Abstract
AbstractRecent studies indicate that consistently stabilized methods for unsteady incompressible flows, obtained by a method of lines approach may experience difficulty when the time step is small relative to the spatial grid size. Using as a model problem the unsteady Stokes equations, we show that the semi‐discrete pressure operator associated with such methods is not uniformly coercive. We prove that for sufficiently large (relative to the square of the spatial grid size) time steps, implicit time discretizations contribute terms that stabilize this operator. However, we also prove that if the time step is sufficiently small, then the fully discrete problem necessarily leads to unstable pressure approximations. The semi‐discrete pressure operator studied in the paper also arises in pressure‐projection methods, thereby making our results potentially useful in other settings. Copyright © 2006 John Wiley & Sons, Ltd.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: International Journal for Numerical Methods in Fluids
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.