Numerical integration of the contravariant form of the two phase flow motion equations

Reservoirs (which are created by the artificial barrage of watercourses) gradually lose the capacity to store water resources owing to the progressive accumulation of solid particles, which are transported by the watercourses, on the bed. In conditions characterized by a flood with a high capacity for transporting large quantities of solid material, turbidity currents could occur; in these situations and in the presence of a steep bed slope, the turbidity currents can reach the bottom outlets. In this paper a model for the simulation of the turbidity currents is proposed; the model is based on the numerical integration of the two phase flow motion equations. These equations are integrated on a three-dimensional generalised curvilinear grid and are directly expressed in contravariant formulation. The numerical procedure adopted is based on a fractional step method and the proposed numerical scheme is conservative and fourth order accurate. The numerical model is validated by comparison between the numerical results and experimental data and is applied to the reservoir of Pieve di Cadore (Italy), in order to verify the possibility of the production of turbidity currents and the possibility of using the bottom outlet to discharge downstream the solid material that reaches the reservoir during flood events.