigen Van-der-Waals-Parameter hergeleitet. Weitere Aspekte sind Wärmeverluste an die Umgebung sowie Wärmeübergänge zwischen Teilsystemen. Auf Grundlage realer Fahrdaten der Nutzfahrzeuge werden verschiedene dynamische und thermodynamische Effekte im Rekuperationssystem analysiert. Ihr Einfluss auf die resultierenden energetischen Einsparungen beim Abbremsen und Beschleunigen wird durch Variation zugehöriger Parameter aufgezeigt. Zuletzt wird mit einem vereinfachten Modell ohne Druck- und Wärmeverluste, aber unter Einbeziehung des Verbrennungsmotors des Fahrzeuges, eine Optimierung der Steuerung des hydraulischen Rekuperationssystems mit Hinblick auf minimalen Kraftstoffverbrauch durchgeführt. Hier zeigt sich eine erhebliche Verbesserung durch die Leistungsaufteilung zwischen Verbrennungsmotor und Rekuperationssystem nach deren Betriebsbereichen mit maximalem Wirkungsgrad. / In this work I use the formalism of endoreversible thermodynamics to model and investigate a hydraulic recuperation system for commercial vehicles. For that, I introduce lossy transfers of extensive quantities between subsystems of an endoreversible system. On the one hand, these allow modeling of leakages and friction losses, which can be represented as particle or torque losses. On the other hand, they can be used as internal extensity transfers in endoreversible engines which, as a result, have a given efficiency or efficiency map and among other things give an expression for their entropy production. Such an engine is used to model the hydraulic unit of the recuperation system. Furthermore, the description of the recuperation system is based on the modeling of the hydraulic fluid as a van der Waals fluid, so that pressure losses can be taken into account in a consistent endoreversible fashion. From given material parameters the necessary van der Waals parameters are derived. Other aspects of the modeling include heat losses to the environment and heat transfers between subsystems. On the basis of real driving data, various dynamic and thermodynamic effects within the recuperation system are observed and their influence as well as the influence of selected parameters on the resulting energy savings for both acceleration and deceleration are shown. Finally, using a simplified model neglecting pressure and heat losses, but including the internal combustion engine of the vehicle, an optimization of the control strategy for the hydraulic recuperation system with regard to minimum fuel consumption is performed. Here, a significant improvement due to a power distribution between combustion engine and recuperation system according to their high efficiency operating ranges can be achieved.

L’objectif de ce travail de thèse est de proposer la Méthodes des éléments finis de Galerkin discontinus (DGFEM) à la discrétisation des équations compressibles de Navier-Stokes. Plusieurs challenges font l’objet de ce travail. Le premier aspect a consisté à montrer l’ordre de convergence optimal de la méthode DGFEM en utilisant les polynômes d’interpolation d’ordre élevé. Le deuxième aspect concerne l’implémentation de méthodes de ‘‘shock-catpuring’’ comme les limiteurs de pentes et les méthodes de viscosité artificielle pour supprimer les oscillations numériques engendrées par l’ordre élevé (lorsque des polynômes d’interpolation de degré p>0 sont utilisés) dans les écoulements transsoniques et supersoniques. Ensuite nous avons implémenté des estimateurs d’erreur a posteriori et des procédures d ’adaptation de maillages qui permettent d’augmenter la précision de la solution et la vitesse de convergence afin d’obtenir un gain de temps considérable. Finalement, nous avons montré la capacité de la méthode DG à donner des résultats corrects à faibles nombres de Mach. Lorsque le nombre de Mach est petit pour les écoulements compressibles à la limite de l’incompressible, la solution souffre généralement de convergence et de précision. Pour pallier ce problème généralement on procède au préconditionnement qui modifie les équations d’Euler. Dans notre cas, les équations ne sont pas modifiées. Dans ce travail, nous montrons la précision et la robustesse de méthode DG proposée avec un schéma en temps implicite de second ordre et des conditions de bords adéquats. / The aim of this thesis is to deal with compressible Navier-Stokes flows discretized by Discontinuous Galerkin Finite Elements Methods. Several aspects has been considered. One is to show the optimal convergence of the DGFEM method when using high order polynomial. Second is to design shock-capturing methods such as slope limiters and artificial viscosity to suppress numerical oscillation occurring when p>0 schemes are used. Third aspect is to design an a posteriori error estimator for adaptive mesh refinement in order to optimize the mesh in the computational domain. And finally, we want to show the accuracy and the robustness of the DG method implemented when we reach very low mach numbers. Usually when simulating compressible flows at very low mach numbers at the limit of incompressible flows, there occurs many kind of problems such as accuracy and convergence of the solution. To be able to run low Mach number problems, there exists solution like preconditioning. This method usually modifies the Euler. Here the Euler equations are not modified and with a robust time scheme and good boundary conditions imposed one can have efficient and accurate results.

Soft soil reinforcement by inclusion is a growing technique caracterized by a pile grid and a granular embankment introduced between the reinforced soil and the structure. Unlike traditionnal methods, the load is partially transferred to the pile heads by arching in the embankment. The application area of this research focuses on the shallow foundations case, in which the thickness of the embankment is small. The litterature review shows that only a few studies were dedicated to that case, and that fundamental questions remains concerning the load transfer in the embankment. Chosen method for this research consists in two-dimensionnal physical modelling, analysis of the conducted simulations, and development of an analytical model in order to predict the load transfer to the piles by arching in the embankment. The results of this PhD thesis provide original elements of evidence of the load transfer in the studied system, proposes an analytical model based on block division of the granular embankment by shear bands - which is in good agreement with experimental data - and lead to a better understanding of arching in soils.

This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.

Compressed sensing has been proposed as a computationally efficient method to estimate the finite-dimensional signals. The idea is to develop an undersampling operator that can sample the large but finite-dimensional sparse signals with a rate much below the required Nyquist rate. In other words, considering the sparsity level of the signal, the compressed sensing samples the signal with a rate proportional to the amount of information hidden in the signal. In this dissertation, first, we employ compressed sensing for physical layer signal processing of directional millimeter-wave communication. Second, we go through the theoretical aspect of compressed sensing by running a comprehensive theoretical analysis of compressed sensing to address two main unsolved problems, (1) continuous-extension compressed sensing in locally convex space and (2) computing the optimum subspace and its dimension using the idea of equivalent topologies using Köthe sequence. In the first part of this thesis, we employ compressed sensing to address various problems in directional millimeter-wave communication. In particular, we are focusing on stochastic characteristics of the underlying channel to characterize, detect, estimate, and track angular parameters of doubly directional millimeter-wave communication. For this purpose, we employ compressed sensing in combination with other stochastic methods such as Correlation Matrix Distance (CMD), spectral overlap, autoregressive process, and Fuzzy entropy to (1) study the (non) stationary behavior of the channel and (2) estimate and track channel parameters. This class of applications is finite-dimensional signals. Compressed sensing demonstrates great capability in sampling finite-dimensional signals. Nevertheless, it does not show the same performance sampling the semi-infinite and infinite-dimensional signals. The second part of the thesis is more theoretical works on compressed sensing toward application. In chapter 4, we leverage the group Fourier theory and the stochastical nature of the directional communication to introduce families of the linear and quadratic family of displacement operators that track the join-distribution signals by mapping the old coordinates to the predicted new coordinates. We have shown that the continuous linear time-variant millimeter-wave channel can be represented as the product of channel Wigner distribution and doubly directional channel. We notice that the localization operators in the given model are non-associative structures. The structure of the linear and quadratic localization operator considering group and quasi-group are studied thoroughly. In the last two chapters, we propose continuous compressed sensing to address infinite-dimensional signals and apply the developed methods to a variety of applications. In chapter 5, we extend Hilbert-Schmidt integral operator to the Compressed Sensing Hilbert-Schmidt integral operator through the Kolmogorov conditional extension theorem. Two solutions for the Compressed Sensing Hilbert Schmidt integral operator have been proposed, (1) through Mercer's theorem and (2) through Green's theorem. We call the solution space the Compressed Sensing Karhunen-Loéve Expansion (CS-KLE) because of its deep relation to the conventional Karhunen-Loéve Expansion (KLE). The closed relation between CS-KLE and KLE is studied in the Hilbert space, with some additional structures inherited from the Banach space. We examine CS-KLE through a variety of finite-dimensional and infinite-dimensional compressible vector spaces. Chapter 6 proposes a theoretical framework to study the uniform convergence of a compressible vector space by formulating the compressed sensing in locally convex Hausdorff space, also known as Fréchet space. We examine the existence of an optimum subspace comprehensively and propose a method to compute the optimum subspace of both finite-dimensional and infinite-dimensional compressible topological vector spaces. To the author's best knowledge, we are the first group that proposes continuous compressed sensing that does not require any information about the local infinite-dimensional fluctuations of the signal.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.

Soft soil reinforcement by inclusion is a growing technique caracterized by a pile grid and a granular embankment introduced between the reinforced soil and the structure. Unlike traditionnal methods, the load is partially transferred to the pile heads by arching in the embankment. The application area of this research focuses on the shallow foundations case, in which the thickness of the embankment is small. The litterature review shows that only a few studies were dedicated to that case, and that fundamental questions remains concerning the load transfer in the embankment. Chosen method for this research consists in two-dimensionnal physical modelling, analysis of the conducted simulations, and development of an analytical model in order to predict the load transfer to the piles by arching in the embankment. The results of this PhD thesis provide original elements of evidence of the load transfer in the studied system, proposes an analytical model based on block division of the granular embankment by shear bands - which is in good agreement with experimental data - and lead to a better understanding of arching in soils. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

This dissertation is a contribution to the development of a unified model of continuum mechanics, describing both fluids and elastic solids as a general continua, with a simple material parameter choice being the distinction between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic media. Additional physical effects such as surface tension, rate-dependent material failure and fatigue can be, and have been, included in the same formalism. The model extends a hyperelastic formulation of solid mechanics in Eulerian coordinates to fluid flows by means of stiff algebraic relaxation source terms. The governing equations are then solved by means of high order ADER Discontinuous Galerkin and Finite Volume schemes on fixed Cartesian meshes and on moving unstructured polygonal meshes with adaptive connectivity, the latter constructed and moved by means of a in- house Fortran library for the generation of high quality Delaunay and Voronoi meshes. Further, the thesis introduces a new family of exponential-type and semi- analytical time-integration methods for the stiff source terms governing friction and pressure relaxation in Baer-Nunziato compressible multiphase flows, as well as for relaxation in the unified model of continuum mechanics, associated with viscosity and plasticity, and heat conduction effects. Theoretical consideration about the model are also given, from the solution of weak hyperbolicity issues affecting some special cases of the governing equations, to the computation of accurate eigenvalue estimates, to the discussion of the geometrical structure of the equations and involution constraints of curl type, then enforced both via a GLM curl cleaning method, and by means of special involution-preserving discrete differential operators, implemented in a semi-implicit framework. Concerning applications to real-world problems, this thesis includes simulation ranging from low-Mach viscous two-phase flow, to shockwaves in compressible viscous flow on unstructured moving grids, to diffuse interface crack formation in solids.