Dear Thank you for commenting on this. I tried and did what you suggested, but I am having trouble making it work.
First, I draw the two orthogonal lines on top of the polymer disc (I'm using Design Modeler, since that is what I'm used to), but they don't show up in the geometry when I open the Model (please see the screenshots below). Therefore, I'm still unable to enforce the mesh to include the center point on the disc in the mesh nodes.
Also, I added the shared topology (third screenshot below), but it does not make the mesh matched between the polymer disc and the water region, so I'm still getting much coarser mesh in the water region, at the boundary between the disc and water. I'm not sure if there is any specific settings I should make for the shared topology though. It does not seem to have any options to choose the bodies, but it says 2 bodies in its properties (which is the total number of the bodies in my structure, so I'm thinking it might be okay.) I also noticed that there is a warning about the shared topology in Design Modeler, based on which the shared topology is not taken into account it seems like, and I don't know how to fix it (the last two screenshots below).
Is there anything I'm missing and I have to change in the settings?
It just came to my mind that it might be necessary that I define a contact region under connection in Model. Is it? Previously, I had it generated automatically, but every time I ran the simulation, a warning showed up that one of the materials involved in that contact is acoustic region, and that it may be overwritten during the simulation.
(I have read some about defining contacts in the help documentation, but I am not able to find the situation where it is defined between acoustic and structural regions. )

I appreciate it if you could share your opinion about these issues.

Thank you Parinaz