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Old   July 22, 2009, 09:28
Default zeroGradient pressure and moving mesh
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Christophe Kassiotis
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Dear all,

I'm currently trying to solved one of the benchmark fsi problem proposed by Wall and co-authors (see for instance Kütller and Wall (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation doi:10.1007/s00466-008-0255-5). The problem consist in a modified lid-driven cavity with a moving bottom, with two unconstrained nodes at the top right and left vertical walls. In the first attached picture, the discretized problem by 32x32 elements is represented, as well as the boundary condition (Picture from the publication given above). The time step considered is 0.1s

For the sake of simplicity, let us consider for the moment the fluid problem only. For the velocity (U) boundary condition, I consider imposed velocity (0 0 0) at walls, (1-cos(2×Pi×t/T) 0.0 0.0) at the top and zeroGradient for the unconstrained faces.
As one can see, the pressure (p) boundary conditions are not define, and therefore, I used zeroGradient everywhere. It is well known that then p is defined to a constant, and playing with pRefCell and pRefValue, i managed to get approximatively good pressure forces ( p×dS ) at the bottom of my cavity (fixing the top right cell to 0).

The problem start when I want to move the mesh. I consider for the moment only imposed motion of the bottom (0.0 L(1-cos(2×Pi×t/T)) 0.0) with L = 0.1. Then, if i'm not fixing one of the pressure, the computation quickly crash (at t=0.9s)

Continuity error cannot be removed by adjusting the outflow.
Please check the velocity boundary conditions and/or run potentialFoam to initialise the outflow.
Total flux              : 0.0509994
Specified mass inflow   : 0.000944722
Specified mass outflow  : 1.87515e-18
Adjustable mass outflow : 0
The problem is that when I fixed the pressure to one (or two) of the output, then the pressure oscillations become to big compared to what they supposed to be.

My questions are the following:
Q1 : is it normal that the problem occurs in Finite Volume, and not with their stabilized Finite Element ? I get a message from Küttler that say that the pressure is not fixed
in their computation, and that pose no problem. Maybe I'm wrong, but this does not depend of the discretisation technic used, as the continuum equation are the same ? So maybe something miss here...
Q2 : as the force applied to the body directly depend of p (and not of its gradient) the constant used here to fixe p is of importance, isn't it ?
Q3 : is it possible to solve a problem with icoDyMFoam and zeroGradient pressure every where for the pressure ? Or is my crash a desired behavior ? Maybe is it hard to adjust phi when the domain is moving ? Is their a way to fix this problem ?
Q4 : as someone any advices for the boundary condition ? I have to say that I try many of them (fixedValue, totalPressure at the inlet, one gives results as close as them for the force at the bottom as the one with zeroGradient) ?

Thank you in advance.

Attached Images
File Type: png problemDefinition.png (29.4 KB, 128 views)
File Type: png p1023.png (6.6 KB, 130 views)
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