The complexity of water flow in open channels is even more significant if these channels have variable geometry. Indeed, any change in the cross-section or direction of a channel, such as contraction, expansion, the presence of an obstacle of any shape, or change in slope, results in an irregular, undulating flow surface. The analysis of free surface flows is based on the one-dimensional Saint Venant equations, also known as the shallow water flow equations. These equations provide a robust framework for simulating dam break flows on horizontal planes, including scenarios with trapezoidal obstacles and Venturi-like channel configurations. In this study, an explicit finite difference numerical scheme based on a modified Lax-Friedrichs method is used to model these phenomena. The obtained results from the simulations are compared with experimental measurements and numerical results from the literature to ensure their accuracy. The modified Lax-Friedrichs scheme demonstrates strong agreement with reference data, highlighting its effectiveness in reproducing complex flow behaviors, whether in channels with obstacles or Complex geometry such as Venturi configurations.