A boundary plasma fluid model that takes into account nonuniform magnetic fields is presented. The model is based on the approach described by LaBombard et al. [Bull. Am. Phys. Soc. 33, 2103 (1988)] but has been enhanced to consider nonuniform magnetic fields and applied to the scrape-off layer (SOL) of a cylindrical plasma. The two-dimensional code based on this model has been developed and used for studying the effect of the large changes in magnetic fields and B×■B drift on the properties of the SOL plasma, which include potential, density, electric field, and plasma particle flux. The code is validated by comparison with experimental results in PISCES using constant magnetic fields. From the numerical simulations, it is observed that particle fluxes in cylindrical SOL plasma are influenced by combined local radial and azimuthal (poloidal) gradients in applied axial magnetic fields. These local steep gradient magnetic fields in the SOL plasma can thus be an effective means to actively control plasma and impurity transport.