Validation and Test Cases for a Free Surface SPH Model

Abstract

The SPH method (smoothed-particle hydrodynamics) is a numerical meshless, particle and lagrangian method. It is used in a lot of fields of engineering and science such as solids mechanics, hydraulics, and astrophysics. The medium is represented, thanks to a set of particles which interact with each other. Nowadays, the SPH method is still under development but is able to deal with a wide range of problems in hydraulics. This article focuses especially on open channel quasi-incompressible flows. While implementing a SPH code, a programmer can face up some difficulties such as the neighbors search, the boundary conditions, the speed of sound, or the initialization of the particles. We have drawn some unexpected conclusions concerning the compressibility of the fluid and the way the particles are initialized. This paper presents also a list of test cases that can be performed in order to validate an SPH code. It includes: (a) a tank of still water, (b) a spinning tank, and (c) a dam break on a dry bed. These test cases allowed us to highlight some undesired effects. Finally, a new test case is developed. It is based on new experimental results of a flow on a spillway. For this test case, open boundaries have been implemented. The results presented in this paper are based on a 3-D code implemented during a master thesis.