Abstract
We develop a numerical method to calculate the dc Josephson current between the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductors. The Josephson junctions are described by the Bogoliubov--de Gennes equation on the two-dimensional tight-binding lattice. The Josephson current is expressed by the Matsubara Green function which is computed by the recursive Green-function method. We find in d-wave-superconductor/dirty-normal-metal/d-wave-superconductor junctions that the ensemble average of the Josephson current disappears for all temperature regimes when the angle between the crystal axis and the normal of the junction interface is $\ensuremath{\pi}/4.$
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