Methods and Applications of Analysis

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

Cheng Wang

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Abstract

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.

Article information

Source
Methods Appl. Anal., Volume 15, Number 4 (2008), 469-476.

Dates
First available in Project Euclid: 2 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.maa/1254492829

Mathematical Reviews number (MathSciNet)
MR2550073

Zentralblatt MATH identifier
1177.76267

Subjects
Primary: 65M06: Finite difference methods 76M20: Finite difference methods

Keywords
Vorticity-stream function formulation local vorticity boundary condition stability condition

Citation

Wang , Cheng. A General Stability Condition for Multi-stage Vorticity Boundary Conditions in Incompressible Fluids. Methods Appl. Anal. 15 (2008), no. 4, 469--476. https://projecteuclid.org/euclid.maa/1254492829


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