NDLI: Long Time Stability of High Order MultiStep Numerical Schemes for Two-Dimensional Incompressible Navier--Stokes Equations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Cheng, Kelong Wang, Cheng
Copyright Year	2016
Abstract	The long-time stability properties of a few multistep numerical schemes for the two-dimensional incompressible Navier--Stokes equations (formulated in vorticity-stream function) are investigated in this article. These semi-implicit numerical schemes use a combination of explicit Adams--Bashforth extrapolation for the nonlinear convection term and implicit Adams--Moulton interpolation for the viscous diffusion term, up to fourth order accuracy in time. As a result, only two Poisson solvers are needed at each time step to achieve the desired temporal accuracy. The fully discrete schemes, with Fourier pseudospectral approximation in space, are analyzed in detail. With the help of a priori analysis and aliasing error control techniques, we prove uniform in time bounds for these high order schemes in both $L^2$ and $H^m$ norms, for $m \ge 1$, provided that the time step is bounded by a given constant. Such a long time stability is also demonstrated by the numerical experiments.
Sponsorship	China Scholarship Council. Directorate for Mathematical and Physical Sciences
Starting Page	3123
Ending Page	3144
Page Count	22
File Format	PDF
ISSN	00361429
DOI	10.1137/16M1061588
e-ISSN	10957170
Issue Number	5
Volume Number	54
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2016-10-26
Access Restriction	Subscribed
Subject Keyword	Adams--Moulton interpolation Stability and convergence of numerical methods Fourier pseudospectral approximation uniform in time estimate Spectral, collocation and related methods Statistical solutions of Navier-Stokes and related equations Adams--Bashforth extrapolation two-dimensional incompressible Navier--Stokes equations multistep schemes
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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