In spite of the recent advances achieved with superconducting fault current limiters, modeling and simulation of such devices are still important issues. Different approaches have been used to model the transient behavior of such devices when submitted to fault currents. In this paper, the alternating direction implicit method is used to numerically solve the thermal equations discretized by the finite-difference method (FDM). That is a fast method to solve the system of differential equations resultant from the FDM discretization. It also allows the insertion of inhomogeneities of the superconducting tapes in the simulation and the study of its influence on fault limitation. The results of simulations models were compared with experimental data. A good agreement between simulated current and voltages with tests has been found in the present work. In addition, the temperature increase and the electrical field in the tapes during the fault time is shown.