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Polynominal Interpolation Methods for Viscous Flow CalculationsHigher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and by Hermitian (Taylor series) finite-difference discretization. The similarities and special features of these different developments are discussed. The governing systems apply for both uniform and variable meshes. Hybrid schemes resulting from two different polynomial approximations for the first and second derivatives lead to a nonuniform mesh extension of the so-called compact or Pad? difference technique (Hermite 4). A variety of fourth-order methods are described and the Hermitian approach is extended to sixth-order (Hermite 6). The appropriate spline boundary conditions are derived for all procedures. For central finite differences, this leads to a two-point, second-order accurate generalization of the commonly used three-point end-difference formula. Solutions with several spline and Hermite procedures are presented for the boundary layer equations, with and without mass transfer, and for the incompressible viscous flow in a driven cavity. Divergence and nondivergence equations are considered for the cavity. Among the fourth-order techniques, it is shown that spline 4 has the smallest truncation error. The spline 4 procedure generally requires one-quarter the number of mesh points in a given coordinate direction as a central finite-difference calculation of equal accuracy. The Hermite 6 procedure leads to remarkably accurate boundary layer solutions.
Document ID
19790071265
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Rubin, S. G.
(Polytechnic Inst. of New York Farmingdale, NY, United States)
Khosla, P. K.
(Polytechnic Inst. of New York Farmingdale, NY, United States)
Date Acquired
August 29, 2013
Publication Date
June 1, 1976
Publication Information
Publication: Journal of Computational Physics
Volume: 24
Issue: 3
Subject Category
Fluid Mechanics And Heat Transfer
Report/Patent Number
AD-A053059
AFOSR-78-0540TR
NASA-CR-157618
Accession Number
79N70773
Funding Number(s)
CONTRACT_GRANT: NAS1-13885
CONTRACT_GRANT: AF-AFOSR-2635-74
Distribution Limits
Public
Copyright
Other

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