Lagrangian versus Eulerian integration errors

Abstract

The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems (Idelsohn etal. 2012; 2014; 2013). The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2).The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.