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continuity & navier stokes....

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Old   March 2, 2007, 08:14
Default continuity & navier stokes....
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Am new to CFD and am getting confused between the continuity and Navier Stokes equations- some papers refer to NS and some to continuity- I was wondering what(if any) is the relationship between the two?

Sorry for asking such a simple question but haven't been able to find anything to clear this up!

Thanks in advance.
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Old   March 2, 2007, 11:10
Default Re: continuity & navier stokes....
Kasper Skriver
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The continuity equation is ONE equation whereas the NS's is several equations.

To answer your question, it is therefore not the same equation.

The continuity equation: nabla(u)=0, simply states that the sum of velocity gradients must be zero.

The NS equations: Can be writen as incompressible with constant viscosity/density, and describes the relation of velocity, pressure, density, viscosity and external forces on the fluid. It is timedependent and non-linear(big problem), but can be averaged using the Reynolds decomposition of instantaneous fluid properties: u = U + u'. This is leading to the RANS equations (Reynolds Averaged NS), the closure problem, and finally equations that can be solved in coarse meshes by numerical methods.

Allways keep in mind that "turbulence is a property of the flow itself, and not of the fluid!" as Bill George puts it.

BR Kasper Skriver
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Old   March 2, 2007, 11:57
Default Re: continuity & navier stokes....
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It has become sort of a convention to refer to the entire set of governing equations for a flow field as the "Navier-Stokes Equations." This set includes equations governing the conservation of mass (Continuity), conservation of momentum (Historical Navier-Stokes equations), and conservation of energy. It is wise to note that the entire set of equations can be deduced rather simply from the general Reynold's Transport Theorem which is a single tensor equation for the conservation of some quantity Q. Hope this helps.

Regards Andrew
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