The development, analysis, and implementation of efficient methods to solve algebraic systems of equations are main research directions in the field of numerical simulation and are the focus of this thesis. Due to their lesser demands for computer resources, iterative solution methods are the choice to make, when very large scale simulations have to be performed. To improve their efficiency, iterative methods are combined with proper techniques to accelerate convergence. A general technique to do this is to use a so-called preconditioner. Constructing and analysing various preconditioning methods has been an active field of research already for decades. Special attention is devoted to the class of the so-called optimal order preconditioners, that possess both optimal convergence rate and optimal computational complexity. The preconditioning techniques, proposed and studied in this thesis, utilise the block structure of the underlying matrices, and lead to methods that are of optimal order. In the first part of the thesis, we construct an Algebraic MultiLevel Iteration (AMLI) method for systems arising from discretizations of parabolic problems, using Crouzeix-Raviart finite elements. The developed AMLI method is based on an approximated block factorization of the original system matrix, where the partitioning is associated with a sequence of nested discretization meshes. In the second part of the thesis we develop solution methods for the numerical simulation of multiphase flow problems, modelled by the Cahn-Hilliard (C-H) equation. We consider the discrete C-H problem, obtained via finite element discretization in space and implicit schemes in time. We propose techniques to precondition the Jacobian of the discrete nonlinear system, based on its natural two-by-two block structure. The preconditioners are used in the framework of inexact Newton methods. We develop two nonlinear solution algorithms for the Cahn-Hilliard problem. Both lead to efficient optimal order methods. One of the main advantages of the proposed methods is that they are implemented using available software toolboxes for both sequential and distributed execution. The theoretical analysis of the solution methods presented in this thesis is combined with numerical studies that confirm their efficiency.

Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys. / QC 20100622

Coupled Thermo-Hydro-Mechanical (THM) behavior in geological porous media has been a subject of great interest in many geoengineering disciplines. Many attempts have been made to develop numerical prediction capabilities associated with topics such as the movement of pollutant plumes, gas injection, energy storage, geothermal energy extraction, and safety assessment of repositories for radioactive waste and spent nuclear fuel. This thesis presents a new numerical modeling approach and a new computer code for simulating coupled THM behavior in geological porous media in general, and compacted bentonite clays in particular, as buffer materials in underground radioactive waste repositories. New governing equations were derived according to the theory of mixtures, considering interactions among solid-phase deformation, flows of water and gases, heat transport, and phase change of water. For three-dimensional problems, eight governing equations were formulated to describe the coupled THM processes. A new thermal conductivity model was developed to predict the thermal conductivity of geological porous media as composite mixtures. The proposed model considers the combined effects of solid mineral composition, temperature, liquid saturation degree, porosity and pressure on the effective thermal conductivity of the porous media. The predicted results agree well with the experimental data for MX80 bentonite. A new water retention curve model was developed to predict the suction-saturation behavior of the geological porous media, as a function of suction, effective saturated degree, temperature, porosity, pore-gas pressure, and the rate of saturation degree change with time. The model was verified against experimental data of the FEBEX bentonite, with good agreement between measured and calculated results. A new finite element code (ROLG) was developed for modeling fully coupled thermo-hydro-mechanical processes in geological porous media. The new code was validated against several analytical solutions and experiments, and was applied to simulate the large scale in-situ Canister Retrieval Test (CRT) at Äspö Hard Rock Laboratory, SKB, Sweden, with good agreement between measured and predicted results. The results are useful for performance and safety assessments of radioactive waste repositories. / QC20100720 / THERESA

Fluid flows mainly driven by capillary forces are presented in this thesis. By means of modeling and simulations, interesting dynamics in capillary-driven flows are revealed such as coalescences, breakups, precursor films, flow instabilities, rapid spreading, rigid body motions, and reactive wetting. Diffuse-interface methods model a fluid interface as having a finite thickness endowed with physical properties such as surface tension. Two diffuse-interface models that are based on the free energy of the system are presented. The binary model, more specifically the coupled Navier-Stokes/Cahn-Hilliard equations, was used to study different two-phase flows including problems related to microfluidics. Numerical issues using this model have been addressed such as the need for mesh adaptivity and time-step restrictions. Moreover, the flexibility of this model to simulate 2D, axisymmetric, and 3D flows has been demonstrated. The factors affecting reproducibility of microdroplet depositions performed under a liquid medium are investigated. In the deposition procedure, sample solution is dispensed from the end of a capillary by the aid of a pressure pulse onto a substrate with pillar-shaped sample anchors. In both the experimental and numerical study it was shown that the deposited volume mainly depends on the capillary-substrate distance and anchor surface wettability. Furthermore, a critical equilibrium contact angle has been identified below which reproducible depositions are facilitated. The ternary model is developed for more complicated flows such as liquid phase sintering. With the introduction of a Gibbs energy functional, the governing equations are derived, consisting of convective concentration and phase-field equations which are coupled to the Navier-Stokes equations with surface tension forces. Arbitrary phase diagrams, surface energies, and typical dimensionless numbers are some input parameters into the model. Detailed analysis of the important capillary phenomena in liquid phase sintering such as reactive and nonreactive wetting and motion of two particles connected by a liquid bridge are presented. The dynamics of the wetting is found to match with a known hydrodynamic theory for spreading liquids. Factors affecting the equilibrium configuration of the particles such as equilibrium contact angles and volume ratios are also investigated. / QC 20100823

Liquid fragmentation phenomenon is explored from both a fundamental (fully resolved) and an engineering (modeled) perspective. The dual objectives compliment each other by providing an avenue to gain further understanding into fundamental processes of atomization as well as to use the newly acquired knowledge to address practical concerns. A compressible five-equation interface model based on a Roe-type scheme for the simulation of material boundaries between immiscible fluids with arbitrary equation of state is developed and validated. The detailed simulation model accounts for surface-tension, viscous, and body-force effects, in addition to acoustic and convective transport. The material interfaces are considered as diffused zones and a mixture model is given for this transition region. The simulation methodology combines a high-resolution discontinuity capturing method with a low-dissipation central scheme resulting in a hybrid approach for the solution of time- and space-accurate interface problems. Several multi-dimensional test cases are considered over a wide range of physical situations involving capillary, viscosity, and gravity effects with simultaneous presence of large viscosity and density ratios. The model is shown to accurately capture interface dynamics as well as to deal with dynamic appearance and disappearance of material boundaries. Simulation of atomization processes and its interaction with the flow field in practical devices is the secondary objective of this study. Three modeling requirements are identified to perform Large-Eddy Simulation (LES) of spray combustion in engineering devices. In concurrence with these requirements, LES of an experimental liquid-fueled Lean Direct Injection (LDI) combustor is performed using a subgrid mixing and combustion model. This approach has no adjustable parameters and the entire flow-path through the inlet swirl vanes is resolved. The inclusion of the atomization aspects within LES eliminates the need to specify dispersed-phase size-velocity correlations at the inflow boundary. Kelvin-Helmholtz (or aerodynamic) breakup model by Reitz is adopted for the combustor simulation. Two simulations (with and without breakup) are performed and compared with measurements of Cai et al. Time-averaged velocity prediction comparison for both gas- and liquid-phase with available data show reasonable agreement. The major impact of breakup is on the fuel evaporation in the vicinity of the injector. Further downstream, a wide range of drop sizes are recovered by the breakup simulation and produces similar spray quality as in the no-breakup case.

Up to date, sludge filterability has been characterized by the Ruth&rsquo / s classical filtration theory and quantified by the well-known parameter specific cake resistance (SCR). However, the complexity of the actual phenomenon is clearly underestimated by the classical filtration theory and SCR is often not satisfactory in describing filterability. Although many scientific studies were conducted for a better analysis and understanding of the filtration theory, still a practically applicable solution to replace the classical theory for a better description of filterability has not been proposed yet. In the present study, blocking filtration laws proposed by Hermans and Bred&eacute / e, dating back to 1936, which have been extensively used in the membrane literature for the analysis of fouling phenomenon and the multiphase filtration theory developed by Willis and Tosun (1980) highlighting the importance of the cake-septum interface in determining the overall filtration rate have been adopted for the analysis of filterability of sludge systems. Firstly, the inadequacy of the classical filtration theory in characterizing the filterability of real sludge systems and also the lack of the currently used methodology in simulating filtration operation was highlighted. Secondly, to better understand the effect of slurry characteristics and operational conditions on filtration, model slurries of spherical and incompressible Meliodent particles were formed. Finally, a methodology was developed with the gathered filtration data to assess the filterability of the sludge systems by both theories. The results clearly show that both approaches were superior to the classical approach in terms of characterizing the filterability of sludge systems. While blocking laws yielded a slurry specific characterization parameter to replace the commonly used SCR, the multiphase theory provided a better understanding of the physical reality of the overall process.

Integrated theoretical and experimental analysis is carried out in this work to investigate the fundamental failure mechanisms and flow patterns involved in the process of fluid injection into dense granular media. The experimental work is conducted with aqueous glycerin solutions, utilizing a novel setup based on a Hele-Shaw cell filled with dense dry sand. The two dimensional nature of the setup allows direct visualization and imaging analysis of the real-time fluid and grain kinematics. The experimental results reveal that the fluid flow patterns show a transition from simple radial flow to a ramified morphology while the granular media behaviors change from that of rigid porous media to localized failure that lead to development of fluid channels. Based on the failure/flow patterns, four distinct failure/flow regimes can be identified, namely, (i) a simple radial flow regime, (ii) an infiltration-dominated regime, (iii) a grain displacement-dominated regime, and (iv) a viscous fingering-dominated regime. These distinct failure/flow regimes emerge as a result of competition among various energy dissipation mechanisms, namely, viscous dissipation through infiltration, dissipation due to grain displacements, and viscous dissipation through flow in thin channels and can be classified based on the characteristic times associated with fluid injection, hydromechanical coupling and viscoelastoplasticity. The injection process is also analyzed numerically using the discrete element method (DEM) coupled with two fluid flow scheme, a fixed coarse grid scheme based on computational fluid dynamics (CFD) and a pore network modeling scheme. The numerical results from the two complementary methods reproduce phenomena consistent with the experimental observations and justify the concept of associating the displacement regimes with the partition among energy dissipation mechanisms. The research in this work, though fundamental in nature, will have direct impacts on many engineering problems in civil, environmental and petroleum engineering such as ground improvement, environmental remediation and reservoir stimulation.

De nouvelles architectures de synthétiseur de fréquence sont proposées basées soit sur la mise en parallèle de boucles (PLL composite), soit la mise en oeuvre d'un comparateur PFD multiphase, soit l'introduction d'un ordre non entier dans le filtre de boucle. A chaque fois, une augmentation sensible de la bande passante est obtenue, permettant en retour une optimisation du bruit de phase du générateur de fréquence.

Gas-Partikel-Stroemungen finden sich in weiten Bereichen der Energie- und Verfahrenstechnik. Beispiele fuer haeu- fig anzutreffende Problemstellungen sind der Transport, die Separation oder die Injektion eines Gemisches aus festen Partikeln und einem Traegergas. Fuer die numerische Simulation solcher disperser Mehr- phasenstroemungen hat sich das Lagrange-Verfahren als besonders geeignet erwiesen. Andererseits stellt die An- wendung dieses Berechnungsverfahrens hoechste Anforderun- gen an die Ressourcen der verwendeten Rechner. Dies gilt im besonderen Masse fuer die Simulation von Stroemungen mit einer moderaten bis hohen Partikelbeladung, in denen die Partikel-Partikel-Kollisionen einen grossen Einfluss auf das Stroemungsverhalten haben. Um das grosse Leistungspotential, das heutige massiv par- allele Hochleistungsrechner bieten, effizient zu nutzen, wurden im Rahmen dieser Arbeit parallele Simulationsalgo- rithmen fuer die numerische Berechnung kollisionsbehafte- ter Gas-Partikel-Stroemungen entwickelt. Die Effizienz dieser Algorithmen wurde anhand verschiedener Testfaelle untersucht. Auf der Grundlage der dabei erzielten Ergeb- nisse wurden Vorschlaege fuer weitere Entwicklungsmoeg- lichkeiten erarbeitet. / Gas-particle-flows can be found widely in the field of energy production and process engineering. Examples for applications of such kind of flows are transport, se- paration or injection of a mixture of solid particles and a gaseous phase. The Lagrangian approach has proved to be a suitable means for the numerical simulation of disperse multiphase flows. On the other hand its application requires a large amount of computational power, especially when flows with a mo- derate or high particle loading are computed and particle- particle collisions have a significant influence on the flow. In order to use efficiently the large computational power that parallel computers provide nowadays, parallel algo- rithms for the numerical simulation of gas-particle flows including particle-particle collisions were developed in the cource of this work. The algorithms' efficiency was investigated considering different test cases. On the basis of the results suggestions for further developments were made.

In dieser Arbeit werden die Zeitpunkte der Kontrastmittelphasen der Leber bei Hunden verschiedener Größe und Rasse untersucht. Diese werden mit klinischen Parametern wie der Körpermasse, dem Alter und der Herzfrequenz zum Zeitpunkt der Untersuchung korreliert. In der vorliegenden Arbeit wird diskutiert, ob anhand dieser einfach erfassbarer Patientenparametern eine zielführende Planung einer Multiphasen-CT möglich ist. Es werden folgenden Zielstellungen bearbeitet: 1. Wann ist der Beginn der früharteriellen, arteriellen und der portalvenösen Phase erreicht? 2. Wann ist der Zeitpunkt des Kontrastmittelpeaks in der Aorta abdominalis und der V. portae erreicht? 3. Erstellen von Korrelationen dieser Zeitpunkte mit dem Alter, dem Gewicht und der Herzfrequenz der Tiere. 4. Erstellen von klinisch anwendbaren Regressionsgleichungen. An insgesamt 145 Tieren wurde das Anflutungsverhalten des jodhaltigen Kontrastmittels Imeron® 300 Bracco in der Leber und den zuführenden Gefäßen (Aorta abdominalis und V. portae) untersucht. Dabei wurden die Programme Bolus Tracking (BT) und das Perfusion Protokoll (dynamisches CT/ DU) mit dem CT Philips Brilliance CT 6 MX 8000 IDT genutzt. Die hierfür verwandten Hunde stammten aus dem Patientengut der Klinik für Kleintiere der Universität Leipzig. Alle Tiere erhielten 2 ml/kg Imeron® 300 Bracco mit 3 ml/s in die rechte oder linke V. cephalica antebrachii mit einem automatischen Injektor durch eine 20 Gauge Flexüle appliziert. Dies entspricht einer Jodmenge von 600 mg/kg. Aufgrund der Einteilung der Tiere in ASA-Gruppen und der weiteren Diagnostik und Therapie wurden vier verschiedene Narkoseprotokolle angewandt. Alle Tiere wurden intubiert und die Narkose mit Isofluran aufrechterhalten. Das Narkoseregime führte bei keinem der untersuchten Parameter zu einem signifikanten Unterschied. Der Beginn der früharteriellen und der portalvenösen Phase wurde mit Bolus Tracking bei 106 Hunden untersucht. Als Beginn wurde ein absoluter Schwellenwert von 100 HE im Aortenlumen auf Höhe des kranialen Leberpols bzw. im Lumen der Vena portae definiert. Mit dieser Methode wurde eine Überschreitung des Schwellenwertes im Aortenlumen im Mittelwert nach 13,12 ± 3,6 Sekunden (64 Tiere) und im Lumen der V. portae nach 31,60 ± 8,6 Sekunden (42 Tiere) gemessen. Eine signifikante Korrelation mit dem Gewicht auf einem zweiseitigen Signifikanzniveau von 0,01 konnte festgestellt werden. Mit der dynamischen CT (DU) wurden 39 Tiere untersucht. Der Beginn der früharteriellen Phase (Schwellenwert von 100 HE im Lumen der Aorta abdominalis) wurde nach 9,77 ± 4,3 Sekunden und der portalvenösen Phase (Schwellenwert von 100 HE im Lumen der Vena portae) nach 27,6 ± 8,7 Sekunden erreicht. Die Korrelationskoeffizienten der mit der DU gemessenen Parameter und der Patientenparametern sind höher als die mit dem BT erstellten und werden deshalb hier aufgeführt. Mit der vorwärtsgerichteten Regression konnten die folgenden Modelle erstellt werden. Früharterielle Phase (s) 0,35 + 0,21 x Körpermasse R = 0,61 Portalvenöse Phase (s) 13,9 + 0,7 x Körpermasse R = 0,67 An denselben Tieren wurde auch der Zeitpunkt des arteriellen und portalvenösen Peaks im Gefäßlumen der Aorta abdominalis und der Vena portae gemessen. Dieser wurde im Mittelwert nach 24,5 ± 8,6 Sekunden und nach 43,6 ± 13,4 Sekunden erreicht. Der Zeitpunkt des arteriellen Peaks weist den höchsten Korrelationskoeffizienten mit dem Gewicht in der vorliegenden Arbeit auf. Anhand einer vorwärtsgerichteten Regression konnten die folgenden Modelle erstellt werden. Arterieller Peak1 (s) 6,13 + 0,63 x Körpermasse R = 0,9 Arterieller Peak2 (s) 12,23 + 0,61 x Körpermasse – 0,07 Herzfrq. R = 0,92 Portalvenöser Peak1 (s) 24,5 + 0,65 x Körpermasse R = 0,6 Portalvenöser Peak2 (s) 17,5 + 0,71 x Körpermasse – 0,07 Alter R = 0,66 Die Ergebnisse zeigen, dass anhand einfach erfassbarer Patientenparametern bedingt eine zielführende Planung einer Multiphasen-CT möglich ist. Aufgrund der sehr hohen Korrelationskoeffizienten zwischen dem arteriellen Peak und den klinischen Parametern ist die Anwendung dieser Gleichungen zum Errechnen des arteriellen Peaks sehr sinnvoll klinisch anzuwenden. Da diese Arbeit den Nachweis erbracht hat, dass zum Zeitpunkt des arteriellen Peaks noch eine auswertbare arterielle Phase im Leberparenchym besteht, kann diese Gleichung sowohl bei der Detektion von Leberherden als auch bei Gefäßanomalien genutzt werden.