The region is bounded by a rectangular box [−1,1]×[−1.5,3]×[−1,1].
Large cavity is a ball of radius 1 with the center at (0,2,0). Small cavity is a ball of radius 0.5 with the center at (0,−1,0).
Connector is a cylinder of radius 0.2 with centers of its bases in the centers of the balls.
A small ball inside larger cavity is centered at (0,2,0.5), and has radius 0.2.
Mesh
Mesh grading of the rectangular box is 20×45×20 was obtained with use of blockMesh utility. Mesh of the dumbbell shaped region was obtained by SnappyHexMesh utility.
Initial condition
The function at zero time is Gaussian distribution centered in a larger cavity
Ψ(x,y,z) = e^{[1/4](−x2−(y+1)2−z2)}.
Boundary conditions
Neumann (zero gradient normal to the boundary).
Calculations
The time step is ∆t = 10^{−4}.
Results
Wave function stays in a smaller cavity, without considerable tunneling. The dumbbell is sliced to show the interior.