Methods and Applications of Analysis

Volume 15 (2008)

Number 4

A General Stability Condition for Multi-stage Vorticity Boundary Conditions in Incompressible Fluids

Pages: 469 – 476



Cheng Wang


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

65M06, 76M20

Published 1 January 2008