Two methods based on the variational nodal transport method have been developed to account for localized heterogeneities and local transport effects in full core calculations. A local mesh refinement technique relies on using the projected partial ingoing surface currents produced during coarse-mesh iterations as boundary conditions for fine-mesh calculations embedded within the coarse-mesh calculations. The outgoing fine-mesh partial currents are averaged to serve in the coarse-mesh iterations. Then, a mixed transport-diffusion method using two levels of angular approximations for the surface partial currents depending on the node considered has been implemented to account for local transport effects in full core diffusion calculations. These methods have been tested for a model of the Superphenix complementary shutdown rods.