Simulation of a Free Surface Laminar Flow Using The SPH Method

Resumo

The Smoothed Particle Hydrodynamics Method (SPH) is a Lagrangian numerical method used to
solve engineering problems, notably on free surface flow. This article deals with numerical simulation using the
SPH method to one-dimensional laminar flow on a free surface in an infinite channel. The numerical code
developed discretizes the fluid domain in particles with constant mass, which do not move during the simulation
and only present variation in their velocity. The boundary conditions at the bottom of the channel were
implemented using ghost particles to reflect the no-slip condition. Ghost particles with corrections are
implemented on the free surface to ensure that the shear stress on the free surface is zero. This correction ensures
that the numerical results obtained in the SPH method are the closest to the analytical ones. The transient
velocity profile was obtained by adopting the Eulerian framework in the SPH method and compared with the
analytical ones, showing agreement between the results.