Low Reynolds Number Instability in icoFoam - Cavity Case

kmooney · October 8, 2009, 10:08

Hello,

I was wondering if anyone has heard of a lower bound to Reynolds number stability...

I have been running highly viscous cases as part of my research and have been running into instability at very low Reynolds numbers ~1e-3. I tried simplifying the problem and running icoFoam with lid driven cavity at Re=1e-3 and it is highly unstable. The velocity grows in an unbound fashion rather quickly. The occurs regardless of the way that low Re is reached i.e. high viscosity or low velocity. This seems counter-intuitive in that typically low Re flows are computational stable.

Has anyone ever experienced this type of instability before or have any incite as to what is going on?

~Kyle

santos · October 8, 2009, 13:21

Hi,

Make sure your icoFoam time step guarantees a Courant number < 1. Remember that at such low Re diffusion governs your transport. In these conditions, the 'Courant' number (or stability parameter) you need is no more Co=U*dt/dx and is now Co=nu*dt/dx^2, where nu is the kinematic viscosity.

Regards,
Jose Santos

kmooney · October 8, 2009, 14:09

Thanks for the response,

Doesn't that CFL condition only apply to explicit treatment of viscosity? I failed to mention that I am treating it implicitly .

~Kyle

October 8, 2009, 10:08	Low Reynolds Number Instability in icoFoam - Cavity Case	#1
kmooney Senior Member Kyle Mooney Join Date: Jul 2009 Location: San Francisco, CA USA Posts: 323 Rep Power: 17	Hello, I was wondering if anyone has heard of a lower bound to Reynolds number stability... I have been running highly viscous cases as part of my research and have been running into instability at very low Reynolds numbers ~1e-3. I tried simplifying the problem and running icoFoam with lid driven cavity at Re=1e-3 and it is highly unstable. The velocity grows in an unbound fashion rather quickly. The occurs regardless of the way that low Re is reached i.e. high viscosity or low velocity. This seems counter-intuitive in that typically low Re flows are computational stable. Has anyone ever experienced this type of instability before or have any incite as to what is going on? ~Kyle

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October 8, 2009, 13:21		#2
santos Senior Member Jose Luis Santos Join Date: Mar 2009 Location: Portugal Posts: 215 Rep Power: 18	Hi, Make sure your icoFoam time step guarantees a Courant number < 1. Remember that at such low Re diffusion governs your transport. In these conditions, the 'Courant' number (or stability parameter) you need is no more Co=Udt/dx and is now Co=nudt/dx^2, where nu is the kinematic viscosity. Regards, Jose Santos

October 8, 2009, 14:09		#3
kmooney Senior Member Kyle Mooney Join Date: Jul 2009 Location: San Francisco, CA USA Posts: 323 Rep Power: 17	Thanks for the response, Doesn't that CFL condition only apply to explicit treatment of viscosity? I failed to mention that I am treating it implicitly . ~Kyle