Field of research in my dissertation

In today's world combustion processes are still the main energy source. Forced by ecological and economical needs the simulation and optimization of these processes plays a more and more growing role in combustion research.

The challenge of model reduction is to overcome the discrepancy between the necessary numerical simulation based on detailed multi-scale mechanisms and the its attended high computational effort. The goal of all model reduction approaches is a low-dimensional but still sufficient approximation of the full reaction mechanism. Many model reduction methods, that are studying the long-term behavior of a system, assume fast time scales to be fully relaxed after a short transition time. The trajectories relax onto so called slow invariant manifolds of low dimension.

In 2004 Lebiedz presented a new variational approach based on maximally relaxed trajectories [1]. Its idea is to find an approximation of a point on the manifold as the solution of an optimization problem.

We are working on further development and examination of this approach for model reduction [2]. Main goal of this work is a complete implementation of a code for model reduction, that can also be used in CFD simulations. So this work combines methods of numerics and optimization with ideas of thermodynamics for the final computation of simplified models of chemical kinetics.

[1] D. Lebiedz. “Computing minimal entropy production trajectories: An approach to model reduction in chemical kinetics”. J. Chem. Phys. 120(15):6890, 2004.

[2] see also in publications.
  • mani1
  • mani2