Weak imposition of Dirichlet boundary conditions in fluid mechanics. (English) Zbl 1115.76040

Summary: Weakly enforced Dirichlet boundary conditions are compared with strongly enforced conditions for boundary layer solutions of 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 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.


76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
76D05 Navier-Stokes equations for incompressible viscous fluids
76F40 Turbulent boundary layers
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