Hello, I am currently trying to do the linear stability around a sphere flow at low Reynolds number (following the work of P. Meliga, J.-M.Chomaz and D.Sippa ( Unsteadiness in the wake of disks and spheres: Instability, receptivity and control using direct and adjoint global stability analyses). I …

Hello Maxime, Usually the variational formulation for the no-stress condition is obtained by taking any test function without any boundary condition nor boundary integral. For the free slip condition one has to impose \vec u \cdot n = 0 and take any test function satisfying the same normality c…

You can see some example implementations here . If you integrate the weak pressure gradient and viscous terms by parts, you simply neglect writing the boundary integral to enforce the free outflow condition. Note that this BC is NOT a no-stress condition, even though it is often incorrectly called th…

Hello François and Chris, I thank you very much for your answers and the explanations, it seems clear to me now. I will have use the example proposed to implement it. Thank you once again, Maxime

Long Time ago I have write slide on this. Subject BC-STOKES.pdf 159.69 KB The example are in the url directory

Hello, I thank you for the document.

You may look at this post for the implementation of the slip condition on a curved boundary. [image] Boundary condition General Discussion If you want to avoid using a Lagrange multiplier (because it enlarges the matrix to invert), some other ways to penalize t…

Hello François, I thank you for your answer, so if I understand well, the difficulty is not really on the outlet boundary condition but rather on inlet and sphere boundaries. Would it be possible to share with you my code because for inlet and sphere boudaries, I tought impose zero velosity on these…

Did you use tgv=-1 or other for the matrix LHS and RHS ? Maybe you should not put boundary condition in the RHS matrix if you use penalty to impose the boundary condition (ex. tgv =1e30) . When you use EPSsolve to solve the eigenvalue problem, the shift-invert methods might be done by the EPSsolve…

Besides, the outlet boundary condition might be called " free outflow" more properly. It is not the strict “no stress”. But for the incompressible NS equations, the results should be almost the same if the viscous terms (with “grad of velocity” or “rate of deformation tensor”) in your variational fo…

Maxime, My message was rather about the external boundary where you impose a slip condition. If I understand well this boundary is curved (in the sense that the normal is not constant on this boundary). On the boundaries where you impose homogeneous Dirichlet I see no particular problem. However …

Boundary condition in eigenvalue problem

General Discussion

fb77 (François Bouchut) May 3, 2024, 9:44am 7

You may look at this post for the implementation of the slip condition on a curved boundary.

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Boundary condition in eigenvalue problem

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