Qualitative analysis of dynamics in Kolmogorov's problem on a flow of a viscous incompressible fluid
type: Item
instance of: scholarly article
title: Qualitative analysis of dynamics in Kolmogorov's problem on a flow of a viscous incompressible fluid
zbMATH Open document ID: 1334.35228
DOI: 10.1134/S0012266115100055
author: N. Evstigneev
author: N. A. Magnitskii
author: D. A. Silaev
published in: Differential Equations
publication date: 2016-01-28T00:00:00Z
review text: In this paper the authors provide a numerical analysis of a 2D periodic viscous incompressible flow excited by an external force. An approximate scheme is based on the Galerkin method coupled to spline approximation. The weak convergence is proved for the approximate scheme and numerical results are compared to alternative methods using trigonometric polynomials, finite volumes or finite element method.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 6536814
zbMATH Keywords: Kolmogorov problem
zbMATH Keywords: Galerkin method
zbMATH Keywords: spline approximation
reviewed by: Bernard Ducomet
MaRDI profile type: Publication
cites work: Investigation of the stability of a stationary solution of a system of equations for the plane movement of an incompressible viscous liquid
cites work: Weak turbulence in periodic flows
cites work: Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori
cites work: Hopf bifurcation of the three-dimensional Navier-Stokes equations
cites work: Bifurcations and inviscid limit of rhombic Navier-Stokes flows in tori
cites work: Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow
cites work: On possible scenarios of the transition to turbulence in Rayleigh-Bénard convection
cites work: Nonlinear dynamics of laminar-turbulent transition in three dimensional Rayleigh-Bénard convection
cites work: The Regularized Spline (R-Spline) Method for Function Approximation
cites work: Q3541491
cites work: Twice continuously differentiable semilocal smoothing spline
cites work: Q3036570
cites work: Q4163866
cites work: Bivariate spline method for numerical solution of time evolution Navier-Stokes equations over polygons in stream function formulation
cites work: Strong stability-preserving high-order time discretization methods
cites work: On the nature of turbulence in Rayleigh-Bénard convection
cites work: Q4840149
full work available at URL: s0012266115100055
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description: scientific article; zbMATH DE number 6536814