NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
A finite difference treatment of Stokes-type flows: Preliminary reportThe equations Laplacian operator omega = 0, (1.1a) and omega = Laplacian operator Chi, (1.1b) describe, in suitable units, 2-D Stokes flow of an incompressible fluid occupying a domain D in which omega is the vorticity and Chi is the stream function. The flow is uniquely determined by specifying the velocity on the boundary B of D, a condition which leads to specifying the stream function Chi and its normal derivative Chi sub n on B. A mathematically similar problem arises in describing the equilibrium of a flat plate in structural mechanics where a related 1-D problem by finite difference or finite element methods is to introduce effective methods for imposing the boundary conditions through which (1.1a) is coupled to (1.1b). These models thus provide a simple starting point for examining the general treatment of boundary conditions for more general time dependent Navier-Stokes incompressible flows. For the purpose of discussion it is assumed that D is a square domain. A standard finite difference method to solve (1.1) is to introduce a uniform grid and then use standard five point finite difference operators to express each equation in (1.1). At any point on the boundary B a value of Chi is specified by the boundary conditions but a value of omega at the same boundary mesh point will also be required to complete the computation. Methods are discussed which overcome the difficulty in solving these problems.
Document ID
19900018654
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Rose, M. E.
(North Carolina Agricultural and Technical State Univ. Greensboro, NC, United States)
Date Acquired
September 6, 2013
Publication Date
September 16, 1989
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
NASA-CR-186480
NAS 1.26:186480
Accession Number
90N27970
Funding Number(s)
CONTRACT_GRANT: NAG1-812
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.
No Preview Available