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A finite-volume Total Variation Diminishing (TVD) scheme is presented for modeling dam-break flows in open channels.This method is used for solving the 2D shallow water equations on arbitrary quadrilateral meshes, based upon a second-order hybrid TVD scheme with an optimum-selected limiter in the space discretization and a two-step Runge-Kutta approach in the time discretization.Verification for a circular dam-break problem is carried out by comparing the present results with others and very good agreement is shown.The present algorithm is then used to predict dam-break flow characteristics in open channels such as in furcated channels.More complicated unsteady flow characteristics in these furcated channels than in the regular channels studied previously can observed in this work.