Weak imposition of Dirichlet boundary conditions in fluid mechanics

Weakly enforced Dirichlet boundary conditions are compared with strongly enforced conditions for boundary layer solutions of the advection-diffusion equation and incompressible Navier-Stokes equations. It is found that weakly enforced conditions are effective and superior to strongly enforced conditions. The numerical tests involve low-order finite elements and a quadratic NURBS basis utilized in the Isogeometric Analysis approach. The convergence of the mean velocity profile for a turbulent channel flow suggests that weak no-slip conditions behave very much like a wall function model, although the design of the boundary condition is based purely on numerical, rather than physical or empirical, conditions. (c) 2005 Elsevier Ltd. All rights reserved.