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2nd order boundary condition for NS eqn

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Old   July 17, 2005, 11:34
Default 2nd order boundary condition for NS eqn
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Quarkz
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Hi,

I'm now using unsteady cartesian FVM cell centered non-staggered fractional step mtd to solve the NS eqns. The scheme is supposed to be 2nd order.

I've read thru the forums. however, i am still a bit confused, esp. the specification of pressure at the boundary for the poisson eqn.

My original BC for wall are: u,v=u,v of wall. du/dx & dv/dy =0 for left/right & top/bottom wall since normal diffusive flux to wall=0 p(boundary)=cell centered p nearest boundary (linear extrapolation)

Will this give me 2nd order BC? I've used this for lid driven cavity and my ans differs from Ghia by 5-10%, depending on Re.

Pls enlighten me. Thank you
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Old   July 17, 2005, 11:37
Default Re: 2nd order boundary condition for NS eqn
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Quarkz
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oh ya, and dp/dn=0 at wall as well.
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Old   July 17, 2005, 15:33
Default Re: 2nd order boundary condition for NS eqn
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Ahmed
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Quarkz I am sorry if this is not your real name, anyway I guess that the library of NUS is good enough and have the following book Computational Fluid Dynamics Principles and Applications by J.Blazek and published by Elsevier. It is a 400 page book developing the FVM from basics. Hope that will help and good luck
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Old   July 17, 2005, 20:11
Default Re: 2nd order boundary condition for NS eqn
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Quarkz
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oh thanks. i've read that book a while ago but now i don't 've access to it anymore. btw, i believe there's some confusion with implementing the BC for poisson eqn since some references stated if the BC is not handled properly, it may not be possible to achieve 2nd order accuracy for projection or fractional step mtd. Hence I hope ppl here can give an updated view.
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Old   July 18, 2005, 04:47
Default Re: 2nd order boundary condition for NS eqn
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andy
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> oh ya, and dp/dn=0 at wall as well

Although often imposed in desperation this is a physically incorrect boundary condition. Extrapolating the pressure from inside would be more physically reasonable although a less stable condition.

The imposition of reasonable time varying boundary conditions at a wall will depend on many of the details of your scheme. The pressure smoothing is going to be a particular problem to get to behave at all reasonably in the presence of significant normal pressure gradients (e.g. swirl).

A literature search will throw up many papers concerning imposing accurate boundary conditions for the Navier-Stokes equations. Fractional step methods for incompressible flow have a rich history of schemes that are not quite right at the boundary and, consequently, a fair few papers talking about it. Reading one or two should help familiarise you with the issues and one two simple test cases for you to check the behaviour of your scheme.
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