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pressure in Navier stokes

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Old   July 2, 2007, 03:53
Default pressure in Navier stokes
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Hi, I am quite new to CFD. I wonder why there is no term like partial(p)/partial(t) in NS equations.

How pressure treated?Is it not time dependent? P=P(x,x,z,t)??

Where is the time dependence ?

Regards, selim
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Old   July 2, 2007, 04:34
Default Re: pressure in Navier stokes
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The pressure is either determined from the equation of state (compressible flow) or the requirement that the velocity field should be solenoidal (incompressible flow). In either case it is related to the conservation of mass. In the incompressible case the pressure must change at every timestep to ensure that the continuity equation is satisfied. In a compressible flow it changes due to changes in density, temperature,... all of which evolve with time.
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Old   July 2, 2007, 09:43
Default Re: pressure in Navier stokes
Jonas Holdeman
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With the incompressible Navier-Stokes equation (NSE), the pressure can be separated from the velocity. One can derive a pressure-free governing equation for the velocity. With appropriate boundary conditions (on the stream function) even so-called pressure-driven problems can be solved without reference to the pressure. The pressure is found to be a function of the velocity. Thus as the velocity evolves in time, the pressure follows. It does not evolve independently in time, so there is no time derivative.

These independent equations for the velocity and pressure are more complicated, except in the weak formulation (which is used in the finite element method). When the independent equations for velocity and pressure are combined, the complications (almost) cancel and resulting equation is the NSE. "Almost" means that the NSE is not the usual differential equation, but is rather a "differential algebraic equation." The dependence of the pressure on velocity still shows through in that there is no time-derivative term for the pressure.
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Old   July 4, 2007, 07:32
Default Re: pressure in Navier stokes
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try to understand the derivation of NS equations... this might clear some of ur doubts
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