For gradually varied two-dimensional, unstea‹ty flows, characteristics and explicit anal implicit finite-difference metliotis have dccii used by a iiuiiificr of investigators (Leendertse 1967; Katopodes and Strelkoff 1978; Benque et a1. 1982; Abbott 1984; Lai 1986). The method of characteristics was used by Katopodes (1978) to simulate the two-dimensional propagation of dam- break flood waves. The bore was isolated and tracked explicitly along the downstream channel. Matsutomi (1983) used the leapfrog scheme to com- pute dam-break flow profiles over a dry bed. He employed shock fitting to track the bore as done by Sakkas and Strelkoff (1973) and used Ritter’s solution for the first few time steps. Katopodes (1984) used a finite-element technique based on the Petrov-Galerkin formulation to solve several discon- tinuous flow situations in two dimensions. Most of these computational pro- cedures fail if subcritical and supercritical flows are present either simulta- neously in different parts of the channel or if they occur in sequence at different times.