Thèse de doctorat en Dynamique des fluides et des transferts
Soutenue en 2008
à Nantes .
Contribution to the development of a SPH method for the numerical simulation of wave-body interactions
Recent development in numerical methods together with the increase of computational power available have allowed the simulations of more and more complex flows. However interfacial flows remain a difficult task, especially when breaking, interface fragmentation or reconnection occurs. Smoothed Particle Hydrodynamics, being meshless and Lagrangian, allows to solve simply and elegantly such problems. A SPH based numerical method has been precedently developped in the Fluid Mechanics Laboratory, but its application to wave propagation problem shows weaknesses compared to other numerical methods. In this PhD the initial solver has been improved in order to solve correctly the wave propagation problem. A particular care was taken concerning the theoretical aspects of the method. In particular the introduction of an exact Riemann solver has noticeably increased the numerical stability. This tool allows to adjust automatically the stabilisation required. The use of renormalization together with a weak formulation of the problem help to solve the characteristic lack of consistancy of the SPH method. Extension to free surface flows has been proposed. The use of smoothing length tensor in place of the classical unidimensional smoothing length allows simulations with spatially variable mesh size. Comparaison of obtained results with both experimental results and theoretical results in a variety of test cases such as dam breaking, Riemann problem, deformation of a patch of fluid, wave propagation, shows good agreement, confirming the contribution of the new improvments. Moreover, a new hybrid scheme is presented for specific problems with wave propagation. This new hybrid method relies on the combination of spectral methods and the SPH solver. The wave propagation problem is first solved accuratly with a spectral method. Then the incident wave train is introduced in a consistant way into the SPH solver. First results seem to be encouraging, showing a significantly decrease in cpu time. Thanks to code organization, three dimensional viscous simulations are possible with minimum adaptation.