How to prevent volumes are filled in overlapping objects?

I hope I can explain what I want to achieve. Here are two intersected objects:

You assume in the image that the blue plane is water and the red semisphere floats half submerged.
Then without using physics nor fluid simulation,

I want that the blue part of the inner of the semisphere “automatically” disappears when the blue plane and semisphere are intersected, looking like this:

I want to make a simple animation frame by frame. But I do not want to have to remove that blue intersection by hand in each frame.
Is it possible to do this automatically on a simple way?

I have tried with Boolean modifier, but I can not imagine how to do it.

a) At the same position as that half sphere (HS) you have a very very slightly larger full sphere (FS).
b) Parent the FS to the HS so that it follows the HS whereever that moves.
c) Add a Boolean Difference modifier to the plane with the FS as object.
d) Make the FS invisible and unrenderable.

Example .blend - just play the animation.

Thank you very much IkariShinji ! . That solves my problem.
I just need a top view, but if necessary, is it possible to make the part of the sphere under de plane keep the sphere material (red) in the render?

So, in opened volumes with more complex geometry, I just need to duplicate the object, slightly increase the size and close the volume of the duplicated object?

As for the material question: Just add a second material slot to the plane object and set that to whatever material the sphere is using:

That should take care of that.

Well, you were asking for a simple solution…:wink:
It might work by using the half sphere (or whatever other object) itself as the boolean object, but from my (limited) experience solids work more reliably when it comes to booleans.

Ok, thanks!