An asymptotic solution for the singularity at the angular point of the lid driven cavity

Abstract

In this paper, we analyse the behaviour of the solution of the Navier—Stokes equations near the corner of the driven cavity where the moving band touches the wall. At this point, the solution is singular. Since the singularity does not depend on the Reynolds number, it is sufficient to study the problem in the case of infinite viscosity, which is governed by the Stokes equations. We present an analytical asymptotic solution near the corner. Furthermore, numerical results are given, which were gained by an efficient multigrid algorithm. We will see that, for decreasing meshsize, the numerical solution converges to the derived analytical solution near the corner.

Citation

Störtkuhl, T., Zenger, C. and Zimmer, S. (1994), "An asymptotic solution for the singularity at the angular point of the lid driven cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 4 No. 1, pp. 47-59. https://doi.org/10.1108/EUM0000000004030