# Stability Conditions for Navier Stokes Eqns

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 November 20, 2014, 14:25 Stability Conditions for Navier Stokes Eqns #1 New Member   Santosh Join Date: Nov 2013 Posts: 11 Rep Power: 4 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!

November 20, 2014, 14:37
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by konangsh 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

 November 20, 2014, 14:44 #3 New Member   Santosh Join Date: Nov 2013 Posts: 11 Rep Power: 4 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!

November 20, 2014, 15:02
#4
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,354
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Quote:
 Originally Posted by konangsh 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

 November 20, 2014, 15:32 #5 New Member   Santosh Join Date: Nov 2013 Posts: 11 Rep Power: 4 Thanks a lot for your replies, Dr. Denaro! FMDenaro likes this.

 Tags cfl condition, navier stokes equations, wave equation

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