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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures (WS 2007/08)


noch laufendeSS-2008WS-2007/08SS-2007WS-2006/07SS-2006WS-2005/06SS-2005WS-2004/05(vor WS-2004/05)

16:00 Uhr
Haakon Haegland
University of Bergen (Norway), Department of Mathematics

Inclusion of transverse diffusion/dispersion in streamline methods using normal lines

Streamline methods have shown great potential for advection dominated problems in porous media. Diffusion dominated problems are however not as well suited for streamline methods since they involve flow transverse to the streamlines. The common way of including diffusion and dispersion is to use an operator splitting combined with a mapping of saturation/concentration from streamlines to the 2D/3D grid used for the pressure solution. Hence, diffusion is not directly incorporated along the streamlines, but must be solved on the pressure grid. If an explicit method is used there may be an efficiency problem due to the CFL-condition, and also the full 2D/3D solution is more time consuming than a set of 1D solutions along streamlines. In addition, the mapping from streamlines to the pressure grid may generate unwanted numerical diffusion.

We propose a new method to handle diffusion in streamline methods for 2D problems. Our method uses 1D normal lines, which are orthogonal to the streamlines. Transverse diffusion can then be handled using a one-dimensional diffusion equation on the normal lines, whereas the longitudinal diffusion and advection is handled by an advection-diffusion equation along the streamlines.

16:00 Uhr
Amel Sboui, PhD
ANDRA (National Radioactive Waste Management Agency), Paris

Mixed Finite Elements and Operator Splitting For Flow and Transport Around a Deep Nuclear Repository

"The aim of my thesis is to model and develop numerical tools adapted to study underground water flow and the propagation of pollutants in a porous medium. The main motivation of this work is a benchmark from GDR Momas and Andra to simulate the 3-D propagation of radionuclides around a deep disposal of nuclear waste.

Firstly, we construct a new mixed finite elements method suitable for general hexahedral meshes. Convergence of the method is proved and shown in numerical experiments. Secondly, we present a method of time dicretisation for the advection equation which allows for the use of different time steps in different subdomains in order to take into account of strong heterogeneities. Finally a numerical method for the calculation of the transport of contaminants is proposed. The techniques above were implemented in a 3-D code and simulation results are shown on the 3-D far field benchmark from GDR Momas and Andra."

16:00 Uhr
Dr. rer. nat. Insa Neuweiler
Leiterin Jungwissenschaftlergruppe: Effective Soil Parameters for Infiltration Processes, Institut für Wasserbau, Uni Stuttgart

Influence of connected structures on upscaled models for flow and transport in the unsaturated zone

Flow velocity of water in the unsaturated zone is described by the Richards equation. Transport of solutes, such as agrochemicals, in the vadose zone is mostly described by an advection-dispersion equation. Soil is in reality highly heterogeneous, so the hydraulic parameters vary in space and their detailed structure is unknown. Heterogeneity of hydraulic soil parameters has a strong influence on flow and transport processes. As an example, it determines dispersion of solute concentration. As water and mass fluxes usually have to be predicted on length scales much larger than the typical length scales of heterogeneities, flow and transport models have to be upscaled to predict spatial averages of state variables (water content or solute concentration). Upscaled models for flow and transport in aquifers are quite well established. In the unsaturated zone, where variances of hydraulic parameters can be extremely high, assumptions such as smoothly varying, moderately heterogeneous hydraulic parameter fields can often not be made to derive upscaled models.

Heterogeneity of soil is usually captured by modeling hydraulic parameters as correlated random fields. These fields are mostly directly or indirectly assumed to be multi-Gaussian. This implies that no information is used upon whether a certain parameter range is spatially connected or forms isolated clusters. However, connectivity has been found to have a strong influence on parameters of upscaled flow models, in particular if the variance of parameters is high.

In this presentation, the influence of connected structures of heterogeneous hydraulic parameter fields on upscaled flow and solute transport models in the vadose zone will be discussed. Upscaled models are derived using homogenization theory. The models are analyzed for different configurations of connected and isolated parameter ranges and for different parameter contrasts. Homogenization theory is based on an expansion of the flow- and transport equation in terms of the ratio between typical large length scale (for example the medium size) and typical small length scale (for example the length scale of a macroscopic representative elementary volume). By analyzing different parameter contrasts, quantified in terms of the expansion parameter, it can be demonstrated that, for example, the occurrence of non-equilibrium effects in the upscaled model depends crucially on the information about connectivity of different parameter ranges. Besides the type of upscaled model, also the effective model parameters depend on this type of information and can deviate significantly from effective parameters derived under the assumption that parameter fields are multi-Gaussian.

16:00 Uhr
Halvor Nilsen, PhD
Dept. of Applied Mathematics, SINTEF, Oslo

Fast methods for incompressible flow with gravity

"We will present the work we are doing on developing fast methods for simulation of CO2 injection into aquifers in the project:

Geological Storage of CO2: Mathematical Modelling and Risk Analysis

Our goal is to do calculation on realistical geological models for future CO2 storage sites. In this talk we will discuss some of the possible methods for achieving this goal and the main difficulties in simulating on geological models. Particularly streamline methods using operator splitting will be considered. At the end preliminary calculations done on data from the Johansen formation which is considered to be the storage site for CO2 from the gas power-plant at Mongstad (Norway) will be presented as an example."

16:00 Uhr
Dipl.-Math. Alexander Weiss
Numerische Mathematik für Höchstleistungsrechner am Institut für Angewandte Analysis und Numerische Simulation, Uni Stuttgart

Variational inequalities for modeling flow in heterogeneous porous media

One of the driving forces in porous media flow is the capillary pressure. In standard models, it is given depending on the saturation. Recently, this relationship was enhanced by a dynamic retardation term which leads to a dependency on the saturation and its time-derivative. The situation becomes even complexer when heterogeneous porous media is considered. Here, the continuity condition for the capillary pressure does not guarantee that the saturation has to be continuous at the material interfaces. Moreover, to model capillary barriers, an entry pressure is often included into the capillary pressure relationship which has to be treated correctly in the numerical simulation.

For the discretization, we use a mortar method on non-matching meshes. More precisely, the flux is introduced as new variable at the interfaces playing the role of a Lagrange multiplier. This method can be applied to both the standard and the enhanced capillary model. To correctly model the penetration process into porous media with entry pressure, we introduce an inequality constraint. The weak formulation of which can be written as a variational inequality. As non-linear solver, we use a primal-dual active-set strategy which can be reformulated as semi-smooth Newton method. Several numerical examples demonstrate the efficiency and flexibility of the new algorithm.

16:00 Uhr
Dr.-Ing. Steffen Oliver Ochs
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung, Institut für Wasserbau, Uni Stuttgart

Simulation of multiphase multicomponent processes in PEM fuel cells

The development of new alternative power sources/supplies is an important task nowadays. Polymer electrolyte membrane (PEM) fuel-cells currently are intensively investigated and improved for applications. This requires a profound understanding of the physical and electrochemical processes elapsing in fuel cells. It has been found that the kinetics of the oxygen reduction at the cathode is a limiting factor for the performance of fuel-cells. The transport of oxygen to the cathode through its porous diffusion layer occurs in a predominantly diffusive manner. The generation of liquid water at the cathode-site constrains this oxygen transport to the reaction layer. Thus, an efficient water management in the cathode diffusion layer is necessary to improve the performance of the fuel-cell.

In the seminar we present a multiphase multicomponent model originally developed at LH2 for the simulation of non-isothermal multiphase processes in the subsurface and the modifications necessary for modeling multiphase processes in the diffusion layer of PEM fuel-cells. The results of two studies one on the influence of capillary pressure and another on the effect of different flow regimes on the system behavior will be discussed.

16:00 Uhr
Dr.-Ing. Jennifer Niessner
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung, Institut für Wasserbau, Uni Stuttgart

Modeling of multi-phase flow in porous media including phase interfaces

"We present a new numerical model for macro-scale two-phase flow in porous media which is based on an existing physically consistent and general theory of multi-phase flow. This model is able to capture physical phenomena that cannot be described by standard two-phase flow models. The standard approach for modeling the flow of two fluid phases in a porous medium consists of a continuity equation for each phase, an extended form of Darcy's law as well as constitutive relationships for relative permeability and capillary pressure. However, it has been shown that this approach is deficient with respect to physics.

The alternative is to use an extended model which is founded on thermodynamic principles and is physically consistent. We present results of a numerical modelling study based on this extended model. In addition to the standard equations, the model uses a balance equation for specific interfacial area and a constitutive relationship for specific interfacial area as function of capillary pressure and saturation. We show that the extended model can capture additional physical processes compared to the standard model, such as hysteresis. New features of the extended model, such as a physically motivated description of mass transfer between phases are discussed."

16:00 Uhr
Robert Klöfkorn
Abteilung für Angewandte Mathematik, Universität Freiburg

Modern Concepts of Software Design with the Application to the Simulation of PEM Fuel Cells with the Software Package DUNE

Numerical simulation of Polymer Electrolyte Membrane (PEM) Fuel Cells using a detailed fuel cell model is a challenging problem. The model under consideration consists of two-phase flow in the porous layers of the fuel cell, transport mechanisms of species in the gaseous phase, as well as oxygen reduction reactions. Apart from a short overview of the governing equations and the presentation of numerical results, the talk will focus on concepts of software design for numerical applications with the underlying complex model and their difficulties. The governing system of equations is discretised by the Local Discontinuous Galerkin (LDG) method. The developed framework for the implementation, DUNE-Fem, of this LDG method can cope with several space dimensions and several polynomial orders of the basis functions of the discrete function space. The Discontinuous Galerkin method is implemented independently from any grid structures by using the generic grid interface of the software package DUNE.

16:00 Uhr
Dr. rer.nat. Bernd Flemisch, M.Sc.
Lehrstuhl für Hydromechanik und Hydrosystemmodellierung, Institut für Wasserbau, Uni Stuttgart

Mimetic finite difference methods

Mimetic finite difference methods constitute an alternative framework for the discretization of partial differential equations. The key idea is to discretize the basic operators gradient, curl, and divergence in such a way that the fundamental mathematical relations of vector calculus can be exactly reproduced in the discrete setting. In physical terms, this corresponds to the most wanted discrete conservation of mass, energy, etc. In addition, mimetic methods appear most promising for managing strong heterogeneities, distorted elements, or hanging nodes. This talk provides an introduction to the methodology, interpretes the resulting numerical model within the frameworks of mixed finite elements and finite volumes, and illustrates the robustness by means of simple numerical examples.

16:00 Uhr
Prof. Dr.-Ing. habil. Michael Manhart
Fachgebiet und Laboratorium für Hydromechanik, TU München

Modellierung und Simulation turbulenter Mehrphasenströmungen

Turbulente Mehrphasenströmungen spielen in zahllosen technischen Anwendungen und umweltrelevanten Prozessen eine zentrale Rolle. Die Vorhersage von Transport, Reaktionen und Stoffumsätzen wird in solchen Strömungen durch mehrere Faktoren erschwert. Die Interaktion der zweiten Phase mit der turbulenten Trägerströmung stellt ein klassisches Multiskalenproblem dar. Für unterschiedliche Anwendungen wurden ganz spezielle Lösungsmethoden entwickelt. In den letzten Jahren treten dabei immer mehr die zeit- und ortsaufgelösten Simulationsmethoden Large-Eddy-Simulation und Direkte Numerische Simulation in den Vordergrund. Es werden Lösungsstrategien für drei unterschiedliche Anwendungsfälle vorgestellt: turbulente Partikelströmungen, Fällung nanoskaliger Partikel in einem Mikromischer und turbulente Strömung verdünnter Fasersuspensionen.

16:00 Uhr
Dipl.-Phys. Florian Doster
Institute for Computational Physics, Uni Stuttgart

Approaches to a new theory on multiphase flow in porous media

The commonly used constitutive theory for multiphase flow in porous media on macroscopic scales -- the extended Darcy theory -- has several drawbacks regarding hysteresis and residual saturations. Experimental evidence shows that the fundamental parameter functions of the theory, i.e. capillary pressure and relative permeabilities are process dependent and hence are not parameter functions. Within this talk I will present a new theory on multiphase flow in porous media which addresses some of these challenges. The resulting equations of motion allow to describe flow processes where drainage and imbibition processes occur simultaneously. To study the dynamics of systems governed by these equations of motion, we develop an implicit finite volume algorithm in one dimension. The numerical studies of the Buckley Leverett problem and a comparison to the analytic solution are presented. A measurement of capillary pressure by measuring saturation profiles in porous column in the gravity field is carried out numerically. We show that the second drainage and imbibition processes can be simulated without adjusting parameters.

16:00 Uhr
Prof. Dr. Hans-Joachim Bungartz
Lehrstuhl für Informatik mit Schwerpunkt Wissenschaftliches Rechnen, TU München

Fluid-Struktur-Interaktion auf kartesischen Gittern

Durch die zunehmende Leistungsfähigkeit von Rechnern einerseits und die wachsenden Genauigkeitsanforderungen an die Simulation andererseits spielen gekoppelte oder Mehrphysik-Probleme eine immer bedeutendere Rolle. Prominentes Beispiel sind Fluid-Struktur-Wechselwirkungen, bei denen elastisch verformbare oder starre Körper mit einem sie um- oder durchströmenden Fluid interagieren. Anwendungen reichen von Zeltdachkonstruktionen über Mikropumpen bis hin zur Blutströmung in Arterien. Bei der numerischen Behandlung solcher Fluid-Struktur-Interaktionen (FSI) unterscheidet man i.A. zwischen monolithischen Ansätzen, bei denen das gekoppelte System als Ganzes diskretisiert wird, und partitionierten Verfahren, die separate Löser für das Strömungs- und das Strukturproblem geeignet zusammenschalten.

Der Vortrag stellt Konzepte zur Simulation von FSI auf fixen kartesischen Gittern dar, die insbesondere im Hinblick auf Implementierungseffizienz Vorteile aufweisen. Diskutiert werden dabei insbesondere die Behandlung der Strömungsseite sowie die effiziente Kopplung über die Schnittstelle FSI*ce.