Fluid Mechanics and the SPH Method

Abstract

This book aims at presenting the SPH method for fluid modelling from a theoretical and applied viewpoint. It comprises two parts that refer to each other. The first, dealing with the fundamentals of Hydraulics, is based on the elementary principles of Lagrangian and Hamiltonian mechanics. The specific laws governing a system of macroscopic particles are built, then the large systems involving dissipative processes are explained. The continua are then discussed; lastly, a fairly exhaustive account of turbulence is given. The second part discloses the bases of the SPH Lagrangian numerical method from the continuous equations, as well as from discrete variational principles, setting out the method's specific properties of conservativity and invariance. Various numerical schemes are compared, permanently referring to physics as dealt with in the first part. Applications to schematic instances are then discussed; ultimately, practical applications to the dimensioning of coastal and fluvial structures are considered. Despite the rapid growth in the SPH field, this book is the first to present this method in a comprehensive way for fluids. It should serve as a rigorous introduction to SPH and a reference for fundamental mathematical fluid dynamics.