Free surface flows with SPH method (French text)

SPH (Smoothed Particle Hydrodynamics) is a Lagrangian method used since the end of the seventeen in the simulating of gas dynamics and high-speed shocks. In this work, an adaptation of this method is given for free surface flows simulations.; First, the SPH is used in the one-dimensional case. This step is dedicated to the evaluation and the adaptation of the method to free surface flows. In the second section, the two-dimensional case is studied in details. The problem of dam break in various configurations is used as the benchmark test.; The result obtained depends on the concerned problem. For the cases of standard and circular dams, the results are quiet encouraging. The capture of shocks and the shape of the waves were successfully revealed. The results were compared with analytic solution, in the ID case, and with result given by the finite volume method. We note that the SPH presents a good reproduction of existing solution. Nevertheless, some oscillations are still present in the solutions.; In addition, a new combined finite element-SPH formulation is presented. This formulation seems to be better than the original SPH version. It gives the possibility to introduce all finite elements techniques of corrections and stabilizations. The results obtained with this new formulation show amelioration especially in the earlier times of simulation. The Lagrangian nature of the method (the lack of particles) is the principle cause of the non-conformity of obtained results with finite-volumes ones.; The success of the SPH in the free surface flows depends on the optimisation of its parameters, a smart choice of particles number, type of the kernel and the smoothing of irregularities in the geometry. Additional works are suggested to give more efficiency to this method that promises an interesting future in fields where the Eulerian methods are unable to tackle.