If you are having trouble with fluid passing through thin walls during a fluid simulation then you can disable “Remove air bubbles” in the Fluid Boundary settings for your Domain object.
If you are rendering an opaque object, such as a coffee mug, then no further steps should be required.
If you are rendering a transparent object, then it is possible that you will also need to increase your Resolution settings, otherwise you will indeed have “air bubbles” in your render. The “remove air bubbles” setting is a great idea, but unfortunately it seems to work very poorly.
The below image has “remove air bubbles” turned off and Final resolution set to 32. You can clearly see the air pockets (the interior of the cup is just a slightly curved cylinder, not that weird shape).
I’ve done a few tests with this scene, and the air pockets remain all the way up to 128 resolution, but they are barely noticeable. At 256 resolution, they are not noticeable, but fluid simulation is very slow.
This may have something to do with how many times my cup has been subdivided. My guess is that the air bubbles go away once the surface geometry of the water is smaller than the surface geometry of the interior of the cup. That’s just a guess though, and I have not tested it.