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- W2519239871 abstract "We present a finite difference-(multi-level) Monte Carlo algorithm to efficiently compute statistical solutions of the two-dimensional incompressible Navier–Stokes equations (NSE), with periodic boundary conditions and for arbitrary high Reynolds number. We propose a reformulation of statistical solutions in the sense of Foiaş and Prodi in the vorticity-stream function form. The vorticity-stream function formulation of the NSE in two-space dimensions is discretized with a finite difference scheme. We obtain a convergence rate error estimate for this approximation which is explicit in the viscosity parameter [Formula: see text], under realistic assumptions on the solution regularity. We also prove convergence and complexity estimates, for the (multi-level) Monte Carlo finite difference algorithm to compute statistical solutions. Numerical experiments illustrating the validity of our estimates are presented. They show that the multi-level Monte Carlo algorithm can significantly accelerate the computation of statistical solutions in the sense of Foiaş and Prodi, even for very high Reynolds numbers." @default.
- W2519239871 created "2016-09-23" @default.
- W2519239871 creator A5035662046 @default.
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- W2519239871 date "2016-12-04" @default.
- W2519239871 modified "2023-09-23" @default.
- W2519239871 title "Numerical approximation of statistical solutions of planar, incompressible flows" @default.
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- W2519239871 doi "https://doi.org/10.1142/s0218202516500597" @default.
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