Transfer Operator Approximations from Lagrangian Trajectories Reduce Cost of Reactive Fluid Simulations

The authors discretize concentration fields into density vectors and advance them via a numerically approximated transfer operator derived from Lagrangian data. Reaction steps are inserted as explicit update rules on these vectors, bypassing full Eulerian CFD for the combined flow-mixing-reaction problem. Tests on benchmark mixing-reaction cases demonstrate that reaction fronts align with Lagrangian coherent structures extracted by the same set-oriented framework, including in three-dimensional domains.

Existing industrial digital-twin workflows remain limited by the prohibitive cost of resolving simultaneous advection, diffusion, and stiff kinetics. The transfer-operator route decouples the expensive trajectory integration from the reaction step, offering a pathway to faster parametric studies of reactor geometry and operating conditions. This approach builds on earlier non-reactive transfer-operator work while adding the reaction layer that most prior Lagrangian methods omitted.

The study is purely methodological and contains no experimental validation data or scaling benchmarks against production CFD codes. Next steps would require side-by-side timing and accuracy comparisons on an industrial-scale reactor geometry with measured outlet concentrations to establish whether the computational savings survive when calibration and uncertainty quantification are included.