Methods and Applications of Analysis
Volume 15 (2008)
A General Stability Condition for Multi-stage Vorticity Boundary Conditions in Incompressible Fluids
Pages: 469 – 476
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.
Vorticity-stream function formulation; local vorticity boundary condition; stability condition
2010 Mathematics Subject Classification