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.