Two-dimensional free surface flow in branch channels by a finite-volume TVD scheme

Free surface flow, in particular caused by dam-breaks in branch channels or other arbitrary geometrical rivers is an attention getting subject to the engineering practice, however the studies are few to be reported. In this paper a finite-volume total variation diminishing (TVD) scheme is presented for modeling unsteady free surface flows caused by dam-breaks in branch channels. In order to extend the finite-difference TVD scheme to finite-volume form, a mesh topology is defined relating a node and an element. The solver is implemented for the 2D shallow water equations on arbitrary quadrilateral meshes, and 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 two typical dam-break problems is carried out by comparing the present results with others and very good agreement is obtained. The present algorithm is then used to predict the characteristics of free surface flows due to dam breaking in branch channels, for example, in a symmetrical trifurcated channel and a natural bifurcated channel, on coarse meshes and fine meshes, respectively. The characteristics of complex unsteady free surface flows in these examples are clearly shown.