Study of Fluid Flows using Smoothed Particle Hydrodynamics: the Modified Pressure Concept Applied to Quiescent Fluid and Dam Breaking

Carlos Alberto Dutra Fraga Filho¹; Julio Tomás Aquije Chacaltana²

¹ Instituto Federal do Espírito Santo; ² Universidade Federal do Espírito Santo

doi:10.20906/CPS/CILAMCE2015-0071

Resumo

Smoothed Particle Hydrodynamics (SPH) is one of the Lagrangian methods used in fluid mechanics to address complex fluid flow with a free surface or interfaces, producing results consistent with those obtained by analytical and experimental techniques. The focus of this work is to show that when the modified pressure concept for quiescent and incompressible fluid is applied, the numerical solution of the Navier-Stokes equations by the SPH method produces better results compared with analytical ones. A code in Fortran language is written to solve the system of algebraic equations. The numerical model, SPH, is applied to analyse the particle movement of quiescent fluid in a reservoir and the particle fluid flow movement when a dam break occurs. In the case of fluid at rest, results obtained using SPH show that particles do not remain in their initial positions and that their movements increase as time progresses. Contrary to literature reports, the modified pressure concept used in this work produces results similar to those provided by analytical solution. In the dam break case, an artificial viscosity was used to avoid instabilities in particle movement. The inconsistency found in the interpolated value of the function near the boundary was corrected by introducing a correction factor. To prevent fluid particles from crossing the rigid boundary, the concept of reflection of particles with a coefficient of restitution of kinetic energy was used. In this case the numerical results agree with those obtained in laboratory experiments, with a maximum difference of 17.86%.

Palavras-chave: SPH method ; fluid at rest; modified pressure; coefficient of restitution of kinetic energy; dam breaking