2021/09/29 by Carlos Parés-Pulido, Parés-Pulido, Carlos · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #35D99 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #G.3 #J.2 #Markov Chains and Monte Carlo Methods #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2109.14521
openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an efficient numerical scheme based on Monte Carlo integration to\napproximate statistical solutions of the incompressible Euler equations. The\nscheme is based on finite volume methods, which provide a more flexible\nframework than previously existing spectral methods for the computation of\nstatistical solutions for incompressible flows. This finite volume scheme is\nrigorously proven to, under experimentally verifiable assumptions, converge in\nan appropriate topology and with increasing resolution to a statistical\nsolution. The convergence obtained is stronger than that of measure-valued\nsolutions, as it implies convergence of multi-point correlation marginals. We\npresent results of numerical experiments which support the claim that the\naforementioned assumptions are very natural, and appear to hold in practice.\n