Physical Sciences and Mathematics Commons^™

Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …