The SPH technique applied to free surface flows

Abstract

This paper deals with an application of the SPH (Smooth Particle Hydrodynamics) technique to treat free surface problems. The SPH technique was originally conceived and developed for treating astrophysical problems and belongs to the class of “meshless” methods that dispense with the requirement of a computational grid. Instead, a cloud of particles is used to represent the continuum, the contact interaction between them is introduced with their subsequent trajectory being computed in the Lagrangian sense. The design and implementation of the method for transport equations and the Euler inviscid equations is fairly well-documented. Applications to the treatment of free surface flows is however more recent. In this work, the computation of three-dimensional free surface flows with the method is presented. The introduction of Riemann solvers to model the breakup of the initial surface discontinuities between particles is a novel feature of this work. For purposes of illustration, a three-dimensional simulation of the Vaiont dam disaster that occurred in 1963 in northern Italy is presented. This is a case where complicated three-dimensional geometries are involved and was chosen to show-off the versatility of the technique. The results are in general agreement with the qualitative observations and reconstruction of the event as reported by experts. The SPH technique is found to be very promising and powerful for application to free surface flows. In particular, the stage is being reached where for hydraulic problems; it may be used as a powerful simulation tool to delineate high-risk zones downstream of a possible dam failure where geometries of almost arbitrary complexity are involved. At the present time, significant progress is being achieved in developing the technique for application in different domains.