A characteristic method for transport calculations in two-dimensional geometries has been developed as a part of the interface-current transport code TDT. A complete description of angular and spatial approximations, as well as numerical implementation is given. A new synthetic acceleration technique has also been developed based on piecewise uniform and isotropic approximations for cell entering and exiting fluxes. Fourier analysis of the accelerated iterations shows the potential of the new acceleration scheme. Numerical results for one-group and multigroup problems involving realistic assembly geometries prove the performance of the acceleration in realistic unstructured geometries.