This work is devoted to the numerical simulation of Shallow Water Equations using Runge-Kutta Discontinuous Galerkin methods. Such methods were implemented in the framework of adaptive mesh refinement method using a block-based approach. The space and time discretization using the Runge-Kutta Discontinuous Galerkin approach is applied to nonlinear hyperbolic Shallow Water Equations. Increasing the order of approximation, spurious oscillations appear and are addressed using moment limiters. Finally, the solver is validated with a one-dimensional dam-break problem and its behavior is tested solving a two-dimensional benchmark.