# A General Probabilistic Approach for Quantitative Assessment of LES Combustion Models

## TL;DR

This paper introduces the Wasserstein metric as a probabilistic, quantitative validation tool for LES combustion models, capable of evaluating multiple scalar quantities and identifying sources of model deviations.

## Contribution

It generalizes the Wasserstein metric for turbulent reacting flows and demonstrates its effectiveness in validating LES combustion models against experimental data.

## Key findings

- Wasserstein metric effectively evaluates multiple scalar quantities.
- The method identifies boundary condition uncertainties and model deficiencies.
- Application to various datasets shows versatility and robustness.

## Abstract

The Wasserstein metric is introduced as a probabilistic method to enable quantitative evaluations of LES combustion models. The Wasserstein metric can directly be evaluated from scatter data or statistical results using probabilistic reconstruction against experimental data. The method is derived and generalized for turbulent reacting flows, and applied to validation tests involving the Sydney piloted jet flame. It is shown that the Wasserstein metric is an effective validation tool that extends to multiple scalar quantities, providing an objective and quantitative evaluation of model deficiencies and boundary conditions on the simulation accuracy. Several test cases are considered, beginning with a comparison of mixture-fraction results, and the subsequent extension to reactive scalars, including temperature and species mass fractions of \ce{CO} and \ce{CO2}. To demonstrate the versatility of the proposed method in application to multiple datasets, the Wasserstein metric is applied to a series of different simulations that were contributed to the TNF-workshop. Analysis of the results allowed to identify competing contributions to model deviations, arising from uncertainties in the boundary conditions and model deficiencies. These applications demonstrate that the Wasserstein metric constitutes an easily applicable mathematical tool that reduce multiscalar combustion data and large datasets into a scalar-valued quantitative measure.