  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.
