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Numerical approximation of statistical solutions of planar, incompressible flows.
- Source :
-
Mathematical Models & Methods in Applied Sciences . Dec2016, Vol. 26 Issue 13, p2471-2523. 53p. - Publication Year :
- 2016
-
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 , 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182025
- Volume :
- 26
- Issue :
- 13
- Database :
- Academic Search Index
- Journal :
- Mathematical Models & Methods in Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 119943533
- Full Text :
- https://doi.org/10.1142/S0218202516500597