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A Finite-Element Solution of the Navier-Stokes Equations for Two-Dimensional and Axis-Symmetric Flow

By Sven Ø. Wille

Abstract

The finite element formulation of the Navier-Stokes equations is derived for two-dimensional and axis-symmetric flow. The simple triangular, T6, isoparametric element is used. The velocities are interpolated by quadratic polynomials and the pressure is interpolated by linear polynomials. The non-linear simultaneous equations are solved iteratively by the Newton-Raphson method and the element matrix is given in the Newton-Raphson form. The finite element domain is organized in substructures and an equation solver which works on each substructure is specially designed. This equation solver needs less storage in the computer and is faster than the traditional banded equation solver. To reduce the amount of input data an automatic mesh generator is designed. The input consists of the coordinates of eight points defining each substructure with the corresponding boundary conditions. In order to interpret the results they are plotted on a calcomp plotter. Examples of plots of the velocities, the streamlines and the pressure inside a two-dimensional flow divider and an axis-symmetric expansion of a tube are shown for various Reynolds numbers

Topics: Finite element method, blood flow, Mathematics, QA1-939, Science, Q, DOAJ:Mathematics, DOAJ:Mathematics and Statistics, Electronic computers. Computer science, QA75.5-76.95, Instruments and machines, QA71-90, DOAJ:Computer Science, DOAJ:Technology and Engineering
Publisher: Norwegian Society of Automatic Control
Year: 1980
DOI identifier: 10.4173/mic.1980.2.4
OAI identifier: oai:doaj.org/article:94897a049e3b4402aee557f941dab0b6
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  • https://doaj.org/toc/0332-7353 (external link)
  • http://www.mic-journal.no/PDF/... (external link)
  • https://doaj.org/article/94897... (external link)
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