Computational Boundary Conditions for the Incompressible Navier-Stokes Equations in Channels and Pipes.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1987
- Accession Number
- ADA193356
Entities
People
- Gerardo A. Ache
Organizations
- University of Wisconsin–Madison