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Foil 18 Simple Model CFD-like Equation in Dimensionless Form

From CPS615-Physical Simulation Techniques and Structure of CFD Equations Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 14 November 96. by Geoffrey C. Fox *
Secs 77.7
What sort of equations does CFD give ?
Put x component of velocity u = v x
and let r be density and p pressure
Take the case of incompressible flow where the density of fluid is constant
r ¶u/ ¶t + r ( v .Ñ) u = - ¶p/ ¶x + m Ñ 2u
Make dimensionless with scaling transformations
x ® x / L
t ® t / T
v ® v / V
u ® u / V
p ® p / ( r V2 )

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