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Poiseuille Flow in a Rectangular Channel
Author

Housam Binous
Organization: KFUPM
Department: Chemical Engineering
URL: http://sites.google.com/site/homepageofdrhousambinous/
Revision date

2007-05-23
Description

LU Decomposition is applied to a sparse banded matrix (A). We show how fill-ins can make solution by elimination not manageable by computing non-zero elements of U and L such that A=LU. The same matrix, A, is used to solve the Poiseuille flow problem in a rectangular channel using the finite differences approach. The result obtained using this numerical technique is in agreement with the one given by the analytical solution, which was derived using separation of variables.
Subjects

*Applied Mathematics
*Applied Mathematics > Numerical Methods
*Engineering > Chemical Engineering
*Engineering > Mechanical and Structural Engineering
*Science > Physics > Fluid Mechanics
Keywords

Poiseuille flow, rectangular channel, LU Decomposition, fill-ins, finite differences, analytical solution, separation of variables
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PoiseuilleFlow.nb (447.4 KB) - Mathematica Notebook [for Mathematica 5.2]