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Stability Conditions for Navier Stokes Eqns

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Old   November 20, 2014, 14:25
Default Stability Conditions for Navier Stokes Eqns
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Santosh
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Hi All,

I have been wondering if the stability conditions from the Wave equation apply directly to the NS eqns. To be more specific, using an explicit time scheme and upwind space scheme for the wave equation, the condition on CFL number is less than 1 for stability. If I use the same schemes for the NS equations, will my simulations be stable with CFL less than 1, or will it be different?

Hope I was clear... Thanks for any insights!
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Old   November 20, 2014, 14:37
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Filippo Maria Denaro
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Originally Posted by konangsh View Post
Hi All,

I have been wondering if the stability conditions from the Wave equation apply directly to the NS eqns. To be more specific, using an explicit time scheme and upwind space scheme for the wave equation, the condition on CFL number is less than 1 for stability. If I use the same schemes for the NS equations, will my simulations be stable with CFL less than 1, or will it be different?

Hope I was clear... Thanks for any insights!

The answer is no ...
1) the linear stability analysis provides some results but are not exactly the same for non-linear equations
2) the NS eq.s have diffusive terms, the linear stability analysis for an advection-diffusion equation provides a stability region in the (CFL, Re_h) plane, not only a limit value
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Old   November 20, 2014, 14:44
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Santosh
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Thank you very much for the quick reply, Dr. Denaro!

Regarding Point #2, are the stability conditions from the advection-diffusion equation 'sufficient' when applied to the full system of NS equations (since the system also includes the continuity equation, in addition to the momentum equation)? Or will the conditions for the system be slightly different?

Thanks again!
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Old   November 20, 2014, 15:02
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Filippo Maria Denaro
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Originally Posted by konangsh View Post
Thank you very much for the quick reply, Dr. Denaro!

Regarding Point #2, are the stability conditions from the advection-diffusion equation 'sufficient' when applied to the full system of NS equations (since the system also includes the continuity equation, in addition to the momentum equation)? Or will the conditions for the system be slightly different?

Thanks again!
the stability region can be quite different and more limitate
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Old   November 20, 2014, 15:32
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Thanks a lot for your replies, Dr. Denaro!
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