# Convergence based on Reynolds Number

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 March 21, 2007, 23:09 Convergence based on Reynolds Number #1 Dominic Guest   Posts: n/a 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

 March 22, 2007, 08:32 Re: Convergence based on Reynolds Number #2 Paolo Lampitella Guest   Posts: n/a 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 ) ?

 March 22, 2007, 09:06 Re: Convergence based on Reynolds Number #3 Jonas Holdeman Guest   Posts: n/a 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.

 March 22, 2007, 11:27 Re: Convergence based on Reynolds Number #4 Dominic Guest   Posts: n/a In the Denominator

 March 22, 2007, 11:35 Re: Convergence based on Reynolds Number #5 Dominic Guest   Posts: n/a 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 ??

 March 22, 2007, 13:24 Re: Convergence based on Reynolds Number #6 desA Guest   Posts: n/a 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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