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SIMPLE algorithm with moving mesh - convergence problems

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Old   June 18, 2022, 09:22
Default SIMPLE algorithm with moving mesh - convergence problems
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Hello everyone,

Currently, I try to write a Matlab code to simulate the incompressible flow generated by an vertically oscillating object (a cube for example) immersed inside a parallelepiped water tank (3 dimensions problem).

Here are the features of my code:

- 3 dimensions unsteady problem
- Staggered grid (cartesian meshes)
- discretisation method: Finite volume method
- Scheme chosen: Central difference scheme with deffered correction for the convective terms (to avoid the local Reynolds number limitations induced by the "normal" central difference scheme)
- Linearisation method of the momemtum equation: Picard linearisation (the convecting velocity component equals the value from the previous iteration)
- Resolution algorithm: SIMPLE algorithm with underrelaxation factor for pressure and velocities applied at each physical computed time.

Due to the vertical oscillating (sinusoidal) movement of the immersed object, the computation mesh follow this movement. It means that, when the object goes down, the mesh is "crushed" below the object, stretched above the object and follows the vertical oscillating movement between the top and bottom faces of the object. In the momemtum equations, these mesh movement imply that the convecting z-velocity is the relative fluid velocity to the mesh velocity (= variation of the control volume face position/time variation). And in the pressure correction equation (obtained from the continuity equation), the unsteady term vanishes due to the conservation of space ("Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries", Demirdzic and Peric). This approch is possible because the mesh moves in only one direction (vertcial direction).

On a coarse mesh, it seems that there is no convergence problem. But when I want to use a finer mesh, divergence occurs after several iterations for the second or third physical time computed. The divergence begin when the velocity at a point becomes higher than the maximum velcoity of the oscillating object (which is not very physical). Does this behaviour remind you something or could you propose me a trouble shooting procedure ?

This is my first post on this forum and I hope that the problem is sufficiently described.
Thank you in advance for your answers.
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convergence problems, moving 3d mesh, simple algorithm

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