Dienstag 23.10.2007 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
CFLcondition, 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
onedimensional diffusion equation on the normal lines, whereas the
longitudinal diffusion and advection is handled by an
advectiondiffusion equation along the streamlines. 
Dienstag 30.10.2007 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 3D 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 3D code and simulation results are shown on the 3D far field benchmark from GDR Momas and Andra." 
Dienstag 06.11.2007 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 advectiondispersion 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 multiGaussian. 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 nonequilibrium
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 multiGaussian.

Dienstag 13.11.2007 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 powerplant at Mongstad (Norway) will be
presented as an example." 
Dienstag 20.11.2007 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 timederivative. 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 nonmatching 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 nonlinear solver, we use a primaldual activeset strategy which can be reformulated as semismooth Newton method. Several numerical examples demonstrate the efficiency and flexibility of the new algorithm. 
Dienstag 27.11.2007 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) fuelcells
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 fuelcells. 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 cathodesite 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 fuelcell.
In the seminar we present a multiphase multicomponent model originally
developed at LH2 for the simulation of nonisothermal multiphase processes
in the subsurface and the modifications necessary for modeling
multiphase processes in the diffusion layer of PEM fuelcells.
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. 
Dienstag 04.12.2007 16:00 Uhr  Dr.Ing. Jennifer Niessner Lehrstuhl für Hydromechanik und Hydrosystemmodellierung, Institut für Wasserbau, Uni Stuttgart

Modeling of multiphase flow in porous media including phase interfaces "We present a new numerical model for macroscale twophase flow in porous media which is based on an existing physically consistent and general theory of multiphase flow. This
model is able to capture physical phenomena that cannot be described by standard twophase 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." 
Dienstag 11.12.2007 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 twophase 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, DUNEFem, 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. 
Dienstag 08.01.2008 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. 
Dienstag 22.01.2008 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 LargeEddySimulation 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. 
Dienstag 29.01.2008 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. 
Dienstag 12.02.2008 16:00 Uhr  Prof. Dr. HansJoachim Bungartz Lehrstuhl für Informatik mit Schwerpunkt Wissenschaftliches Rechnen, TU München 
FluidStrukturInteraktion auf kartesischen Gittern Durch die zunehmende Leistungsfähigkeit von Rechnern einerseits und die wachsenden Genauigkeitsanforderungen an die Simulation andererseits spielen gekoppelte oder MehrphysikProbleme eine immer bedeutendere Rolle. Prominentes Beispiel sind FluidStrukturWechselwirkungen, 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 FluidStrukturInteraktionen (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. 