No recirculation zone, why??
I have developed a code to simulate a flow past a circular cylinder using Immersed Boundary Method.
I set Re=40, and the free stream inlet velocity to 1 and the diameter of the cylinder 0.1. The resultant streamlines results have no recirculation zone behind the cylinder . Could any one help me to know what is the reason? 
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i am using ABCN discretisation on a staggered grid, the mesh size 0.1D, and a time step of 0.01.
I think i reached the steady state because there is no change in the velocity contours or the vorticity contours is taking place. 
an intersting thing happened when i changed the Re to 500 i could watch a steady state recirculation zone ????
is my inlet velocity has to be adjusted according to the Re ?? I mean if Re =40 then the inlet velocity should be U=viscosity*Re/(D) because i specified the inlet velocity to be 1, with no relation to Re 
Fix your Re number, then you have to fix two among the parameters U, D, viscosity.
Furthermore, ABCN is a time integration scheme, but says nothing about the spatial discretization 
sorry, i used second order centeral difference for the spatial discretization.
I will repeat what you say from my understanding to it: So, for example if i want to make a simulation at Re= 40 around a cylinder with a diameter 0f 0.1 using the kinematic viscosity of water, then the free stream velocity (inlet velocity) will be equal to: (fixing the diameter and viscosity) U=40*1.04e6/0.1=4.16e4 m/s and in the case of Re=150, the free stream velocity will be: U=150*1.04e6/0.1=1.56e3 m/s 
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correct ;) be sure you respect the stability constraint for the ABCN scheme with central second order discretization 
Thanks a lot for your help.
About the stability condition, i think because i am using an implicit way for the treatment of the viscous term then, the restrict constrain of time will be relaxed, so: dt<=dx/U However, i am not sure about the IBM, may be it add additional constrain on the time step!!! 
I have a very strange results:
When i set the kinematic viscosity as 1.04e6 i have no recirculation zone. however, when i set it to 1e2 i clearly see the recirculation zone. i calculate the free stream velocity according to the relation i mentioned above in both cases of viscosity. could you please explain to me why this happened??? 
by retaining the same reynolds number? :confused:

I am using the nondimensional form of NS equation, So i have to set the Reynolds no. and the inlet velocity explicitly, the viscosity does not appear explicitely in the momentum equations.
So, lets say i want to make a simulation of flowing water past a circular cylinder with a diameter D=0.1 at Re=40 and the kinematic viscosity of water is 1.04e6, then the calculated inlet velocity will be U=40*1.04e6/0.1=4.16e4 m/s. I set the parameters like that in my problem, however i didn't have any circulation. However, when i changed the kinematic viscosity to 1e2 (i do not know what fluid have such a value) i got circulation zone!!!!!!!!!!!! So, my question why i do not have a circulation zone for water??? 
Diameter=0.1; % cylinder diameter
%kinematicviscosity=1.04e6; %water at 20 'C kinematicviscosity=0.01; ineltvelocity=Re*kinematicviscosity/Diameter; 
I do not understand what you are done... if you have nondimensional equations (and a non dimensional domain), the only parameter to set is the Reynolds number!

So, how can i specify the inlet velocity (Dirchilit B.C) on a recatangular domain ?

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So, if i have a rectangular domain of 40D * 30D, and a grid size 0.05D
then, the non dimensional diameter will be equal to 1 and the non dimensional inlet velocity will be equal to 1 and the rectangular domain will be equal to 40*30 and the grid size will be equal to 0.05 
x*=x/D, u*=u/U, t*=t.(U/D)

.... yes ! :)

Thank's a lot. :)

Dear Dr. Filippo
i have some strange results: when i set the mesh size to 0.1D, i have a good results for the length of the recirculation zone and the drag coefficient. l/D=2.33 & Cd=1.55 On the other hand, when i decrease the size of the mesh to 0.05D, which is supposed to give better results, it gives worth results: l/D=2.03 & Cd=1.39 Could you tell me please what could be the reason ??? 
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