Volume 14, Issue 3
Modeling the Lid Driven Flow: Theory and Computation.

Makram Hamouda, Roger Temam & Le Zhang

DOI:

Int. J. Numer. Anal. Mod., 14 (2017), pp. 313-341

Published online: 2017-06

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  • Abstract

Motivated by the study of the corner singularities in the so-called cavity flow, we establish in the first part of this article, the existence and uniqueness of solutions in L²(Ω)² for the Stokes problem in a domain Ω, when Ω is a smooth domain or a convex polygon. This result is based on a new trace theorem and we show that the trace of u can be arbitrary in L²(∂Ω)² except for a standard compatibility condition recalled below. The results are also extended to the linear evolution Stokes problem. Then in the second part, using a finite element discretization, we present some numerical simulations of the Stokes equations in a square modeling thus the well known lid-driven flow. The numerical solution of the lid driven cavity flow is facilitated by a regularization of the boundary data, as in other related equations with corner singularities ([9], [10], [45], [24]). The regularization of the boundary data is justified by the trace theorem in the first part.

  • Keywords

Stokes and related (Oseen etc.) flows weak solutions existence uniqueness regularity theory lid driven cavity

  • AMS Subject Headings

76D07 35D30 76D03

  • Copyright

COPYRIGHT: © Global Science Press

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