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If one has to simulate oscillating plate/solid wall ( sinusoidal function of time) in a domain (a simple piston movement in 'y' direction), the obvious way would be scenario 1. For brevity, assume there is no topological changes involved.

Scenario 1: To use dynamic mesh and move the mesh points via the prescribed equation.

Scenario 2: The fluid near wall takes up a zero velocity (assuming no slip). Now, With this in mind, using an oscillating velocity boundary condition in 'U' at the plate/solid wall (working out the velocity of the fluid for the plate's displacement amplitude) as the fluid should obey the no slip condition and produce the flow features similar to a moving mesh ?

Will the result of scenario 2 be different to scenario 1? Is scenario 2 the right way to represent a near wall fluid with no slip? what happens to 'k' and 'pressure' in scenario 2?

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One and two do not lead to the same flow. One is like a piston that actually compresses the flow, two will behave differently. The details are dependent on the inlet flow characteristics, but you should not expect the same behavior. If the flow is slow ($M \ll 1$), you might be able to get away with a short-time simulation of the starting conditions in a fixed box, but the two cases will rapidly diverge. You might also be able to simulate a speaker/diaphragm this way, but solving the compressible Navier-Stokes equations for very small amplitudes is usually overkill.

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  • $\begingroup$ does it mean that if the mesh motion amplitudes are insignificant such that they dont affect the overall domain, then scenario one should equal scenario two? Well, I think it needs to be tested though. But is it worth investigating i.e by replacing mesh motion with wall velocities or is it abruptly wrong physics to try that out? $\endgroup$ – Thangam Apr 1 '15 at 10:19
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    $\begingroup$ No, it means that they are close. Equality is a strong requirement. The smaller the amplitude, the closer they will be, at least for short times. E.g. for weak sound waves, you can probably get away with it, but if that's what you're modeling, you'd probably be better off solving the Helmholtz equations rather than the compressible Navier-Stokes equations. $\endgroup$ – Bill Barth Apr 2 '15 at 14:32

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