Model-based computational study of reactive fluid systems using transfer operator methods

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 digital 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. In this work, we incorporate chemical reactions into the classical transfer operator method. This novel approach allows us to model different chemical reaction processes such as a simple chemical reaction scheme using the underlying reaction rate or a more complex competitive consecutive reaction from 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. 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 approximate using set-oriented methods that also work well on three dimensional data.