The Poisson Problem: a Comparison between Two Approaches Based on SPH Method

Abstract

In this paper two approaches to solve the Poisson problem are presented and compared. The computational schemes are based on Smoothed Particle Hydrodynamics method which is able to perform an integral representation by means of a smoothing kernel func- tion by involving domain particles in the discrete formulation. The first approach is derived by means of the variational formulation of the Poisson prob- lem, while the second one is a direct differential method. Numerical examples on different domain geometries are implemented to verify and compare the proposed approaches; the computational efficiency of the developed methods is also studied.