Model-based computational study of reactive fluid systems using transfer operator methods
Abstract
In many industrial applications one aims for the design of efficient chemical reactions. This is often done using experimental analysis of the reactors in combination with numerical twins. However, the simultaneous modeling of flow, mixing and chemical reaction remains a complicated task because the computational costs are still significant and oftentimes prohibitive. Here, we model and analyze mixing processes of chemical substances by a transfer operator method using the Lagrangian trajectories of passive particles. In practice, we represent the spatial distributions of the chemical species concentrations by density vectors. These are evolved by means of a stochastic transition matrix, which is obtained as a numerical approximation of a transfer operator. In a further step, we model the reaction of the fluids by specific update rules of the density vectors. The method is applicable for closed and open example systems and different chemical processes such as competitive consecutive reactions. We demonstrate that the dynamic processes are reflected well by this method. Furthermore, we evaluate the interdependence of the reaction fronts with Lagrangian coherent structures which we define using set-oriented methods that also work well on three dimensional data.
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BibTeX
@misc{gobel2026modelbased,
title = {{Model-based computational study of reactive fluid systems using transfer operator methods}},
author = {Anja Göbel and Anna Klünker and Alexandra von Kameke and Kathrin Padberg-Gehle},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28635},
eprint = {2610.28635},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28635},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model-based computational study of reactive fluid systems using transfer operator methods
AU - Anja Göbel
AU - Anna Klünker
AU - Alexandra von Kameke
AU - Kathrin Padberg-Gehle
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.28635
UR - https://arxiv.org/abs/2610.28635
AB - In many industrial applications one aims for the design of efficient chemical reactions. This is often done using experimental analysis of the reactors in combination with numerical twins. However, the simultaneous modeling of flow, mixing and chemical reaction remains a complicated task because the computational costs are still significant and oftentimes prohibitive. Here, we model and analyze mixing processes of chemical substances by a transfer operator method using the Lagrangian trajectories of passive particles. In practice, we represent the spatial distributions of the chemical species concentrations by density vectors. These are evolved by means of a stochastic transition matrix, which is obtained as a numerical approximation of a transfer operator. In a further step, we model the reaction of the fluids by specific update rules of the density vectors. The method is applicable for closed and open example systems and different chemical processes such as competitive consecutive reactions. We demonstrate that the dynamic processes are reflected well by this method. Furthermore, we evaluate the interdependence of the reaction fronts with Lagrangian coherent structures which we define using set-oriented methods that also work well on three dimensional data.
ER -