Lyapunov exponent and Wasserstein metric as validation tools for assessing short-time dynamics and quantitative model evaluation of large-eddy simulation

TL;DR

This paper introduces Lyapunov exponents and Wasserstein metrics as efficient tools for evaluating the short-time predictability and quantitative accuracy of large-eddy simulations, especially in complex reacting flows.

Contribution

It presents novel application of Lyapunov exponents and Wasserstein metrics for LES validation, demonstrating their effectiveness in assessing mesh dependency and simulation accuracy.

Findings

Lyapunov exponents are more sensitive indicators of mesh independence.

Wasserstein metric provides a quantitative measure of simulation accuracy.

Methods require less computational resources than traditional turbulence statistics.

Abstract

In this work, methods for the evaluation of LES-quality and LES-accuracy are presented, which include the Lyapunov exponent for the analysis of short-time predictability of LES-calculation and the Wasserstein metric for the quantitative assessment of simulation results. Both methods are derived and evaluated in application to the Volvo test case. Both the non-reacting and reacting cases are calculated. For the non- reacting cases, good agreement with the experimental data is achieved by solvers at high numerical resolution. The reacting cases are more challenging due to the small length scale of the flame and the suppression of sinuous mode of absolute instability by the density ratio. The analysis of the turbulent simulation data using the concept of the Lyapunov exponent and the Wasserstein metric provides a more quantitative approach to assess the mesh dependency of the simulation results. The convergence of the Lyapunov exponent is shown to be a more sensitive and stronger indication of mesh-independence. Though grid convergence for the reacting cases cannot be reached with the chosen resolutions, the Lyapunov exponents and the Wasserstein metric are shown to be capable of identifying quantity-specific sensitivities with respect to the numerical resolution, while requiring significantly less computational resources than acquiring profiles of conventional turbulent statistics.