CONTACT

Dr. Jonas Unger
Phone: +49 (0)731 / 50-23937
Fax: +49 (0)731 / 50-23548

Postal Address
Ulm University
Institute for Numerical Mathematics
Helmholtzstraße 20 (Room 1.04)
D-89081 Ulm
Germany

FIELD OF RESEARCH

A large number of technical applications include chemically reactive flows comprising an interplay between convective and diffusive species transport and chemical reaction processes. In many realistic kinetic models the occurrence of a large number of chemical species and reactions as well as a high degree of stiffness due to multiple time scales give rise to significant challenges for numerical simulations and call for multiscale approaches and model reduction techniques.
The goal of this project is the development of a practical numerical reduction technique that can be applied to high-dimensional realistic chemical reaction mechanisms and automatically computes slow invariant manifolds (SIM) as low-dimensional approximations of long-term system dynamics in chemical kinetics with multiple time scales and spectral gaps.

Publications

2016

Dissertation:
On fundamental concepts for model reduction in multiscale combustion models.
Supervisor: Prof. Dr. Dirk Lebiedz
File: Dissertation.pdf

Lebiedz, D., Unger, J.
On Unifying Concepts for Trajectory-Based Slow Invariant Attracting Manifold Computation in Kinetic Multiscale Models.
Math. Comp. Model. Dyn. (accepted)

2013

Lebiedz, D., Unger, J.
A Boundary Value View on the Reverse Trajectory-Based Optimization
Approach for Kinetic Model Reduction.
Proceedings of the 4th International Workshop on Model Reduction in Reacting Flows, San Francisco.

2012

Lebiedz, D., Unger, J.
Model Reduction in Chemical Kinetics via Slow Manifold Computation.
Proceedings of the Second International Workshop on Model Reduction for Parametrized Systems, Günzburg.

2011

Dedner, A., Fein, M., Klöfkorn, R., Kröner, D., Lebiedz, D., Siehr, J., Unger, J.
On the Computation of Slow Manifolds in Chemical Kinetics via Optimization and their Use as Reduced Models in Reactive Flow Systems.
Proceedings of the 13th International Conference on Numerical Combustion, Corfu.

Lebiedz, D., Siehr, J. Unger, J.
A Variational Principle for Computing Slow Invariant Manifolds in Dissipative Dynamical Systems.
SIAM J. Sci. Comput. 33, 703.

2010

Lebiedz, D. Reinhardt, V., Siehr, J. Unger, J.
Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories.
In "Coping with complexity: Model reduction and data analysis''.
Springer Series "Lecture Notes in Computational Science and Engineering''.

Diploma Thesis:
On the Analysis of an Optimization Approach to Slow Manifold Computation in Chemical Kinetics.
Supervisor: PD Dr. Dirk Lebiedz
File: Diplomarbeit.pdf