A two-dimensional numerical model is developed to simulate turbulent shallow-water flow. The model is based on two-dimensional depth-averaged Navier-Stokes equations. A second-order Godunov-type upwind finite volume scheme with augmented HLLC Riemann solver is implemented. The conservative variables near the edges of cells are linearly reconstructed by the MUSCL scheme. The reconstructions are based on the primitive variables. The time marching scheme is a second-order TVD Runge-Kutta scheme, which can prevent the occurrence of oscillation in every intermediate stage. The model uses first-order approximations for the wet-dry fronts and boundaries, which make the solution as robust as possible. An additional flux is calculated to keep the scheme well balanced. To provide body-fitted mesh, the Cartesian cut-cell method is adopted. The κ - ε turbulence model is implemented as the turbulence model closure. The model is tested against several laboratory experiments and field measurements. In all test cases, the simulated results agree well with the observations.