Current projects

2016 -

proMT — Prognostic model-based online MR-thermometry during minimally invasiv thermoablation for the treatment of liver tumors

Subproject: Model reduction for prognostic online MR-thermometry

Funding Agency Federal Ministry of Education and Research (BMBF)
Partner TU Kaiserslautern, Fraunhofer ITWM, In­sti­tute for Diagnostic and Interventional Radiology Frankfurt University Clinic, Siemens Healthcare GmbH
Participants Prof. Dr. Nicole Marheineke, Kevin Meligan
Dates 2016 – 2019

In view of the intended prognostic online simulation capability, this subproject aims at the development and analysis of reduced models by means of model order reduction (MOR) techniques. The combination of MOR and space-mapping promises a further increase in performance, which is assessed qualitatively and quantitatively for the specific application of MR-thermometry.

MathEnergy — Mathematical key techniques for energy networks in a state of change

Subproject: Analysis and application of reduced models

Funding Agency Bundesministerium für Wirtschaft und Energie (BMWi)
Partner Fraunhofer SCAI, Fraunhofer ITWM, Max-Planck-Institut Magdeburg, TU Berlin, TU Dortmund, HU Berlin, PSI AG
Participants Prof. Dr. Nicole Marheineke, Björn Liljegren-Sailer, Philipp Werner
Dates 2016 – 2020

The main objective of this mathematically oriented subproject is the development of methods and analysis of reduced models or model hierarchies and their application to dynamic state estimations for model-predictive control.

2014 - 2015

Microaggregates: Formation and turnover of the structural building blocks of soils

PM: Mechanistic Modeling of the Formation and Consolidation of Soil Microaggregates

Funding Agency DFG Research Unit FOR2179
Partner U Jena (Coord.), TU München, FZ Jülich, U Kassel, U Hannover, U Halle, U Bonn
Participants Dr. Nadja Ray (PI), Dr. Alexander Prechtel (PI), Andreas Rupp
Dates 2015 – 2018

Soil functions are decisively related to the structure of soil microaggregates. Thus, the understanding of soil processes and functions also requires a concept of the formation and consolidation of soil structural elements. We develop such a general model framework including the interactions of prototypic building units, as e.g., specific minerals and/or organic matter.

The identified and implemented relevant aggregation processes include electrostatic forces, attraction by gluing and cementing agents, geochemical reactions, or diffusion. They are taken into account in a mechanistic framework using cellular automaton rules and non-linearly coupled systems of partial differential equations with algebraic constraints. The resulting microaggregate structures are investigated quantitatively by morphological analysis that provides comprehensive insights into structural similarities found for aggregates formed under various conditions.

With that we heuristically investigate effects of the prototype composition, charge, size ratio, and concentration on microaggregate formation. Moreover, the model permits to illuminate the temporal evolution of aggregate formation in multiple scenarios and therefore provides estimates of soil aggregation behavior in case an observation is inhibited by experimental limitations. The numerical implementation uses advanced discontinuous Galerkin methods and a massively parallel implementation.

Mathematical modeling, simulation and optimization at the example of gas networks

TP C02: Hierarchical PDAE-surrogate models and stable PDAE-discretiziation for simulating large instationary gas networks

Funding Agency SFB / Transregio 154
Partner FAU Erlangen-Nürnberg, HU Berlin, TU Berlin, TU Darmstadt, ZIB, WIAS, Univ. Duisburg-Essen
Participants Prof. Dr. Nicole Marheineke, Björn Liljegren-Sailer, Prof. Dr. Caren Tischendorf (HU Berlin)
Dates 2014 – 2018

The on-line (possible real-time) control and parametric optimization of gas transport requires the stabil and fast simulation of large instationary networks that are modeled by huge coupled systems of partial differential and algebraic equations. This project aims at the development of an appropriate numerical discretization adapted to the network topology and in regard of a small perturbation index. Establishing a PDAE-surrogate model hierarchy by using model order reduction techniques promises to yield an efficient compromise between complexity and accuracy.

Simulation of highly dynamic turbulence-driven spinning processes
Funding Agency Deutsche Forschungsgemeinschaft (DFG)
Partner Fraunhofer ITWM
Participants Prof. Dr. Nicole Marheineke, Stefan Schießl
Dates 2014 – 2017

The objective of this project is the simulation of highly dynamic spinning processes, geared to the key challenge of understanding the melt-blowing process with its complex dependency on the driving turbulent hot air streams together with the arising large stretching of the liquid fiber jet. For the underlying instationary viscous Cosserat rod model, system of partial and ordinary differential equations with random source term, numerical schemes are developed with focus on appropriate refinement strategies.


Free boundary propagation and noise: analysis and numerics of stochastic degenerate parabolic equations

DFG Research Grant

Dates: 2018-2020
Participants: Prof. Dr. Günther Grün, Hubertus Grillmeier, M.Sc.

The porous-medium equation and the thin-film equation are prominent examples of nonnegativity preserving degenerate parabolic equations which give rise to free boundary problems with the free boundary at time t > 0 defined as the boundary of the solution’s support at that time.
As they are supposed to describe the spreading of gas in a porous-medium or the spreading of a viscous droplet on a horizontal surface, respectively, mathematical results on the propagation of free boundaries become relevant in applications. In contrast to, e.g., the heat equation, where solutions to initial value problems with compactly supported nonnegative initial data
instantaneously become globally positive, finite propagation and waiting time phenomena are characteristic features of degenerate parabolic equations.
In this project, stochastic partial differential equations shall be studied which arise from the aforementioned degenerate parabolic equations by adding multiplicative noise in form of source terms or of convective terms. The scope is to investigate the impact of noise on the propagation of free boundaries, including in particular necessary and sufficient conditions for the occurrence
of waiting time phenomena and results on the size of waiting times. Technically, the project relies both on rigorous mathematical analysis and on numerical simulation.

Modeling of ocean overflows using statically and dynamically adaptive vertical discretization techniques
Funding Agency German Research Foundation (DFG)
Grant Type Individual Grant
Dates 09/2013 — 08/2016
Participants Vadym Aizinger (PI), Balthasar Reuter (University of Erlangen-Nuernberg)

The goal of the project is the development of a novel vertical discretization that can substantially alleviate or resolve a number of shortcomings associated with the standard vertical coordinates used in the current general circulation models. 
Those ideas will be further developed by adding a procedure that enables the vertical mesh layers to dynamically change according to the flow conditions. The new methodology incurs negligible computational overhead and preserves all local conservation properties of the algorithm. The numerical scheme is based on the discontinuous Galerkin finite element method implemented in UTBEST3D.

Filtered density function uncertainty assessments for reactive transport in groundwater
Funding Agency Deutsche Forschungsgemeinschaft (AT 102/7-1 & KN229/15-1 & SU 415/2-1)
Dates 01/2013 — 12/2015
Participants PD Dr. Nicolae Suciu, Professor Dr. Peter Knabner, Opens external link in new windowProfessor Dr. Sabine Attinger (UFZ)

Modelling the fate of contaminants in groundwater requires solutions for reactant species concentrations, representative at some spatial scales, as well as assessments of uncertainty induced by sub-scale aquifer's heterogeneity. Under stochastic parameterizations of hydraulic conductivity, one arrives at systems of stochastic partial differential equations and the complete solution is given by probability density functions of species concentrations. When instead of stochastic averaging one performs a spatial filtering of system's heterogeneity, one defines the filtered density function (FDF), which plays the same role as a probability density in uncertainty assessments. In this way, the spatial scale of the prediction is explicitly defined and the cumbersome Monte Carlo reference solutions are replaced by less expensive direct numerical simulations consisting of solving reactive transport problems on finer grids. Although a long standing approach in turbulence, the FDF method has not yet been applied to groundwater. In developing a FDF method for reactive transport in groundwater we schedule two main tasks. The first one consists of modelling sub-grid processes. Here, the challenge is the interdependence between up-scaling flow and transport and modeling sub-grid mixing. The second task is to develop accurate and computationally efficient solvers for the FDF problem. This involves solutions to filtered equations for flow and to FDF evolution equations. The latter will be solved with a global random walk method which supersedes the limitations of currently used particles methods and, therefore, could also improve the efficiency of FDF simulations in turbulence. A guiding line in designing the FDF method will be its applicability to Bayesian inference for monitored contaminated sites. Opens external link in new windowDetails >>

Completed projects

2013 and later

Mathematical Modeling and Numerical Simulation of Steel Rolling Processes
Funding Siemens AG
Participants Prof. Dr. Nicole Marheineke, Kevin Meligan
Dates 2013 – 2014
Identifikation, Optimierung und Steuerung für technische Anwendungen
Funding Agency
Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst; Elitenetzwerk Bayern
Dates 2006 - 2013
ParticipantsProf. Dr. Peter Knabner, Dr. Michael Blume, Dr. Mathias Herz

In dem Internationalen Doktorandenkolleg wird vor dem Hintergrund konkreter Anwendungsprobleme der Bogen von der mathematischen Modellierung über die mathematische Analyse und die Entwicklung numerischer Methoden bis hin zum Wissenschaftlichen Rechnen und der Implementierung von Software auf Hoch- und Höchstleistungsrechnern gespannt. Dies geschieht auf den Gebieten der Identifikation, Optimierung und Steuerung komplexer technischer, medizinischer, naturwissenschaftlicher und wirtschaftswissenschaftlicher Systeme.

Identifikation, Optimierung und Steuerung haben eine große Bedeutung für die technologische Entwicklung. Die Fokussierung auf dieses Gebiet ist deshalb das besondere Merkmal dieses mathematisch orientierten Netzwerkes. Im nordbayerischen Raum bieten sich wegen der dort gegebenen Konzentration international anerkannter Wissenschaftler in diesem Forschungsumfeld die besten Voraussetzungen. Das Ziel des Doktorandenkollegs ist es, den Schritt von der modellbasierten Simulation zum modellgestützten optimalen Design und Steuerung zu vollziehen. Dieser Schritt wird erst durch die Verzahnung der rasanten Entwicklung mathematischer Methoden der Optimierung und der Numerik und mit Hilfe von Hochleistungsrechnern möglich.

Eine stärkere Einbindung von Ingenieurprojekten in der zweiten Phase des Kollegs wird die Integration der erarbeiteten Konzepte und Algorithmen in konkrete Anwendungsbereiche ermöglichen. Darüber hinaus lassen spezifische Betreuungs- und Lehrkonzepte die fachübergreifende Zusammenarbeit fruchtbar werden. Link >>


OPAL – Optimization of airlay-processes

TP1: Kinetic modeling and simulation of fiber-loaded flows

Funding Agency Bundesministerium für Bildung und Forschung (BMBF)
Partner FAU Erlangen-Nürnberg, TU Kaiserslautern, Fraunhofer ITWM, Autefa Solutions Germany GmbH, IDEAL Automotive GmbH
Participants Prof. Dr. Nicole Marheineke, Alexander Vibe
Dates 2013 – 2016

The manufacturing of modern lightweight components is often based on aerodynamic laydown processes. In the airlay-process a porous structure is formed by a fiber-loaded air flow on a conveyor belt and then bonded. The material properties of the finalized product, such as structural strength or bulk modulus, depend on the parameters of the production process. OPAL aims the optimization of the production process and the material properties on basis of the consistent mathematical description of the process chain. The focus of this subproject lies on the kinetic modeling of the fiber-loaded flow.

2010 - 2012

MPFA and MHFE methods for flow and transport in porous media
Funding Agency Deutscher Akademischer Austauschdienst (DAAD), PPP Projektbezogener Personentausch mit Norwegen
Funding Period
2012 —2013
Prof. Dr. Inga Berre, Prof. Dr. Florin Radu, University of Bergen, Norway
Participants Prof. Dr. Peter Knabner, Dr. Alexander Prechtel, Fabian Brunner

Nonlinear (multiphase) flow and reactive multicomponent transport problems in highly heterogeneous porous media and their numerical simulation are of great interest for evaluating site remediation, energy exploitation or CO2 sequestration scenarios.   The resulting advection-diffusion-reaction-systems are coupled nonlinear parabolic partial differential equations, and we have parabolic or elliptic nonlinear flow equations, possibly degenerate. The development of convergent and efficient numerical schemes is very challenging and the mixed (hybrid) finite element method M(H)FEM and the multipoint flux approximation MPFA are powerful locally mass conservative choices. They offer also the advantage of continuous flux approximations over the element faces.  Analogies between the two techniques should help to prove order of convergence estimates and monotonicity for the multicomponent transport problems, but also for multiphase flow.  Furthermore numerical diffusion of the schemes should be quantified to assess the accuracy of the methods.  Simulation examples should include realistic scenarios on heterogeneous, log normally distributed random parameter fields.

Diffusive interface models for transport processes at fluidic interfaces (Part 1)

DFG Priority Programme SPP 1056 "Transport processes at fluid interfaces"

Dates 2010 — 2013
Participants Professor Dr. Günther Grün, Dipl.-Math. Fabian Klingbeil

Topological transitions like droplet coalescence or droplet break-up are fundamental features of two-phase flows. In recent years, diffuse interface models turned out to be a promising approach to describe such phenomena. Species transport across fluidic interfaces and the effects exerted by soluble and insoluble surfactants are additional issues of still increasing technological importance.
For those phenomena, novel thermodynamically consistent diffuse interface models shall be developed taking in particular general densities into account. Based on rigorous mathematical analysis, existence and qualitative behaviour of solutions will be investigated, this way enhancing the understanding of the fundamental model properties. Starting from energy and entropy inequalities, stable and convergent numerical schemes shall be formulated and implemented in two and three spatial dimensions. By numerical simulations, the models shall be validated and further improved.

Interfaces, ComplexStructures, and Singular Limits in Continuum Mechanics
DFG Research Training Group GRK 2339

Dates: 2018-2022 (first funding period),
Participants at FAU: Proff. Bänsch, Burger, Grün (Co-Spokesperson), Knabner, Pratelli, Neuss-
Radu, and Dr. Ray.

The DFG Research Training Group IntComSin is a joint doctorate program of FAU and University of Regensburg in Applied Mathematics. The research focuses on many aspects of advanced mathematical modeling, analysis and numerics with the perspective to understand complex phenomena observed in fluid mechanics, material engineering, biological systems and other applied sciences. Typically interfaces, multiple scales/fields and small parameters (singular limits) are the core features of the problems to be studied. The doctoral program offers a structured course program in partial differential equations, calculus of variations, numerical analysis, scientific computing, mathematical modeling and professional skills. The topics explored in the doctoral projects address:
• interfaces (two-phase flows, transport processes at interfaces, fluidic and elastic effects in membranes, shape optimisation, fluid-structure interactions),
• complex structures ( multiple scales, homogenisation of porous media, micro-macro models for complex fluids, microstructures generated by non-convex variational problems),
• singular limits and dimension reduction (thin film limits, plates/shells and beams, asymptotic limits in phase field models).
For further information, see
Efficient Numerical Methods for Large Partial Differential Complementary Systems arising in Multispecies Reactive Transport with Minerals in Porous Media (Nachfolgeprojekt)
Funding AgencyDeutsche Forschungsgesellschaft (KN 229/12-2)
Dates 11/2010 — 05/2013
ParticipantsPD Dr. Serge Kräutle, Professor Dr. Peter Knabner
See below (KN 229/12-1).
ProFil – Stochastic production processes in manufacturing of filaments and nonwoven materials

TP3: Turbulent fiber and fluid dynamics

Funding Agency Bundesministerium für Bildung und Forschung (BMBF)
Partner TU Kaiserslautern, Univ. Kassel, Fraunhofer ITWM, ADVANSA GmbH, Johns Manville GmbH, Oerlikon Neumag
Participants Prof. Dr. Nicole Marheineke, Thomas Cibis
Dates 2010 – 2013

In the production process of nonwoven materials filaments are spun from a polymer melt by aerodynamic stretching, then entangled by turbulent air flows and finally delivered onto a conveyor belt. The quality of the product is fundamentally influenced by the stochastic properties of the production process. ProFil contributes to innovations in this field with regard to material savings and quality improvements through mathematical modeling and numerical simulation of the process chain «melting-spinning-entangling-deposition». This subproject deals with fiber-fluid interactions and turbulence modeling.

2005 - 2009

Development of filtration systems for air cleaning from nanoparticles, organic admixtures and bacteria with the help of numerical simulations
Funding AgencyBMBF (RUS 09/B12), Internationale Zusammenarbeit in Bildung und Forschung mit Russland, 
Dates 2009 - 2012
ParticipantsPD Dr. Nicolae Suciu, Dr. Alexander Prechtel, Prof. Dr. Peter Knabner
The project was a cooperation of a group of applied mathematicians with the Russian company Aeroservice for the development and optimization of new photocatalytic filter systems for air cleaning of nanoparticles and organic substances with the help of mathematical simulation tools. For the simulation of aerosol transport in the filter made of polypropylene fibers, which is used in hospitals or airports, e.g., mathematical models and efficient solution algorithms had to be developed. These allow on the one hand to take stochastic components into account, as the heterogeneous conductivity distribution in the filter. On the other hand these methods were coupled with highly accurate computation schemes as mixed finite element methods, which guarantee local mass conservation for the transport processes. The design parameters of real experiments can be optimized with the help of such simulation tools and their sensitivity with respect to filter efficiency analysed. Among the used methods are particle filtration in porous media, based on the Darcy equation, and coupled Eulerian and Lagrangeian simulation of transport processes, including Monte Carlo approaches with given filter geometries.


DAAD project "Mathematical Analysis and Numerical Simulation of Dynamic Electrowetting" ("projektbezogener Personenaustausch Spanien")
PartnerUniversidad Autónoma Madrid (Prof. Marco Fontelos)
Funding period 2007 - 2008
Principal InvestigatorsProf. Dr. Günther Grün, Prof. Dr. Marco Fontelos (CSIC Madrid)

Electric fields may influence the wetting behaviour of charged droplets. This effect may be used to manipulate droplet motion and to enforce droplet coalescence or break-up. It is summarized under the notion of electrowetting. First studied in the late 19th century by Lippmann and others, very recently this effect gained the interest of physicists and engineers on account of a variety of applications in micro-fluidics ("lab-on-a-chip"). However, mathematical modeling of this effect is still in its childhood -- the dependency of contact angles on the applied voltage is modeled by the so called Lippmann formula which may hold true at most in a small voltage regime. In this project, new thermodynamically consistent models shall be derived to describe the evolution of droplet, voltage and thereby to shed light on the mechanisms underlying electrowetting. Existence of solutions shall be proven and efficient numerical schemes shall be developed as well. Poster>>



Efficient Numerical Methods for Large Partial Differential Complementary Systems arising in Multispecies Reactive Transport with Minerals in Porous Media
Funding AgencyDeutsche Forschungsgemeinschaft (KN 229/12-1 & KN 229/12-2)
Dates 2007 - 2013
ParticipantsPD Dr. Serge Kräutle, Professor Dr. Peter Knabner, Opens external link in new windowProfessor Dr. Christian Kanzow (Würzburg), Dr. Joachim Hoffmann
A description of an equilibrium reaction with a mineral has to consider both a saturated case and the state of complete dissolution of the mineral. A unified description of the equilibrium state can be expressed by a complementarity condition. The project focuses on the accurate and efficient numerical treatment of time-dependent reactive transport problems with many species in porous media in 2 or 3 space dimensions. The problem of multispecies reactive transport with minerals takes the form of a differential algebraic set of equations and complementarity constraints, consisting of time dependent (possibly convection-dominated) semilinear partial differential equations (PDEs), nonlinear ordinary differential equations, nonlinear algebraic equalities, and inequalities. Taking a typical species number of 20 and of nodal degrees of freedom of 10^6, also for an appropriate (e.g., local mass conservative) discretization, the solution of the emerging finite dimensional complementarity system is a formidable task to be attacked as one principal choice by algorithms of semismooth Newton type. Aims are the investigation and improvement of the algorithms w.r.t. efficiency and robustness, and comparing them to other (e.g., interior-point-) methods. The algorithms to be developed heavily take advantage of knowledge about the substructuring of the problem. The emerging methods and software, also for parallel computers, is supposed to handle several large real world problems, not yet treatable satisfactorily.


The Influence of Colloids on Water Flow and Solute Transport in Soils: Side Effect or Key Process?
Funding AgencyDeutsche Forschungsgemeinschaft (KN 229/9-1 & KN 229/9-2)
Dates 2006 - 2010
Prof. Dr. Peter Knabner, Dr. Alexander Prechtel,  Dr. Florian Frank
Prof. Dr. Kai Uwe Totsche, FSU Jena
Soil colloids may influence the interaction between solutes and the immobile solid phase. A coupling to the fluid transport is possible by processes of sedimentation, flocculation, precipitation, filtration and deposition. The objective of this research project is the qualitative and quantitative examination of the crucial aspects of colloidal-influenced solute- and fluid transport by means of systematic, prognostic simulation. In detail,
  1. the attachment and detachment of colloids under consideration air-water interface of the soil,
  2. the transformation of the pore space and the thus induced coupling to the fluid transport in soil, and
  3. the transformation of the surface properties of the solid phase and the thus induced coupling to the solute transport

have to be analyzed. The main hypothesis of this project states that the couplings incorporated in the model conception affect the praxis-relevant situations not only qualitatively, but also quantitatively in a significant way. The deterministic description of the physicochemical mechanisms on basis of the conservation laws for mass, impulse and energy results in systems of time-dependent non-linear partial differential equations. In order to make the model operative with respect to the problem formulation, one has to approximate it via numerical methods and to implement those in a software tool. For each level of complexity which has to be achieved, a comparison with existing experimental data has to be accomplished. In particular, these datasets have is to be used to obtain a realistic parametrization of the model via inverse modelling.


Erstellen von 1D-Simulationsrechnungen zum Schadstofftransport mit vom Auftraggeber bereitgestellten Daten
EmployerDr. Rietzler & Heidrich GmbH
Dates 09/2005 — 10/2005
ParticipantsDr. Alexander Prechtel


Global random walk stochastic simulations for the assessment of the contamination risk in groundwater systems
Funding AgencyDeutsche Forschungsgemeinschaft (SU 415/1-1,2)
Dates 06/2005 — 05/2008
ParticipantsDr. Nicolae Suciu, Prof. Dr. Peter Knabner

The fate of contaminants in groundwater has been investigated through two-dimensional simulations of transport in synthetic velocity fields, which reproduce the characteristics of actual aquifers, using the Global Random Walk method. The predictability of the classical stochastic model has been quantified by sample to sample fluctuations, via simple-sampling Monte Carlo simulations on parallel computers. The Fokker-Plank equation and its equivalent Itô representation have been used to analyze the dependence of the effective transport coefficients on the problem parameters. In this way, some new features arising in the numerical experiments were explained and used to assess conditions for the reliability of the stochastic approach. The codes used in stochastic simulations were tested against field experiments by comparisons with measured data recorded at Krauthausen (Research Center Jülich, Germany). Opens external link in new windowDetails


2000 - 2004

Modelling of the reactive transport of contaminants in the (un-)saturated zone for the prognosis of natural attenuation
Funding AgencyBMBF - Part of the joint research project KORA dealing with natural attenuation (Förderschwerpunkt "Kontrollierter natürlicher Rückhalt und Abbau von Schadstoffen bei der Sanierung kontaminierter Böden und Grundwässer" KORA).
Dates 2004 - 2008
ParticipantsProf. Dr. Peter Knabner, Dr. Alexander Prechtel; Dr. Florian Frank, Dr. Joachim Hoffmann, Dr. Stephan Oßmann
The evaluation of the potential of contaminated sites concerning natural attenuation needs comprehensive process descriptions and accurate, reliable numerical algorithms. Numerical errors may lead to qualitatively completely wrong conclusions concerning the potenial of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the qualitiy and efficiency of the calculations ensured by modern numerical methods as well as the usability. The existing software platform RICHY has been extended, which is already intensely and successfully used by universities, institutes and consultants for the simulation of reactive transport and parameter identification. Among previous modules for coupled sufactant transport, preferential, unsaturated flow or carrier facilitated transport the project could realize new model components that surpass most of all existing software packages. The extensions contain complete descriptions of microbially catalysed degradation with arbitrary reaction partners and inhibition, general multicomponent reactions including the effects of ionic strength, as well as mineral dissolution and precipitation. The efficient and highly accurate, newly developed mathematical solution algorithms for the resulting coupled systems of partial differential equations could show their qualitiy in complex international benchmark studies. Locally mass conserving, mixed hybrid finite element discretisations of the flow problem have been combined with globally impliciten, reactive multicomponent models. Novel reduction methods for the latter rely on the linear transformation of the equation systems and varialbes and lead to the consideration of conservation quantities which can be handeled efficiently, as a part of the transport – reaction – equations decouples. Another approach that has been pursued simultaneously relys on a modified Newton method and results in efficiency enhancements by the neglection of coupling terms in the Jacobian matrix. This algorithm can be applied fully adaptively, in 1D as well as in 2D. Both approaches could be combined with adaptive techniques for the automatic, efficient choice of time steps and spatial grid sizes, which makes the calculation of these complex problems feasible on PCs.


Development of a simulation tool for the prognosis of the spreading and the degradation of contaminants in the saturated and vadose zone
Funding AgencyBavarian Ministry BayStMLU (Bayerisches Staatsministerium für Landesentwicklung und Umweltfragen) under coordination of the Gesellschaft zur Altlastensanierung in Bayern mbH (GAB); Part of the joint research project "Sustainable remediation involving natural attenuation" (Bayerisches Verbundvorhaben "Nachhaltige Altlastenbewältigung unter Einbeziehung des natürlichen Reinigungsvermögens")
Dates 2001 - 2003
ParticipantsProf. Dr. Peter Knabner, Dr. Alexander Prechtel; Dr. Markus Bause, Dr. Sandro Bitterlich, Dr. Andreas Brand, Dr. Florin Radu, Dr. Reinhard Zapata

The project included the mathematical modelling of natural attenuation processes in the subsurface and the extension of a software tool for complex reactive multicomponent processes in the framework of mixed hybrid and conforming finite elements. New  parameter identification methods allow the parametrization of unknown functions or a formfree optimization, and help to overcome the dilemma of missing data in complex models. Work included instationary 3D simulations and scenarios of  contaminated sites explored by project partners. The findings of the joint research project resulted in guidelines for authorities and consulting engineers dealing with natural attenuation at contaminated sites.

Opens external link in new windowLink

Quantification of Contaminant Sources and Transport Prognosis in Aquifers
Funding AgencyBMBF Verbundvorhaben Sickerwasserprognose
Dates 2001 - 2004
ParticipantsDr. Sandro Bitterlich, Dr. Alexander Prechtel, Prof. Dr. Peter Knabner
Mathematical simulation tools allow the quantitative integration of competing transport and transformation processes which are relevant for a seepage water risk prognosis. Therefore model simulations have to contain a comprehensive process description, while they can serve for parameter identification by inverse modelling of suitable column or batch experiments, and allow to quantify the dependence of a key variable on parameters through a simultaneous sensitivity analysis. The software platform RICHY1D has been extended and is already intensively and successfully used in universities, institutes and by consultants for the 1D simulation of complex reactive transport and for parameter identification. It stands out by the application of efficient and highly accurate mathematical solution strategies for the resulting systems of partial differential equations (e.g. locally mass conserving mixed hybrid finite element discretisations, modified Newton’s method). Besides the formerly existing modules for coupled surfactant-water transport, multiphase flow, saturated-unsaturated flow or carrier facilitated transport, the extensions contain in particular source terms (boundary conditions, distributed sources, arbitrarily time dependent, nonlinear and multiple (de-)sorption kinetics, mobilisation from a residual NAPL phase), preferential flow with solute transport, and heat transport in soils with coupling to reaction parameters of the contaminant transport like Monod degradation parameters, e.g.. The parameter identification is possible for the model extensions as well, which allows the identification of multiple complex parametrizations from suitable experiments (for example for source terms or microbially mediated degradation, sorption characteristics and hydraulic parameters). There is no need to impose a certain functional shape of these nonlinearities, the so-called form-free identification is also feasible, and furthermore a closed-flow experiment design can be accounted for. The sensitivity analysis is provided separately for the evaluation of the dependence of a key variable like the concentration of arbitrary model parameters, what represents a powerful tool in a transport simulation to identify controlling factors and evaluate uncertainties of the data.


1999 and before

A parallel hybrid FEM-spectral Navier-Stokes solver for viscous channel flow
Funding Agencyjoint French-German CNRS-DFG research project Numerical Flow Simulation
Dates 1997 - 2001
ParticipantsSerge Kräutle, Professor Dr. Wolfgang Borchers, Professor Dr. Raimund Rautmann, et al.
The goal of the project is the construction of a parallel Navier-Stokes solver on channel-like domains. The parallelization is done by the domain decomposition method CGBI (Conjugate Gradient Boundary Iteration). A main aspect is the coupling of Chebyshev spectral solvers on rectangular subdomains with Finite Element solvers on subdomains of complicated geometry. A pressure correction scheme decouples each Navier-Stokes timestep into elliptic and hyperbolic problems. The hyperbolic equation (i.e. the transport equation) is solved with a method of characteristics, and the elliptic problems with CGBI. One main purpose of this project lies in the investigation of CGBI. Special interest is laid on the development of efficient preconditioners for CGBI. In contrast to other domain decomposition methods, our preconditioners only act on the interfaces between the subdomains. Thus, no additional subdomain-based problems have to be solved. Nevertheless, we achieve error reduction rates of one or even two power(s) of ten in each CGBI step. These convergence rates are independent on the number of subdomains and on the discretization parameter. Numerical test runs for the parallel Navier-Stokes solver for a cylinder in a channel (modelled in 2d) and for a backward facing step show the robustness and the accuracy of the method. The Reynolds numbers for our tests vary between 50 and 4000.
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