Natural vorticity boundary conditions on solid walls

• We devise vorticity boundary conditions on solid walls, which possess physical and geometrical information relevant to near-boundary vortex dynamics.
• The conditions are local and enforced in the Galerkin formulation through a right-hand side functional depending on the pressure.
• Two numerical schemes are suggested that benefit from the new conditions and solve for velocity, vorticity, and pressure in a decoupled time-stepping fashion.

We derive a new kind of boundary conditions for the vorticity equation with solid wall boundaries for fluid flow problems. The formulation uses a Dirichlet condition for the normal component of vorticity and Neumann type conditions for the tangential components. In a Galerkin (integral) formulation the tangential condition is natural, i.e., it is enforced by a right-hand side functional and does not impose a boundary constraint on trial and test spaces. The functional involves the pressure variable, and we discuss several velocity–vorticity formulations where the proposed condition is appropriate. Several numerical experiments are given that illustrate the validity of the new approach.