Research

Term: 01.04.2018 - 30.09.2022
Funding source: DFG / Graduiertenkolleg (GRK)
Acronym: IntComSin
Project leader: Günther Grün

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Term: 01.01.2012 - 31.12.2013
Funding source: Deutscher Akademischer Austauschdienst (DAAD)
Project leader: Peter Knabner

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 numerica…

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Term: 01.10.2009 - 30.09.2011
Funding source: Bundesministerium für Forschung, Technologie und Raumfahrt (BMFTR)
Project leader: 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…

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Term: 01.01.2007 - 31.12.2011
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: Peter Knabner, Serge Kräutle

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 with local complementarity conditions as essential ingredient. The problem 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,…

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Term: 01.11.2006 - 31.12.2009
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: Peter Knabner

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,the attachment and detachment of colloids under considerat…

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Term: 01.06.2006 - 30.04.2010
Funding source: Bayerisches Staatsministerium für Bildung und Kultus, Wissenschaft und Kunst (ab 10/2013)
Project leader: Peter Knabner

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 wirtschaftswissensc…

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Term: 01.04.2004 - 31.12.2008
Funding source: BMFTR / Verbundprojekt
Project leader: Peter Knabner, Alexander Prechtel

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 potential of the site for degradation. It has been developed a comprehensive and flexible simulation tool, that is outstanding concerning the variety of processes, the quality and efficiency of the calculations ensured by modern numerical met…

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Term: 01.06.2001 - 31.05.2003
Funding source: Bayerisches Staatsministerium für Umwelt und Gesundheit (StMUG) (bis 09/2013)
Project leader: Peter Knabner, Ulrich Rüde

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…

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Term: 01.01.2001 - 31.12.2004
Funding source: Bundesministerium für Forschung, Technologie und Raumfahrt (BMFTR)
Project leader: 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…

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