Numerical comparison of the Particle Finite Element Method against an Eulerian formulation

JUAN M. GIMENEZ; PEDRO MORIN; NORBERTO M. NIGRO; SERGIO R. IDELSOHN

Advances in Computational Fluid-Structure

Birkhauser

Año: 2015;

The main goal of this paper is to validate experimentally the principal conclusions previuosly published in [Idelsohn2015].Two manufactured test cases were considered with their respective analytic solutions.First, a scalar transport equation is considered written in such a way that several parameters are included to stress the limiting situationwhere the Eulerian and the Lagrangian approaches behave better.The results show conditions to be fulfilled in order to choose between both formulations, according to the problem parameters.A brief discussion about the projection needed for PFEM-2 method is included, specially due to its impact on the error convergencerate.Lately, an extension to Navier-Stokes equations is introduced using also a manufactured case to verify again the sameconclusions.This paper intends to establish the first steps towards a mathematical error analysis for the Particle Finite Element Methodwhich support the preliminary theoretical and experimental results presented here.