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Old   March 21, 2007, 23:09
Default Convergence based on Reynolds Number
  #1
Dominic
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Hi,

The paper "Accurate Three Dimensional Lid-Driven cavity flow" J.comp.Phy 206(2005) 536-558 by Albensoeder & Kuhlmann, defines in Page 543, a Convergence criteria for steady flow as :

max( u(X,t) - u(X,t-dt) ) / dt*Re < epsilon, X is a vector here. My question is : Why is Reynolds number appearing here ?

Regs, Dominic

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Old   March 22, 2007, 08:32
Default Re: Convergence based on Reynolds Number
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Paolo Lampitella
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Is the Re number at numerator or denominator:

1) ( max ( u(X,t) - u(X,t-dt) ) / dt ) * Re

or

2) max ( u(X,t) - u(X,t-dt) ) / ( dt * Re )

?

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Old   March 22, 2007, 09:06
Default Re: Convergence based on Reynolds Number
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Jonas Holdeman
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Put in the definition of the Reynolds number in terms of the reference velocity and other things, and you will see that the criterion says that the incremental velocity in a time step needs to be small compared to the reference velocity. How small depends on the other things. This is to make the criterion independent of the velocity scale.
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Old   March 22, 2007, 11:27
Default Re: Convergence based on Reynolds Number
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Dominic
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In the Denominator
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Old   March 22, 2007, 11:35
Default Re: Convergence based on Reynolds Number
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Dominic
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Thanks, If we put in the dimensions of each quantity, i see that, the entire term goes as x/t^2 < epsilon ... where x, t are length and time scales respectively. Something like an acceleration ??
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Old   March 22, 2007, 13:24
Default Re: Convergence based on Reynolds Number
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desA
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max ( u(X,t) - u(X,t-dt) ) / ( dt * Re )

= max (u(X,t) - u(X,t-dt))/dt * (1/Re )

= acc * (1/Re)


'acc' represents the temporal acceleration, determined between two successive temporal-stations (time-snapshots) for a slowly-evolving solution. This term should go to zero as a steady solution is approached - if it exists.

I'm wondering why they multiply 'acc' by (1/Re)?

desA
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