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Old   December 8, 2009, 14:54
Default Interpolation question
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I'm a newbie to CFD and I am having some trouble with interpolation.

I am trying to implement a 1D flow using the SIMPLE algorithm. I am using Pantakar's Heat Transfer and Fluid Flow for reference. Accordingly, I'm setting up a main grid and staggered grid. Also, I am ignoring diffusion for now.

My problem has to do with setting up the momentum equation for the staggered grid. In order to do so, I need the following term:

where m is the mass flux and u is the velocity, both at interface E (which is pt E on the main grid). m_E is just the density at E times the velocity at E. I need to interpolate the velocity here. For arguments sake, lets say I use a central differencing scheme, or u_E=0.5*(u_e+u_ee) for equal grid spacing.
My question is this: when I calculate m_E*u_E, can I now use an upwind scheme for convecting m_E? That is, can I write:

m_E*u_E=u_e*Max|m_E,0| - u_w*Max|-m_E,0| ?

I feel like there are issues with this statement, since I am effectively trying to convect velocity based on the direction of the mass flow. How does one convect velocty?! The other problem I see is that I have two different values for velocity at E! Any advice?

Thanks in advance,

Last edited by sdk; December 8, 2009 at 18:33.
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