Over the past decade, nanotechnology has set the industrial world on a new development path. Experimental and theoretical scientists are interested in discovering new structures of soft materials with potential applications in nanotechnology, including nanoporous storage media, fabrication for nanoelectronics, soft robotics, energy harvesting, and biomedical. Mathematicians are predicting novel morphologies of diblock copolymer systems through mathematical modelling and computer simulations studying nanostructures in the presence of a surface field, which leads to the identification of new dimensions of melt. Confinement improves the frustration in nanostructures and leads to new patterns of nanoparticles. The computational study of novel nanostructures is done through simulation models. The cell dynamic simulation model provides large-scale simulations of nanomaterials quickly and efficiently. This computational investigation confines lamellar, cylindrical, and spherical structures into asymmetric diblock copolymers (𝑓𝐴 ≠ 𝑓𝐵) in circular annular discs. For the simulations requirement of this model, the continuum macromolecule of the diblock copolymers system is discretized on a 17-point isotropic stencil to approximate the Laplacian in a polar mesh. FORTRAN codes have been developed for the PDEs included in the model. The simulation results are visualized with Open Dx.