Accession Number : ADA193356
Title : Computational Boundary Conditions for the Incompressible Navier-Stokes Equations in Channels and Pipes.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV-MADISON CENTER FOR MATHEMATICAL SCIENCES
Personal Author(s) : Ache, Gerardo A
PDF Url : ADA193356
Report Date : Oct 1987
Pagination or Media Count : 38
Abstract : This document derives inflow and outflow boundary conditions for the incompressible Navier-Stokes equations in cylindrical geometries. The purpose of these boundary conditions is to allow computations in a finite domain, that model flow in an unbounded domain, in a way that the accuracy of the finite difference solution is retained, making the computation more efficient. We use an approach similar to a previous documents to represent the solution asymptotically, far downstream and upstream, as a series expansion which involves eigenvalues and eigenfunctions. These eigensolutions satisfy certain systems of ordinary differential equations. The boundary conditions are represented by a family of differential operators in a way similar to what was done by Bayliss, Gunzberger and Turkel. To demonstrate the effectiveness of these boundary conditions we applied them in numerical computations of the incompressible Navier-Stokes equations in a channel with a step adn in a pipe with a sudden enlargement of the cross section. To numerically solve the Navier-stokes equations we used a second order accurate finite difference scheme, also the boundary operators were approximated using second order accurate finite difference formulas. The numerical results show the effectiveness and the increase accuracy obtained by using the higher-order boundary conditions. Keywords: Poiseuille flow; Reynolds number.
Descriptors : *NAVIER STOKES EQUATIONS, *PIPES, *CHANNEL FLOW, ACCURACY, BOUNDARIES, COMPUTATIONS, CROSS SECTIONS, CYLINDRICAL BODIES, DIFFERENTIAL EQUATIONS, EIGENVALUES, EIGENVECTORS, EXPANSION, FINITE DIFFERENCE THEORY, FLOW, INCOMPRESSIBILITY, MODELS, NUMERICAL ANALYSIS, REYNOLDS NUMBER, SERIES(MATHEMATICS), SOLUTIONS(GENERAL)
Subject Categories : Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE