Convergence based on Reynolds Number
 

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

Re: Convergence based on Reynolds Number
 

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 )

?

Re: Convergence based on Reynolds Number
 

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.

Re: Convergence based on Reynolds Number
 

In the Denominator

Re: Convergence based on Reynolds Number
 

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 ??

Re: Convergence based on Reynolds Number
 

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