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Beschreibung: In this paper we revisit the a priori turbulent flame speed tabulation (TFST) technique for a given parameter space within the region of flamelet combustion-regimes. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. First results are compared quantitatively with direct numerical simulations (DNS) taken from literature. Then it is illustrated in one example how the new method could help to fix constants in algebraic models for turbulent flame speeds. Further it is shown how the technique can be extended to incorporate turbulent strain effects. Finally we investigate the effect of the use of detailed and tabulated chemistry under unsteady conditions.

Beschreibung: A world-wide used program for the simulation of fire-induced flows is the Fire Dynamics Simulator (FDS) which originally was developed for a purely serial execution on single-processor computing systems. Due to steadily increasing problem sizes and accuracy requirements as well as restrictions in storage capacity and computing power on single-processor systems, the efficient simulation of the considered fire scenarios can only be achieved on modern high-performance systems based on multi-processor architectures. The transition to those systems requires the elaborate parallelization of the underlying numerical methods which must guarantee the same result for a given problem as the corresponding serial execution. Unfortunately, one fundamental serial serial solver of FDS, the pressure solver, only possesses a low degree of inherent parallelizm. Its current parallelization may cause additional numerical errors, casually leading to significant losses of accuracy or even numerical instabilities. In order to ensure that the parallelization errors are limited by the leading error of the numerical scheme such that second order convergence for the whole method can be acchieved, optimized parallelization concepts must be designed. With respect to these considerations this articles gives an overview of the current parallel pressure solver as well as the problems related to it and presents an alternative method, SCARC, to overcome the existing complicacies. Part I explains the theory, concept and implementation of this new strategy, whereas Part II describes a series of validation and verification tests to proof its correctness.

Beschreibung: Because CFD programs, like FDS, generally consist of a large number of different components representing the variety of participating numerical algorithms and chemical / physical processes, it is nearly impossible to verify such codes in their entirety, for example with comparisons of fire tests. Instead, a careful verification and validation with respect to the underlying mathematical conditions and applied numerical schemes is indispensable. In particular, error cancelations between single program components can only be detected by such detailed component-level tests. In part I of this article series a conceptual deficiency of the FDS program package with regard to multi-mesh computations was illustrated and an alternative domain decomposition strategy FDS-ScaRC was introduced. In this second part we will present the structure of a comprehensive test concept and the needs for a more mathematically and numerically orientated test procedure that is much more suited for a reliable evaluation than only a simple visual comparison of the numerical results with experimental fire tests. After a general introduction of our test concept we will demonstrate the high potential of the new FDS-\scarc{} technique compared to the FDS-FFT technique which is used in the FDS program package as yet. Based on this concept, we will present a comprehensive set of analytical and numerical test results.

Beschreibung: In this paper we propose a technique for a priori turbulent flame speed tabulation (TFST) for a given parameter space in standard combustion-regime diagrams. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. Results are compared to an algebraic model and to direct numerical simulations (DNS).

Beschreibung: The influence of thermal stratification on autoignition at constant volume and high pressure is investigated under turbulent conditions using the one-dimensional Linear-Eddy Model (LEM) and detailed hydrogen/air chemistry. Results are presented for the influence of initial temperature inhomogeneities on the heat release rate and the relative importance of diffusion and chemical reactions. The predicted heat release rates are compared with heat release rates of Chen et al. and Hawkes et al. obtained by two-dimensional Direct Numerical Simulations (DNS). Using the definition of Chen et al. for the displacement speed of the H2 mass fraction tracked at the location of maximum heat release, and a comparison of budget terms, different combustion modes including ignition front propagation and deflagration waves are identified and the results are compared to the DNS data. The LEM approach shows qualitatively and quantitatively reasonable agreement with the DNS data over the whole range of investigated temperature fluctuations. The results presented in this work suggest that LEM is a potential candidate as a sub-model for CFD calculations of HCCI engines.

Beschreibung: Asymptotic analyses of the three dimensional compressible flow equations coupled with transport equations for the mixing ratios of water vapour, cloud water and rain water are described. We obtain reduced systems of equations for two particular regimes of length and time scales: Models for the long time evolution of deep convective columns and for the short time evolution of shallow convective layers. The asymptotic deep convective column model is anelastic, yet the vertical motion is pressure free, i.e., it evolves freely in interaction with buoyancy while the horizontal divergence adjusts to fullfil the anelastic constraint. The perturbation pressure guaranteeing compliance with the horizontal divergence constraint obeys a Poisson-type equation. Surprisingly, the vertical velocity plays an important role in the horizontal dynamics through the Coriolis term. The vertical acceleration in a saturated column is directly determined by the buoyancy induced by potential temperature differences relative to the background stratification. This potential temperature deviation is a conserved quantity. Evaporation is the only important microphysical process in the undersaturated regime. The evaporation rate depends on the saturation deficit and the amount of rain water present and determines the (downward) vertical velocity and the distribution of water vapour. To connect the deep convective column solutions to top and bottom boundary conditions, a different flow regime needs to be accounted for. Within shallow layers whose depth is comparable to the column diameters, adjustment to physical boundary conditions can take place. This is the second regime considered in this report. The shallow convective layer regime is shown to be asymptotically described by Boussinesq-type equations. These equations are closed by evolution equations which show that, in the saturated regime, the distributions of potential temperature and cloud water are determined by a condensation rate that is directly proportional to the vertical velocity. In the undersaturated regime, the potential temperature distribution is determined by the amount of rain present, since the water vapour in this case is shown to be a conserved quantity. In both regimes the distribution of rain water depends on the rain water flux.

Beschreibung: By use of asymptotic analysis Carqué et al. [ZIB-Report 08-03] derived an asymptotic column model for deep convective clouds based on the three dimensional compressible flow equations and a bulk microphysics parameterization. In the present study we check the plausibility of the reduced model equations by comparing implications of the model for the scaling of various terms in the governing equations with those extracted from large eddy simulation data based on the computational model UCLA-LES1.1. This code solves an anelastic system of equations with complete droplet based microphysics and LES closures. We observe that the simulation data corroborate the basic assumptions of the asymptotic analysis and the main conclusions implied by the asymptotically reduced model. The code output reflects the scales of space and time: The deep convective clouds show an anisotropic structure where the horizontal scale is considerably narrower than the vertical scale; with a period of about 20 min, from emergence to breakup, the life cycle of one particular deep convective cloud corresponds exactly to the reference time of the reduced model. The characteristic properties of dynamics as predicted by the reduced model are also reflected in the simulation data: The horizontal flow is controlled by the pressure field; the vertical velocity develops freely independent of pressure over the depth of the convective column; the vertical velocity is directly determined by the buoyancy induced by the potential temperature deviation relative to the background stratification. With respect to grid resolution we observe that refining the spatial step size of the equidistant computational grid from 125 m to 62.5 m does not influence the results: Even with the coarser grid the relevant physical phenomena are sufficiently resolved. Somewhat surprisingly, the Coriolis term involving vertical velocity and acting on the horizontal (east-west) velocity component appears at leading order in the asymptotics. Accordingly, we expected to find a nontrivial impact of this Coriolis effect on the horizontal flow velocity components within columns of updrafts. However, switching the term on and off in subsequent simulations did not sizeably affect the results.

Beschreibung: A theoretical and numerical small-scale study of the evaporative cooling phenomenon that might appear in the stratocumulus-topped boundary layers is presented. An ideal configuration of a cloud-top mixing layer is considered as defined by two nonturbulent horizontal layers, stably stratified and with buoyancy reversal within a certain range of mixture fractions due to the evaporative cooling. Linear stability analysis of the shear-free configuration is employed to provide a new interpretation of the buoyancy reversal parameter, namely, in terms of a time-scale ratio between the unstable and the stable modes of the system. An incompressible high-order numerical algorithm to perform direct numerical simulation of the configuration is described and two-dimensional simulations of single-mode perturbations are discussed. These simulations confirm the role of the different parameters identified in the linear stability analysis and show that convoluted flow patterns can be generated by the evaporative cooling even for the low levels of buoyancy reversal found in stratocumulus clouds. They also show that there is no enhancement of entrainment of upper layer fluid in the shear-free configuration, and mixing enhancement by the evaporative cooling is restricted to the lower layer.

Beschreibung: In der Arbeit wird die computergestützte Planung von chirurgisch gesetzten Knochenfrakturen bzw. Knochenschnitten (sogenannten Osteotomien) an dreidimensionalen, computergrafischen Schädelmodellen, sowie die Umpositionierung separierter knöcherner Segmente im Kontext der rekonstruktiven MKG-Chirurgie behandelt. Durch die 3D Modellierung und Visualisierung anatomischer Strukturen, sowie der 3D Osteotomie- und Umstellungsplanung unter Einbeziehung der resultierenden Weichgewebedeformation wird den Chirurgen ein Werkzeug an die Hand gegeben, mit dem eine Therapieplanung am Computer durchgeführt und diese in Hinblick auf Funktion und Ästhetik bewertet werden kann. Unterschiedliche Strategien können dabei erprobt und in ihrer Auswirkung erfasst werden. Dazu wird ein methodischer Ansatz vorgestellt, der zum einen die chirurgische Planung im Vergleich zu existierenden Ansätzen deutlich verbessert und zum anderen eine robuste Weichgewebeprognose, durch den Einsatz geeigneter Planungsmodelle und eines physikalisch basierten Weichgewebemodells unter Nutzung numerischer Lösungsverfahren in die Planung integriert. Die Visualisierung der Planungsergebnisse erlaubt sowohl eine anschauliche und überzeugende, präoperative Patientenaufklärung, als auch die Demonstration möglicher Vorgehensweisen und deren Auswirkungen für die chirurgische Ausbildung. Ferner ergänzen die Planungsdaten die Falldokumentation und liefern einen Beitrag zur Qualitätssicherung. Die Arbeit ist in sieben Kapitel gegliedert und wie folgt strukturiert: Zuerst wird die medizinische Aufgabenstellung bei der chirurgischen Rekonstruktion von Knochenfehlbildungen und -fehlstellungen in der kraniofazialen Chirurgie sowie die daraus resultierenden Anforderungen an die Therapieplanung beschrieben. Anschließend folgt ein umfassender Überblick über entsprechende Vorarbeiten zur computergestützten Planung knochenverlagernder Operationen und eine kritische Bestandsaufnahme der noch vorhandenen Defizite. Nach der Vorstellung des eigenen Planungsansatzes wird die Generierung individueller, qualitativ hochwertiger 3D Planungsmodelle aus tomografischen Bilddaten beschrieben, die den Anforderungen an eine intuitive, 3D Planung von Umstellungsosteotomien entsprechen und eine Simulation der daraus resultierenden Weichgewebedeformation mittels der Finite-Elemente Methode (FEM) ermöglichen. Die Methoden der 3D Schnittplanung an computergrafischen Modellen werden analysiert und eine 3D Osteotomieplanung an polygonalen Schädelmodellen entwickelt, die es ermöglicht, intuitiv durch Definition von Schnittlinien am 3D Knochenmodell, eine den chirurgischen Anforderungen entsprechende Schnittplanung unter Berücksichtigung von Risikostrukturen durchzuführen. Separierte Knochensegmente lassen sich im Anschluss interaktiv umpositionieren und die resultierende Gesamtanordnung hinsichtlich einer funktionellen Rehabilitation bewerten. Aufgrund des in dieser Arbeit gewählten, physikalisch basierten Modellierungsansatzes kann unter Berücksichtigung des gesamten Weichgewebevolumens aus der Knochenverlagerung direkt die resultierende Gesichtsform berechnet werden. Dies wird anhand von 13 exemplarischen Fallstudien anschaulich demonstriert, wobei die Prognosequalität mittels postoperativer Fotografien und postoperativer CT-Daten überprüft und belegt wird. Die Arbeit wird mit einem Ausblick auf erweiterte Modellierungsansätze und einem Konzept für eine integrierte, klinisch einsetzbare Planungsumgebung abgeschlossen.

Beschreibung: In cranio-maxillofacial surgery, physicians are often faced with skeletal malformations that require complex bone relocations. Especially in severe cases of congenital dysgnathia (misalignment of upper and lower jaw) or hemifacial microsomia (asymmetric bone and tissue development), where multiple bone segments are to be mobilized and relocated simultaneously and in relation to each other, careful preoperative planning is mandatory. At present in clinical routine not all possible strategies can be planned and assessed with regard to functional rehabilitation. Moreover, the aesthetic outcome, i.e. the postoperative facial appearance, can only be estimated by a surgeon's experience and hardly communicated to the patient. On this account, a preoperative planning of complex osteotomies with bone relocations on a computerized model of a patient's head, including a reliable three-dimensional prediction and visualization of the post-surgical facial appearance is a highly appreciated possibility cranio-maxillofacial surgeons are longing for. This work, being performed at Zuse Institute Berlin (ZIB), addresses such a computer based 3D~surgery planning. A processing pipeline has been established and a simulation environment has been developed on basis of the software Amira, enabling a surgeon to perform bone cuts and bone rearrangements in an intuitive manner on virtual patient models. In addition, a prediction of the patients' postoperative appearance according to the relocated bone can be simulated and visualized realistically. For a meaningful planning of surgical procedures, anatomically correct patient models providing all relevant details are reconstructed from tomographic data with high fidelity. These patient models reliably represent bony structures as well as the facial soft tissue. Unstructured volumetric grids of the soft tissue are generated for a fast and efficient numerical solution of partial differential equations, describing tissue deformation on the foundation of 3D elastomechanics. The planning of osteotomies (bone cuts) for the mobilization and relocation of bone segments is performed in accordance to the planning on basis of life size replicas of a patient's skull, i.e. stereolitographic models. Osteotomy lines can be drawn on top of the polygonal planning models using suitable input devices. After evaluation of the consequence of a planned cut with regard to vulnerable inner structures (nerves, teeth etc.) the model is separated accordingly. A relocation of bone segments can be performed unrestrictedly in 3D or restricted to a translation or rotation within arbitrarily chosen planes under consideration of cephalometric guidelines. Bone and tooth collisions can be evaluated for functional analysis or orthodontic treatment planning with possible integration of digitized dental plaster casts. As a result of the preoperative planning, a single transformation matrix, encoding translation and rotation, or a sequence of such matrices are provided for each bone segment. Both the osteotomy paths and the transformation parameters can finally be used for intra-operative navigation. In the course of the planning, the relocated positions of bone segments serve as an input for the simulation of the resulting soft tissue deformation. Since bone and surrounding soft tissue share common boundaries that are either fixed or translocated, the resulting configuration of the entire tissue volume can be computed from the given boundary displacements by numerical minimization of the internal strain energy on basis of a biomechanical model, using a finite-element approach. In collaboration with different surgeons and hospitals more than 25 treatments have been accompanied by preoperative planning so far ranging from mandibular and midfacial hypoplasia to complex hemifacial microsomia. 13 of these cases are presented within this work. Simulation results were validated on the basis of photographs as well as of postoperative CT data, showing a good correlation between simulation and postoperative outcome. Further aspects of improving the modeling approach are discussed. It has been demonstrated that 3D~osteotomy planning on virtual patient models can be performed intuitively, and that 3D~tissue deformation for cranio-maxillofacial osteotomy planning can be predicted numerically without using heuristic ratios. It can be stated that by using 3D~planning software, a surgeon gains a better spatial understanding of complex dysplasia, and the 3D~soft tissue prediction gives an additional criterion for the assessment of the planned strategy. It turned out that, especially in complex cases such as hemifacial microsomia or for decisions bet­ween mono- and bimaxillary advancements, a 3D~planning aid is extremely helpful. The conclusion is, that images and animations created within the planning phase provide a valuable planning criterion for maxillofacial surgeons as well as a demonstrative information for patients and their relatives, thus greatly enhancing patient information, as well as surgical education. All data that result from the planning are also important for documentation and quality assurance. 3D osteotomy planning, including soft tissue prediction, likely will become a new paradigm of plastic and reconstructive surgery planning in the future. An assortment of results can be found under: http://www.zib.de/visual/medical/projects