Numerical Solutions Applied To Heat Transfer And Fluid Mechanics Problems

Allen's Method

Notes are provided in a MicroSoft Word Document or PDF format.

Allen's method does not generate an error estimate like DEM. Taylor series expansions must be substituted into the final difference equation. This produces the terms from the original PDE evaluated at the expansion point, and error terms. I have provided some Mathematica input files that perform such substitutions for some specific difference equations associated with transient fluid flow (math.in, math1.in and math2.in)

Obtaining the finite different approximation and error terms with DEM involves more algebra than you want to do by hand. I've provided two sample MathCad files (DEM1.mcd and DEM2.mcd) that generate difference equations and error terms. If you don't have MathCad on your computer, you can view what I've done in DEM1.pdf and DEM2.pdf.

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Created by Frank Schmidt

Maintained by John Mahaffy : jhm@psu.edu