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We present an efficient numerical scheme based on Monte Carlo integration toapproximate statistical solutions of the incompressible Euler equations. Thescheme is based on finite volume methods, which provide a more flexibleframework than previously existing spectral methods for the computation ofstatistical solutions for incompressible flows. This finite volume scheme isrigorously proven to, under experimentally verifiable assumptions, converge inan appropriate topology and with increasing resolution to a statisticalsolution. The convergence obtained is stronger than that of measure-valuedsolutions, as it implies convergence of multi-point correlation marginals. Wepresent results of numerical experiments which support the claim that theaforementioned assumptions are very natural, and appear to hold in practice.

Finite volume methods for the computation of statistical solutions of the incompressible Euler equations