An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Numerical modelling of the impact of climate change on the morphology of Saint-Lawrence tributaries

Cette thèse examine les impacts sur la morphologie des tributaires du fleuve Saint-Laurent des changements dans leur débit et leur niveau de base engendrés par les changements climatiques prévus pour la période 2010–2099. Les tributaires sélectionnés (rivières Batiscan, Richelieu, Saint-Maurice, Saint-François et Yamachiche) ont été choisis en raison de leurs différences de taille, de débit et de contexte morphologique. Non seulement ces tributaires subissent-ils un régime hydrologique modifié en raison des changements climatiques, mais leur niveau de base (niveau d’eau du fleuve Saint-Laurent) sera aussi affecté. Le modèle morphodynamique en une dimension (1D) SEDROUT, à l’origine développé pour des rivières graveleuses en mode d’aggradation, a été adapté pour le contexte spécifique des tributaires des basses-terres du Saint-Laurent afin de simuler des rivières sablonneuses avec un débit quotidien variable et des fluctuations du niveau d’eau à l’aval. Un module pour simuler le partage des sédiments autour d’îles a aussi été ajouté au modèle. Le modèle ainsi amélioré (SEDROUT4-M), qui a été testé à l’aide de simulations à petite échelle et avec les conditions actuelles d’écoulement et de transport de sédiments dans quatre tributaires du fleuve Saint-Laurent, peut maintenant simuler une gamme de problèmes morphodynamiques de rivières. Les changements d’élévation du lit et d’apport en sédiments au fleuve Saint-Laurent pour la période 2010–2099 ont été simulés avec SEDROUT4-M pour les rivières Batiscan, Richelieu et Saint-François pour toutes les combinaisons de sept régimes hydrologiques (conditions actuelles et celles prédites par trois modèles de climat globaux (MCG) et deux scénarios de gaz à effet de serre) et de trois scénarios de changements du niveau de base du fleuve Saint-Laurent (aucun changement, baisse graduelle, baisse abrupte). Les impacts sur l’apport de sédiments et l’élévation du lit diffèrent entre les MCG et semblent reliés au statut des cours d’eau (selon qu’ils soient en état d’aggradation, de dégradation ou d’équilibre), ce qui illustre l’importance d’examiner plusieurs rivières avec différents modèles climatiques afin d’établir des tendances dans les effets des changements climatiques. Malgré le fait que le débit journalier moyen et le débit annuel moyen demeurent près de leur valeur actuelle dans les trois scénarios de MCG, des changements importants dans les taux de transport de sédiments simulés pour chaque tributaire sont observés. Ceci est dû à l’impact important de fortes crues plus fréquentes dans un climat futur de même qu’à l’arrivée plus hâtive de la crue printanière, ce qui résulte en une variabilité accrue dans les taux de transport en charge de fond. Certaines complications avec l’approche de modélisation en 1D pour représenter la géométrie complexe des rivières Saint-Maurice et Saint-François suggèrent qu’une approche bi-dimensionnelle (2D) devrait être sérieusement considérée afin de simuler de façon plus exacte la répartition des débits aux bifurcations autour des îles. La rivière Saint-François est utilisée comme étude de cas pour le modèle 2D H2D2, qui performe bien d’un point de vue hydraulique, mais qui requiert des ajustements pour être en mesure de pleinement simuler les ajustements morphologiques des cours d’eau.

Studies on Some Aspects of Light Beam Propagation Through Certain Nonlinear Media

This thesis deals with the study of light beam propagation through different nonlinear media. Analytical and numerical methods are used to show the formation of solitonS in these media. Basic experiments have also been performed to show the formation of a self-written waveguide in a photopolymer. The variational method is used for the analytical analysis throughout the thesis. Numerical method based on the finite-difference forms of the original partial differential equation is used for the numerical analysis.In Chapter 2, we have studied two kinds of solitons, the (2 + 1) D spatial solitons and the (3 + l)D spatio-temporal solitons in a cubic-quintic medium in the presence of multiphoton ionization.In Chapter 3, we have studied the evolution of light beam through a different kind of nonlinear media, the photorcfractive polymer. We study modulational instability and beam propagation through a photorefractive polymer in the presence of absorption losses. The one dimensional beam propagation through the nonlinear medium is studied using variational and numerical methods. Stable soliton propagation is observed both analytically and numerically.Chapter 4 deals with the study of modulational instability in a photorefractive crystal in the presence of wave mixing effects. Modulational instability in a photorefractive medium is studied in the presence of two wave mixing. We then propose and derive a model for forward four wave mixing in the photorefractive medium and investigate the modulational instability induced by four wave mixing effects. By using the standard linear stability analysis the instability gain is obtained.Chapter 5 deals with the study of self-written waveguides. Besides the usual analytical analysis, basic experiments were done showing the formation of self-written waveguide in a photopolymer system. The formation of a directional coupler in a photopolymer system is studied theoretically in Chapter 6. We propose and study, using the variational approximation as well as numerical simulation, the evolution of a probe beam through a directional coupler formed in a photopolymer system.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Thermoaktive Bauteilsysteme - Ein neuer simulationstechnischer Berechnungsansatz

Thermoaktive Bauteilsysteme sind Bauteile, die als Teil der Raumumschließungsflächen über ein integriertes Rohrsystem mit einem Heiz- oder Kühlmedium beaufschlagt werden können und so die Beheizung oder Kühlung des Raumes ermöglichen. Die Konstruktionenvielfalt reicht nach diesem Verständnis von Heiz, bzw. Kühldecken über Geschoßtrenndecken mit kern-integrierten Rohren bis hin zu den Fußbodenheizungen. Die darin enthaltenen extrem trägen Systeme werden bewußt eingesetzt, um Energieangebot und Raumenergiebedarf unter dem Aspekt der rationellen Energieanwendung zeitlich zu entkoppeln, z. B. aktive Bauteilkühlung in der Nacht, passive Raumkühlung über das kühle Bauteil am Tage. Gebäude- und Anlagenkonzepte, die träge reagierende thermoaktive Bauteilsysteme vorsehen, setzen im kompetenten und verantwortungsvollen Planungsprozeß den Einsatz moderner Gebäudesimulationswerkzeuge voraus, um fundierte Aussagen über Behaglichkeit und Energiebedarf treffen zu können. Die thermoaktiven Bauteilsysteme werden innerhalb dieser Werkzeuge durch Berechnungskomponenten repräsentiert, die auf mathematisch-physikalischen Modellen basieren und zur Lösung des bauteilimmanenten mehrdimensionalen instationären Wärmeleitungsproblems dienen. Bisher standen hierfür zwei unterschiedliche prinzipielle Vorgehensweisen zur Lösung zur Verfügung, die der physikalischen Modellbildung entstammen und Grenzen bzgl. abbildbarer Geometrie oder Rechengeschwindigkeit setzen. Die vorliegende Arbeit dokumentiert eine neue Herangehensweise, die als experimentelle Modellbildung bezeichnet wird. Über den Weg der Systemidentifikation können aus experimentell ermittelten Datenreihen die Parameter für ein kompaktes Black-Box-Modell bestimmt werden, das das Eingangs-Ausgangsverhalten des zugehörigen beliebig aufgebauten thermoaktiven Bauteils mit hinreichender Genauigkeit widergibt. Die Meßdatenreihen lassen sich über hochgenaue Berechnungen generieren, die auf Grund ihrer Detailtreue für den unmittelbaren Einsatz in der Gebäudesimulation ungeeignet wären. Die Anwendung der Systemidentifikation auf das zweidimensionale Wärmeleitungsproblem und der Nachweis ihrer Eignung wird an Hand von sechs sehr unterschiedlichen Aufbauten thermoaktiver Bauteilsysteme durchgeführt und bestätigt sehr geringe Temperatur- und Energiebilanzfehler. Vergleiche zwischen via Systemidentifikation ermittelten Black-Box-Modellen und physikalischen Modellen für zwei Fußbodenkonstruktionen zeigen, daß erstgenannte auch als Referenz für Genauigkeitsabschätzungen herangezogen werden können. Die Praktikabilität des neuen Modellierungsansatzes wird an Fallstudien demonstriert, die Ganzjahressimulationen unter Bauteil- und Betriebsvariationen an einem exemplarischen Büroraum betreffen. Dazu erfolgt die Integration des Black-Box-Modells in das kommerzielle Gebäude- und Anlagensimulationsprogramm CARNOT. Die akzeptablen Rechenzeiten für ein Einzonen-Gebäudemodell in Verbindung mit den hohen Genauigkeiten bescheinigen die Eignung der neuen Modellierungsweise.

A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.

A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

Benchmarking 2D hydraulic models for urban flooding

This paper describes benchmark testing of six two-dimensional (2D) hydraulic models (DIVAST, DIVASTTVD, TUFLOW, JFLOW, TRENT and LISFLOOD-FP) in terms of their ability to simulate surface flows in a densely urbanised area. The models are applied to a 1·0 km × 0·4 km urban catchment within the city of Glasgow, Scotland, UK, and are used to simulate a flood event that occurred at this site on 30 July 2002. An identical numerical grid describing the underlying topography is constructed for each model, using a combination of airborne laser altimetry (LiDAR) fused with digital map data, and used to run a benchmark simulation. Two numerical experiments were then conducted to test the response of each model to topographic error and uncertainty over friction parameterisation. While all the models tested produce plausible results, subtle differences between particular groups of codes give considerable insight into both the practice and science of urban hydraulic modelling. In particular, the results show that the terrain data available from modern LiDAR systems are sufficiently accurate and resolved for simulating urban flows, but such data need to be fused with digital map data of building topology and land use to gain maximum benefit from the information contained therein. When such terrain data are available, uncertainty in friction parameters becomes a more dominant factor than topographic error for typical problems. The simulations also show that flows in urban environments are characterised by numerous transitions to supercritical flow and numerical shocks. However, the effects of these are localised and they do not appear to affect overall wave propagation. In contrast, inertia terms are shown to be important in this particular case, but the specific characteristics of the test site may mean that this does not hold more generally.

The three-dimensional vortical nature of atmospheric and oceanic turbulent flows

Using a novel numerical method at unprecedented resolution, we demonstrate that structures of small to intermediate scale in rotating, stratified flows are intrinsically three-dimensional. Such flows are characterized by vortices (spinning volumes of fluid), regions of large vorticity gradients, and filamentary structures at all scales. It is found that such structures have predominantly three-dimensional dynamics below a horizontal scale LLR, where LR is the so-called Rossby radius of deformation, equal to the characteristic vertical scale of the fluid H divided by the ratio of the rotational and buoyancy frequencies f/N. The breakdown of two-dimensional dynamics at these scales is attributed to the so-called "tall-column instability" [D. G. Dritschel and M. de la Torre Juárez, J. Fluid. Mech. 328, 129 (1996)], which is active on columnar vortices that are tall after scaling by f/N, or, equivalently, that are narrow compared with LR. Moreover, this instability eventually leads to a simple relationship between typical vertical and horizontal scales: for each vertical wave number (apart from the vertically averaged, barotropic component of the flow) the average horizontal wave number is equal to f/N times the vertical wave number. The practical implication is that three-dimensional modeling is essential to capture the behavior of rotating, stratified fluids. Two-dimensional models are not valid for scales below LR. ©1999 American Institute of Physics.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Lagrangian validation of numerical drifter trajectories using drifting buoys: Application to the Agulhas system

The skill of numerical Lagrangian drifter trajectories in three numerical models is assessed by comparing these numerically obtained paths to the trajectories of drifting buoys in the real ocean. The skill assessment is performed using the two-sample Kolmogorov–Smirnov statistical test. To demonstrate the assessment procedure, it is applied to three different models of the Agulhas region. The test can either be performed using crossing positions of one-dimensional sections in order to test model performance in specific locations, or using the total two-dimensional data set of trajectories. The test yields four quantities: a binary decision of model skill, a confidence level which can be used as a measure of goodness-of-fit of the model, a test statistic which can be used to determine the sensitivity of the confidence level, and cumulative distribution functions that aid in the qualitative analysis. The ordering of models by their confidence levels is the same as the ordering based on the qualitative analysis, which suggests that the method is suited for model validation. Only one of the three models, a 1/10° two-way nested regional ocean model, might have skill in the Agulhas region. The other two models, a 1/2° global model and a 1/8° assimilative model, might have skill only on some sections in the region

Predicting natural ventilation in a two-zone building driven by combined forces.

Natural ventilation relies on less controllable natural forces so that it needs more artificial control, and thus its prediction, design and analysis become more important. This paper presents both theoretical and numerical simulations for predicting the natural ventilation flow in a two-zone building with multiple openings which is subjected to the combined natural forces. To our knowledge, this is the first analytical solutions obtained so far for a building with more than one zones and in each zone with possibly more than 2 openings. The analytical solution offers a possibility for validating a multi-zone airflow program. A computer program MIX is employed to conduct the numerical simulation. Good agreement is achieved. Different airflow modes are identified and some design recommendations are also provided.

Simulation of thermal performance of horizontal slinky-loop heat exchangers for ground source heat pumps

This paper presents results obtained from a numerical simulation for the horizontal slinky-loop heat exchanger of a ground-source heat pump system. A three-dimensional numerical model was developed and the results of the thermal performance of various heat exchanger configurations are presented. The investigation was carried out on five types of loop pitch (loop spacing), three types of loop diameter, three values of soil thermal properties, and allowing continuous and intermittent operation. Comparison was made for the heat transfer rate, the amount of pipe material needed, as well as excavation work required for the horizontal slinky-loop heat exchanger. The results indicate that system parameters have a significant effect on the thermal performance of the system