A finite difference level set projection algorithm on multi-staged quadrilateral grids for simulation of a split liquid film between two rollers. From one stage to the next, the number of meshes in the vertical direction changes by a select factor to provide a good balance between resolution and number of meshes. Having fewer meshes at the nip (the smallest gap between the rollers), the multi-staged quadrilateral grid allows a much bigger time step and requires much less CPU time to reach the steady state.