The splits you have will give an O-grid, very popular in the 90s but not used much now. If you use inflation with a reasonable aspect ratio freezing the liquid in the channels will be OK. Just watch you retain enough space for the moving fluid and enough mesh resolution.
The splits I'm suggesting cut across the channel so you'll have a series of straight and curved sections. It just gives the mesh something to anchor too, an axial split in the xy plane will help with that too.
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