Building on the results of the first funding period, we aim to develop reliable error estimates for numerical simulations of compressible flows, with particular emphasis on methods that remain informative at high Reynolds numbers. These estimates will be extended to statistical solutions and combined with adaptive multilevel Monte Carlo methods for efficient uncertainty quantification. We also plan to extend the framework to the full Navier–Stokes–Fourier system. The project thus brings together mathematical analysis, numerical simulation, and uncertainty quantification.