We present self-consistent calculations of supercurrent flows in a realisti
c tilt grain boundary. We obtain the current-phase characteristics in both
s-wave and d-wave superconductors. We do this self-consistently within the
framework of the Bogoliubov-de Gennes equations, using a realistic microsco
pic model of the grain boundary. This yields the s- and d-wave superconduct
or order parameters in the vicinity of the boundary and the respective quas
iparticle local density of states. [S0163-1829(99)00529-9].