Determining the characteristics of a free jet in 2-D by the SPH method

The Smoothed Particle Hydrodynamic method is a numerical method developed in 1977 to
solve astrophysical problems. This numerical method is meshless, particle and Lagrangian
and has been adapted to hydraulic field.
In this master’s thesis, the method is positioned relative to the classical numerical
methods. The SPH formalism and its adaptation to hydraulic domain is exposed. The
basics of SPH formalism are firstly the integral representation of a function and its
derivative and secondly the particle approximation. The application of the SPH method
to hydraulic domain is made by writting Navier Stokes equations in Lagrangian and
SPH formalisms. Then, the specificities implemented in the code are tackled. These
specificities are the state equation, the viscosity, the boundary conditions, the neighbors
search and the problem initialization.
Afterward, a modification of the initial didactic program, usable for constant domain
in 3D, is performed. The changes are embodied to enable both 2D and 3D simulations
with particle inflows and outflows.
The validation of this modified code is performed thanks to four test cases. These test
cases permit to validate the code and highlight the limitations of the method implemented
such as kernel and the viscosity choices.
Finally flows over sharped-crest weir have been simulated. These simulations were compared
to results from the literature and experimental tests performed in the hydraulic
laboratory. If some improvements are possible, such as injection and initialization of
incoming particles, the results of these simulations show that the overall behavior of the
free-jet is depicted. Indeed, the simulated jet admits a profile close to the experimental
profiles.