Kinematics of a Fluid at Rest within a Reservoir and of the Flow due to the Dam Breaking using the Lagrangian Smoothed Particle Hydrodynamics Model

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/COB-2015-1089

Resumo

The Lagrangian modelling technique for understanding problems of fluid mechanics with heat and mass transfer is gaining the attention of the researchers. In particular, the particle method named Smoothed Particle Hydrodynamics (SPH) is used in fluid mechanics, for both in hydrostatic and hydrodynamic, in order to address the fluid flow with free surface or with interfaces, producing consistent results with those obtained by analytical and experimental techniques. The focus of this work is to apply the SPH methodology to analyze the water flow in a reservoir and the fluid flow that occurs after the dam break. The concepts of modified pressure and artificial viscosity are used to develop the mathematical and numerical models. The inconsistency found in the value of the interpolated function near the boundary is corrected by introducing a correction factor. To prevent the fluid particles pass through solid contours is used the concept of elastic reflection, with full restitution of kinetic energy. A code written in Fortran language is designed to solve the system of algebraic equations. Numerical results are compared with those obtained by analytical solutions and experiments in the laboratory. In the case of a fluid at rest, the results reported in the literature using Lagrangian SPH modelling show a change in position of the fluid particles over time. This paper presents numerical results identical to the analytical solution. In the case of the dam breaking, the numerical results agree with those obtained in laboratory experiments, with a maximum difference of 17.86%.

Palavras-chave: Lagrangian SPH model; reservoir; fluid at rest; modified pressure; dam breaking