Numerical modeling of impulsive loads using the smoothed particle hydrodynamics method

Abstract

The present thesis aims to enhance the applicability of Smoothed Particle Hydrodynamics (SPH) method to simulate impulsive loads. This type of pressure load appears in problems related to wave impacts, which are relevant to the offshore industry and, particularly, in the context of floating platforms for wind energy generation. To that aim, special emphasis is set on deepening into the mathematical grounds of the method. This research conducted during the completion of this thesis has been structured around three blocks: a theoretical study of the convergence of the SPH method; an experimental campaign involving a case where impulsive loads play a relevant role, i.e the dam break experiment; validation of the computation of impulsive loads with SPH by comparing the simulations with the experimental results. The convergence of the SPH method is still an open problem. While some interesting research has been carried out, the results are still partial and a global understanding of conditions required for convergence in the general case is still an open issue. Herein, the convergence of the SPH hydrostatic problem in 1D, considering a free surface, is studied at both the integral and discrete levels of approximation. The consistency of this problem is also addressed. Moreover, the convergence of the integral SPH solution to diffusion problems, including the heat and the advection-diffusion equations, is established using Fourier analysis. The convergence of their discrete versions is also studied numerically. Boundary conditions and their influence on both consistency and convergence are also open problems within SPH. Several aspects regarding the treatment of boundary conditions are considered herein. In particular, the treatment of the free surfaces is studied in the case of the hydrostatic problem. The semi-analytical formulation of the Boundary integrals methodology is revisited and applied to the computational experiments. The role of the time integration scheme in energy conservation and the numerical stability of the method is addressed. To that aim, the error produced at the discrete level due to the time integration scheme is studied. An explicit formula to compute that error is provided. Numerically, several algorithms are compared. A stable simulation is presented using an implicit time integration scheme. This allows for avoidance of the use of artificial viscous terms, so common in the context of SPH to ensure stability. An experimental campaign using the dam break problem with an obstacle has been carried out. The presence of an obstacle induces three-dimensional effects in the flow. The results have been statistically characterized by performing enough repetitions of each case until the statistical parameters (mean and standard deviation) converged. Regarding validation, the dam break problem has been numerically simulated using SPH. More precisely, the open-source code AQUAgpusph has been used. This allowed us to validate the computation of impulsive loads in the context of three-dimensional flows. The numerical simulations show, in general, good agreement with the experimental results. The role of the approximation parameters and the influence of the choice of the kernel have been addressed.