# Time-varying sensitivity analysis for mixing in chaotic flows: a comparison study

## TL;DR

This study compares different global sensitivity analysis methods applied to time-varying mixing in chaotic flows, highlighting their efficiency and reliability in complex, high-dimensional models.

## Contribution

It provides a comparative evaluation of Sobol, Morris, and activity scores methods for sensitivity analysis in chaotic flow mixing, especially in high-dimensional settings.

## Key findings

- Morris method is significantly more computationally efficient than Sobol.
- All methods show comparable sensitivities in simpler flow models.
- Morris and activity scores provide consistent results in high-dimensional models.

## Abstract

Engineered injection and extraction systems that create chaotic advection are promising procedures for enhancing mixing between two species. Mixing efficiencies vary considerably, so carefully selecting the design parameters, like pumping rates, well locations, or operation times, is crucial. While numerous studies investigate the conditions required to achieve chaotic flow, sensitivity analyses addressing its impact on mixing have rarely been performed. However, selecting a suitable sensitivity analysis method depends on the underlying system and is often restricted by the computational cost, especially when considering complex, high-dimensional models. Moreover, the most appropriate metric to quantify mixing (e.g., plume area, peak concentration) can also be system-specific. We perform a time-varying sensitivity analysis on the mixing enhancement of two chaotic flow fields with different complexities. The rotated potential mixing (RPM) flow is parametrized using two or four hyperparameters, while the quadrupole flow utilizes 16 hyperparameters. We compare three global sensitivity analysis methods: Sobol indices, Morris scores, and a modification of the activity scores. We evaluate the temporal evolution of the sensitivity of the design parameters, compare the performance of the three methods, and highlight their potential in analyzing parameter interactions. The analysis of the RPM flow shows comparable sensitivities for all methods. Additionally, our numerical experiments show that Morris is the cheapest method, needing at most four times fewer model evaluations than Sobol to reach convergence. This motivates us to only use the computationally cheaper but as reliable Morris and activity scores on the 16-dimensional model, yielding again consistent results.