Ali,
I am not familiar with non-uniform grids in MIKE, but I have experience with non-uniform 3-D meshes in other software. What exactly are you attempting to model? Can you include a screencap of the grid? It is difficult, otherwise, to diagnose numerical instability.
My initial guess would be that your grid and/or time discretization are too large for the flow velocity you are attempting to model (see Courant Number, CFL criteria). What values are you using?
Instability could also be caused by poor mesh/grid quality. I'm not sure what freedoms MIKE gives you for non-uniform meshes, but an abrupt 'jump' in cell size can bring about numerical error, especially if a large gradient encounters such a cell (in this case, position or velocity, but the same is true with heat, pressure, shear stress, etc.)
Hope this helps.