A stability condition is provided for a class of vorticity boundary formulas used with the second order finite-difference numerical scheme for the vorticity-stream function formulation of the unsteady incompressible Navier-Stokes equations. These local vorticity boundary formulas are derived using the no-slip boundary condition for the velocity. A new form of these long-stencil formulas is needed to classify the stability property, in which local terms are controlled by global quantities via discrete elliptic regularity for the stream functions.
"A General Stability Condition for Multi-stage Vorticity Boundary Conditions in Incompressible Fluids." Methods Appl. Anal. 15 (4) 469 - 476, December 2008.