Implementation of the SPH method for fluid flow modelling – part 1

mathematical formulation and method generalities

Abstract

Lately new numerical implementations in meshless particle methods are being developed, highlighting the Smoothed Particle Hydrodynamics method (SPH), which have important applications in mechanics of solids and fluids. This paper is intended to address the implementation of the SPH method in fluid and fluid-structure simulations and also propose a general method for its validation. Therefore, the main objective of this first article in a series of two is to present a study on the formulation of the SPH method, on the fluid-structure modeling and on the boundary conditions. Thus, a simulator for two dimensional problems applied in examples of confined fluids and free surface flow was implemented. Promissory results were achieved in examples commonly referenced in the literature such as the "Shear Driven Cavity", the "Dam Break", the "Dam Collapse" and the Fourier heat transfer problem. This presents applications for the solution of a fluid under a defined geometry, in conditions of temperature, speed and variable displacement using a coupled formulation that employs the conservative equations of time, mass and energy. Comparison with experimental problems provided in the literature and other models were also performed with satisfactory results.