Multi-resolution Mesh
 

Is it possible to create the multi-resolution 2D mesh?
For example,
In region A (0,1)X(0,1), the resolution is 32X32; in region B (1,2)X(0,1), the resolution is 128X128; region A and B is connected by the face at plane X=1.

Yes, it's fairly simple too. All you have to do is define a block mesh with two blocks (using 12 points).

I use the two blocks with 12 points, but it doesn't work. The OpenFoam complains "The edge is not consist at the X=1" .
So, I use two blocks with 16 points and 4 pair of points have the same coordinate. The OpenFoam does't complain, but the two blocks are not connected.
I don't know how to do.

You need 12 points in the vertices list. The order of the vertices should be consistent to what you find for a hexahedron on U-127 in the user guide. Then you can define to blocks

hex (0 1 2 3 4 5 6 7) (32 32 1) simpleGrading (1 1 1)
hex (1 8 9 2 5 10 11 6) (128 128 1) simpleGrading (1 1 1)