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Northstar March 6, 2006 21:23

Modify NS eqns for moving body
May I know if I need to add linear acceleration terms like mass X acceleration into the momentum eqn if I am going to model a moving body. the grid will stay with the body and move together with it up and down sinusoidally ?

If so, what is the term exactly that must be added?

thank you.

ganesh March 7, 2006 04:24

Re: Modify NS eqns for moving body
Dear Northstar,

The velocities need to be replaced by (Velocity minus Grid Velocity), leading to the so called ALE formulation. You could refer to papers on moving grids for more information on the same. It is trivial to see that the formulation reduces to the standard one when grid velocity vanishes ie. static case.

Hope this helps



Northstar March 8, 2006 12:03

Re: Modify NS eqns for moving body
thank you Ganesh!

however, since it is moving up/down sinusoidally , there will be acceleration (by differentiating twice) up/down as well. hence is there a need to add some sort of "grid acceleration" into the momentum eqn as well?

thanks again.

ganesh March 9, 2006 01:53

Re: Modify NS eqns for moving body
Dear Northstar,

It is improtant to note that the ALE formulation takes the relative velocity into picture. Thus the fluxes would read as rho*(u-grid_vel) rather than rho*u only. If you derive the equations, or just replace the velocity componenents, by the relative velocity you would see the effect. The fact that the grid is in motion is actually absorbed into the ALE formulation. It is also nice if you start the derivation from the basics, just use a CV approach, with the boundary in motion, and you will see the relative velocity in picture.

Please do not confuse the ALE formulation as such with non-inertial frame of reference, where the reference frame itself is in motion, and hence other issues such as Coriolis forces will come into play. The present formulation is essentially inertial, the refernce frame is moving with the body and the relative velocity accounts for it.

Hope this helps.



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