Spectral element discretization of the circular driven cavity. Part IV: The Navier-Stokes equations
Date
2004ISSN
1422-6928Source
Journal of Mathematical Fluid MechanicsVolume
6Issue
2Pages
121-156Google Scholar check
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This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.