Normally, any disturbance in the course of supercritical or high-velocity flow may result in the generation of a series of shocks. The numerical simulation of shallow flows in the presences of such discontinuities is rather difficult by the conventional methods. The shocks and the bores may be divided into two main groups of stationary and dynamic shocks. In the stationary shocks, the shock location does not vary with time, such as hydraulic jump. In this paper, we employed the second order Roe-TVD scheme for the numerical simulation of shallow flows both in one and two dimensions. The numerical results are then compared with the experiments and the available analytical solutions. Next, a series of fully developed 2D stationary shocks caused by the interaction of a supercritical flow and a cross barrier was simulated. The numerical results were in close agreement with our measurements in a laboratorial setup. It may be deduced that, the scheme of Roe-TVD is a robust method for the simulation of complicated stationary shocks in shallow water flows.

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