Stokes' First problem

11092016, 09:59 AM
(This post was last modified: 11092016 05:33 PM by Ángel Martin.)
Post: #1




Stokes' First problem
Stokes’ First Problem. [ P1STOKE ]
From the author’s Engineering Collection, included in the ETSII4 module (ETI4 on the CL Library) This program calculates the velocity at a point placed at a distance Y from the bottom and an instant t in an unsteady viscous boundary layer flow. The bottom is suddenly imposed at t=0 a constant velocity U0 and the fluid has a kinematic viscosity "nu". Vertical distances (y) are measured from the bottom (y=0) up. The expression for the instant velocity at a distance y can be related to the cumulative probability function of a normal distribution as follows: U(y,t) = 2 U0 [ 1 F( y / sqr(2 nu t) ) Example: for U0 = 1 m/s, nu = 10 m^2/s; Y = 0.5 m and t = 2 s the result is: U(Y,T) = 0.911 m/s The original version of this program used a polynomial approximation to calculate F, with an accuracy limited to 4 to 6 decimal places, depending on the value of the argument. A modern version based on the ERF implementation on the SandMath brings that to at least 8 decimal places and a much faster execution – thanks to MCODE and the improved algorithm used. U(y,t) = U0 [ 1 – erf { [ y / 2 sqr( nu t) ] } Below you can see the program listing using the new approach. Note that R00R03 are used by ERF: Code:


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