Lagrangian versus Eulerian integration errors

• Published in: Computer methods in applied mechanics and engineering 2015-08, Vol.293, p.191-206
• Main Authors: Idelsohn, Sergio, Oñate, Eugenio, Nigro, Norberto, Becker, Pablo, Gimenez, Juan
• Format: Article
• Language: English
• Subjects: Anàlisi numèrica; Incompressible Navier–Stokes equations; Integració numèrica; Lagrange formulations; Matemàtiques i estadística; Multi-fluids flows; Mètodes numèrics; Numerical integration; Numerical integration errors; Particle methods; Àrees temàtiques de la UPC
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2015.04.003

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 et al. 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. •The errors between the use of an Eulerian or a Lagrangian frame have been studied.•For low Reynolds numbers the Eulerian frame is more competitive.•Moderated-high Reynolds numbers are the cases that Lagrangian frames are competitive•In a Lagrangian frame, a strategy to improve the projection errors is essential.•For multi-fluid or free-surface flows the Lagrangian frames are more suitable.