Numerical comparison of the particle finite element method against an Eulerian formulation

GIMENEZ, JUAN; MORIN, PEDRO; NIGRO, NORBERTO; IDELSOHN, SERGIO

Tokyo

Congreso; Advances in Computational Fluid-Structure Interaction and Flow Simulation (AFSI 2014); 2014

"The main goal of this paper is to validate experimentally the principal conclusions previously published in [MR3395905]. 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 situation where 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 convergence rate. Lately, an extension to Navier-Stokes equations is introduced using also a manufactured case to verify again the same conclusions. This paper intends to establish the first steps towards a mathematical error analysis for the particle finite element method which supports the preliminary theoretical and experimental results presented here.