Search

We have demonstrated the rich set of hydrodynamic phenomena that operate in a natural lake. State-of-the-art experimental methods yeild a wealth of data that are highly resolved in time and in one space axis. The orthogonal space is sampled only very sparsely, however. Still, such data allow the estimation of crucial effective parameters like vertical diffusion coefficients. Numerical simulations, on the other hand, yeild high resoution results for theentire space. They are thus inherently more powerful than experimental observations and heuristic analysis whenever a complicated to pography is crucial. However, even with the current most advanced slovers, such high-resolution studies of most phenomena on realistic time scales is beyond reach. Confining experiemntal and numerical approaches hence appears as the optimal way to reach a deeper understanding of the lake hydrodynamics. [ABSTRACT FROM AUTHOR]

In this paper we develop higher-order Discontinuous Galerkin finite element methods for the simulation of two-phase flow in heterogeneous porous media and experimental methods to determine structure and saturation in two-dimensional Hele-Shaw cells with high resolution in space and time. Together with additional measurements of governing parameters this allows us to compare experiments with numerical simulations. Results are shown to be in good qualitative agreement. [ABSTRACT FROM AUTHOR]

The increasing amount of 3D data in measurements and simulations needs a tool to visualize the interior in a convenient way. This can be done with so-called volume rendering techniques that allow for treating voxel-based data by assigning appropriate opacities to it. [ABSTRACT FROM AUTHOR]

In this work we describe an easy to use and easy to modify open-source program that was developed for the needs of several projects in the SFB 359. The utility is based on the powerful open-source visualization toolkit VTK, the de facto industry standard for visualization. It is an interactive visualization and graphics/movie-generation utility for multicomponent 2D- and 3D-data in the VTK-format. The data is the result of numerical computations such as e.g. computational fluid dynamics or computational structure mechanics. The main features of VisuSimple are shown based on examples. [ABSTRACT FROM AUTHOR]

The features and the design concept of the visualization software HiVision are presented. The platform HiVision which was primarily developed for the exploration of data in the area of Computational Fluid Dynamics (CFD), is being used nowadays in numerous applications related to numerical simulation. The main strength of the HiVision package lies in its object-oriented design and in the integration of several powerful external toolkits (VTK,Qt,MPI). The features of HiVision are demonstrated by means of selected examples. [ABSTRACT FROM AUTHOR]

In this contribution we study the calculation of effective coefficients for media with periodic heterogeneities. We use finite element methods of high order which allows to obtain high accuracy with relatively low computational effort. This is shown both theoretically and practically. [ABSTRACT FROM AUTHOR]

Homogenization techniques have been applied successfully to pore scale models of porous media, at least in the description of single-phase fluids. In the case that two phases are present (e.g. water and oil) one expects upscaled equations in the form of the Leverett two-phase flow system. Unfortunately, due to the appearance of many interfaces inside the porous medium and a lack of control of the geometric properties of the domains, no rigorous derivation of the Leverett system can be expected in the near future. In this contribution we report on rigorous derivations for geometries that allow a uniform description of the interfaces. [ABSTRACT FROM AUTHOR]

In this report we present results concerning the study of processes in complex media. Starting from model equations at microscopic level and using the techniques of the multi-scale analysis, we determine macroscopic descriptions for reactive flow in porous media, flow at interfaces between free flow and filtration flow, flow along rough boundaries and flow through a network of channels. [ABSTRACT FROM AUTHOR]

This paper presents a finite element method for solving the resonance line transfer problem in moving media. The algorithm is capable of dealing with three spatial dimensions, using hierarchically structured grids which are locally refined by means of duality-based a posteriori error estimates. Application of the method to coherent isotropic scattering and complete redistribution gives a result of matrix structure which is discussed in the paper. The solution is obtained by way of an iterative procedure, which solves a succession of quasi-monochromatic radiative transfer problems. It is therefore immediately evident that any simulation of the extended frequency-dependent model requires a solution strategy for the elementary monochromatic transfer problem, which is fast as well as accurate. The present implementation is applicable to arbitrary model configurations with optical depths up to 103-104. Additionally, a combination of a discontinuous finite element method with a superior preconditioning method is presented, which is designed to overcome the extremely poor convergence properties of the linear solver for optically thick and highly scattering media. The contents of this article is as follows: IntroductionOverview: numerical methodsMonochromatic 3D radiative transferPolychromatic 3D line transferTest calculationsApplicationsMulti-model preconditioningConclusion [ABSTRACT FROM AUTHOR]

The earliest phase of evolution of planetary system is determined by the intimate coupling of a number of physical and chemical processes: turbulent hydrodynamic flows under the action of gravity, radiative transfer in a dusty gas, extensive mixing of material by large scale flows and turbulent duffusion, vaporization and condensation of ices and minerals, chemical reactions in the gas phase and at the surface of dust grains, and agglomeration of dust into planets. The project attempted to develop the first numerical model calculations which account for at least the most important ones of these processes in a consistent way. The chemistry and mineralogy in the planetary formation region of protoplanetary disks was investigated and the basic processes which have to be included in a numerical model were determined. Stationary and time dependent models for protoplanetary disks including the basic chemistry and mineralogy were constructed in different approximations in one and two space dimensions. These allow to determine the composition of the disk material which determines the raw material for planet formation. Preliminary comparison with observations of primordial material in comets and meteorites from the formation time of the solar system shows that the models already reproduce successfully some basic observational features. [ABSTRACT FROM AUTHOR]

To investigate the transport and the diffusion of scalars in a turbulent channel flow, direct numerical simulations (DNS) are performed and experiments with the same geometry have been set up to examine details of the near-wall region. Transport and diffusion are observed with flow-tagging methods. In one setup the deformation of a line of tracer-molecules, placed perpendicular to the flow direction, is investigated. Furthermore the seeding and detecting of tracer-molecules into the boundary layer has been realized in two different configurations, in order to investigate species transport between the bulk flow and the boundary layer. [ABSTRACT FROM AUTHOR]

The scope is the modeling and simulation of turbulent spray flames where the emphasis is the modeling of the interaction of the vaporization and the turbulent flow field. In particular, the mixing process as well as the interaction of the turbulent flame with the vaporization are studied. These processes are least understood when it comes to the simulation of dilute spray flames. [ABSTRACT FROM AUTHOR]

Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can be derived rigorously for low-pressure conditions from the microscopic model, which is characterized as a moderately interacting many-particle system, in the limit as the particle number tends to infinity. Also the mesoscopic model is given by a many-particle system. However, the particles move on a lattice, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspon-dence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena of stochastic origin can be observed in experiments. The models include a new approach to the platinum phase transition, which allows for a unification of existing models for Pt(100) and Pt(110). The rich nonlinear dynamical behavior of the macroscopic reaction kinetics is investigated and shows good agreement with low pressure experiments. Furthermore, for intermediate pressures, noise-induced pat-tern formation, which has not been captured by earlier models, can be reproduced in stochastic simulations with the mesoscopic model. [ABSTRACT FROM AUTHOR]

The Large-Eddy simulation (LES) method can be used in order to break the multi-scale complexity within turbulent flow simulations, since not all turbulent length scales have to be resolved, but will be given by an appropriate subgrid model. Beside this filtering in space, a filtering in time allows for larger time steps as well and gives rise to implicit methods, where an algebraic system of equations has to be solved. Multigrid as a numerical multi-scale approach matches LES quite well with that respect and will be applied. It is essential to control the numerical error introduced by the discretisation and numerical solver in order to minimize the influence on the turbulent solution and hence, being able to identify the model error of the subgrid model. Two different stabilization methods, that are used within the collocated Finite Volume dicretisation for unstructured grids, are investigated with respect to their mass conservation error. The obtained solutions will be compared with benchmark solutions found in literature. The used subgrid model takes advantage of mesh dependent parameters. A practical solution within the multigrid procedure is to derive the model parameter on the finest grid level and inject it successively to the coarser grid levels. By this strategy good convergence rates result. [ABSTRACT FROM AUTHOR]

In this article results of studies are reported in which in-situ infrared-visible sum-frequency generation (IR-VIS SFG) surface vibrational spectroscopy was combined with density functional theory (DFT) ab initio computations to investigate the adsorption of carbon monoxide (CO) on rhodium (Rh) catalyst surfaces at elevated substrate temperatures (Ts ≥ 300K) over a wide pressure-range (pco = 10−8−1000 mbar). The experimental studies demonstrated the reversible molecular adsorption of CO up to a pressure of ca. 10 mbar. For higher CO pressures, however, the onset of a new irreversible dissociative CO adsorption pathway could be observed already at a substrate temperature of Ts=300 K. CO dissociation was found to result in the formation of carbon on the surface as the only detectable dissociation product, indicating that CO dissociation occurs via the Boudouard reaction: 2CO → C(ad) + CO2. To rationalize the experimental findings DFT studies were performed the results of which suggest the possibility of a novel low-temperature/high-pressure CO/Rh(111) dissociation pathway where a gas-phase CO(g) molecule reacts with a CO molecule chemisorbed on the catalyst surface, CO(ad), to yield gas-phase CO2 (g) and surface carbon C(ad) through an Eley-Rideal mechanism. The contents of the article is as follows: IntroductionExperimental and theoretical methodsPressure and temperature dependence of CO adsorption on rhodiumSummary [ABSTRACT FROM AUTHOR]

We discuss the modeling, simulation, and, for the first time, optimization of the reactive flow in a channel of a catalytic monolith with detailed chemistry. We use boundary layer approximation to model the process and obtain a high dimensional PDE. We discuss numerical methods based on the efficient solution of high dimensional stiff DAEs arising from spatial semi-discretization and SQP method for the optimal control problem parameterized by the direct approach. We have investigated the application of conversion of ethane to ethylene which involves a complex reaction scheme for gas phase and surface chemistry. Our optimization results show that the maximum yield, an improvement of a factor of two, is achieved for temperatures around 1300 K. [ABSTRACT FROM AUTHOR]

In the present contribution laser spectroscopic studies are described in which the chemical kinetics of benchmark elementary reaction steps in different laminar flow reactors were experimentally investigated along with detailed numerical modeling calculations (see the article Carraro/Heuveline/Rannacher [5] in this vol-ume). Coherent anti-Stokes Raman spectroscopy (CARS) was utilized to study the collisional relaxation and vibrational energy transfer of vibrationally excited molec-ular hydrogen H2(v = 1) in a low-temperature discharge flow reactor (T = 110 — 300 K). In theses studies wall deactivation probabilities and thermal rate constants for the vibrational energy transfer gas-phase reaction H2(v = 1) + D2(v = 0) → D2(v = 1) + H2(v = 0) could be derived from a direct comparison of measured con-centration profiles with results from a detailed numerical modeling. Further experi-ments were performed, in which CARS for molecular hydrogen detection along with OH laser-induced fluorescence (LIF) spectroscopy was utilized to determine the rate constant for the gas-phase reaction OH + H2(v = 1) → H + H2O. Finally a high-temperature flow reactor setup will be described, which allows for kinetics studies of elementary reactions using the pulsed laser photolysis (LP)/laser induced fluores-cence (LIF) pump-and-probe technique. The latter technique was employed in the present work to investigate the temperature dependence of the reaction of electron-ically excited oxygen atoms with molecular hydrogen, O(1D) + H2 → H + OH. The contents of the present article is organized as follows: IntroductionExperimental SectionResults and DiscussionSummary [ABSTRACT FROM AUTHOR]

This article describes the development of a numerical tool for the simulation, the estimation of parameters and the systematic experimental design optimization of chemical flow reactors. The goal is the reliable determination of unknown kinetic parameters of elementary reactions from measurements in a wide range of (laminar) flow conditions, from low to high temperature and from low to high pressure. The corresponding experiments have been set-up in the physical-chemistry group of J. Wolfrum at the PCI, Heidelberg; see the article Hanf/Volpp/Wolfrum [24] in this volume. The underlying mathematical model is the full set of the compressible Navier-Stokes equations accompanied by the balance equations for the chemical species. This system is discretized by a finite element method with mesh adaptivity driven by duality-based a posteriori error estimates (‘DWR method'); see the article Becker et al. [12] in this volume. The parameter estimation uses the Lagrangian formalism by which the problem is reformulated as a nonlinear saddle-point boundary value problem which is solved on the discrete level by the Newton or Gauß-Newton method. The contents of this article is as follows: IntroductionMathematical modelNumerical approachThe low-temperature flow reactorThe high-temperature flow reactorA step towards optimal experimental designConclusion and outlookReferencesAppendix [ABSTRACT FROM AUTHOR]

We present a systematic approach to error control and mesh adaptation in the numerical solution of optimal control problems governed by partial differential equations. By the Lagrangian formalism the optimization problem is reformulated as a saddle-point boundary value problem which is discretized by a finite element Galerkin method. The accuracy of the discretization is controlled by residual-based a posteriori error estimates. The main features of this method are illustrated by examples from optimal control of heat transfer, fluid flow and parameter estimation. The contents of this article is as follows: Preliminary thoughtsA general framework for a posteriori error estimationSolution process and mesh adaptationExamples of optimal control problemsConclusion and outlookReferences [ABSTRACT FROM AUTHOR]

Optimization of dynamic processes described by partial differential-algebraic equations (PDAE) is a challenging task due to dimension and complexity of the problems. Fast solutions methods are achieved by using a simultaneous approach for a close coupling of the optimization aspect of the overall algorithm with the solution method of the dynamic system. Especially using partially reduced sequential quadratic programming (PRSQP) approaches reduces the computational complexity while still being able to incorporate inequality constraints. An effective and straightforward generalization of the methods to treat optimization tasks modeled as multiple set point optimization problems is shown. Based on the simultaneous approach for optimization problems in NMPC an efficient real-time iteration technique is developed. As industrial applications we present shape optimization of turbine blades, operation optimization of a catalytic tube reactor and the real-time optimization of a continuous distillation column. [ABSTRACT FROM AUTHOR]

Estimating model parameters from experimental data is crucial to reliably simulate dynamic processes. In practical applications, however, it often appears that the data contains outliers. Thus, a reliable parameter estimation procedure is necessary that delivers parameter estimates insensitive (robust) to errors in measurements. Another difficulty that occurs in practical applications is that the experiments performed to obtain measurements for parameter estimation are expensive, but nevertheless do not guarantee satisfactory parameter accuracy. The optimization of one or more dynamic experiments in order to maximize the accuracy of the results of a parameter estimation subject to cost and further technical inequality constraints leads to very complex non-standard optimal control problems. Newly developed successful methods and software for design of optimal experiments for nonlinear processes are based on the expansion of the problem at the nominal value of parameters which lie in a (possibly large) confidence region. Robust optimal experiments, that are insensitive against uncertainties in parameter values, should be obtained if we optimize the experiments in min-max fashion (worst-case design) over the whole range (confidence region) of an uncertainty set. The paper presents new effective algorithms for robust parameter estimation and design of robust optimal experiments in dynamic systems. Numerical results for a real-life application from biochemical engineering are presented. [ABSTRACT FROM AUTHOR]

We describe recent developments in the design and implementation of finite element methods for the compressible Navier-Stokes equations modeling chemically reactive flows. The emphasize is on the low-Mach number regime including the limit case of incompressible flow. The most important ingredients are appropriate finite element discretizations, residual driven a posteriori mesh refinement, fully coupled defect-correction iteration for linearization, and optimal multigrid preconditioning. The potential of automatic mesh adaptation together with multilevel techniques is illustrated by 2D and 3D simulations of laminar methane combustion including detailed reaction mechanisms. [ABSTRACT FROM AUTHOR]

The use of PC-clusters gives the opportunity to solve three-dimensional flow problems to high accuracy at reasonable costs. The use of adaptive mesh refinement can increase the efficiency of such computations even more. However, the combination of multigrid, local mesh refinement and parallelization is not trivial. Therefore, this work addresses the following two topics in order to develope a tool for the simulation of complex flows: (i) multigrid algorithms on locally refined meshes, and (ii) the extension of multigrid to be used on parallel machines. [ABSTRACT FROM AUTHOR]

This work addresses two aspects. The first one is the practical realization of the dual weighted residual (DWR) method of Becker & Rannacher [6] to three dimensional flow problems. The second aspect is its extension to modeling errors. This gives the possibility to use on the one hand locally refined meshes, and on the other hand, a hierarchy of models in order to reduce the numerical costs without sacrifying accuracy. The issue of modeling errors is of importance in many fields, especially in reactive flow computations where sophisticated models are developed but not feasable to be used in multidimensional computations due to the high numerical costs. [ABSTRACT FROM AUTHOR]

Mathematical analysis provides several powerful tools for describing dynamic processes in science and economics. Here the role of ordinary and partial differential equations within the SFB 359 is briefly sketched. Then two examples are presented in more detail: Firstly, the analytical description of gradostat demonstrates how sensitively a system of ODEs might depend on its parameters. Secondly, shape evolutions show how the tools of set-valued analysis provide an alternative to level-set methods. The key aim here is to extend evolution equations beyond vector spaces. [ABSTRACT FROM AUTHOR]

We give an overview over results concerning viscous fluids with a free boundary, modelling e.g. the motion of water with a water-air interface. We describe the relevant tools and the major problems in the analysis of the corresponding equations. Our focus are results that concern existence, analysis of spectra, bifurcation, contact angles, coupling with elastic materials, and asymptotic behavior. [ABSTRACT FROM AUTHOR]