The Particle Finite Element Method-Second Generation: an overview

Abstract

The main idea of the Particle Finite Element Method in both versions: with moving mesh or with fixed mesh, are to have a set of particles that move in a Lagrangian frame convecting all the physical and mathematical variables (for instance, the density, the viscosity or the conductivity, but also the velocity, the pressure or/and the temperature). These physical and mathematical values are projected at the end of each time-step on a moving mesh or on a fixed mesh. The second possibility has been named PFEM-Second Generation or simply PFEM-2.

One of the main drawback of the time integrations using Eulerian formulations are the restricted time-step size that is necessary to use due to the lack of accuracy of the convective terms. Both time integrations, explicit or implicit are, in most cases, limited to small CFL numbers. The cases in which the problem to be solved include free-surfaces or moving internal interfaces, like multi-fluids of fluid-structure interactions this time-step limitation is even worse.

The objective of this presentation is to make an overview of recent examples solved using PFEM-2 and to demonstrate why this method based on particles that move in a Lagrangian frame projecting the results on a fixed mesh is faster than a classical Eulerian Finite Element Method. The authors claim that nowadays, the best way to improve the efficiency of the majority of the CFD problems is the use of a particle-based method like PFEM-2.

Recording of the presentation

Location: Technical University of Catalonia (UPC), Vertex Building.

Date: 28 - 30 September 2015, Barcelona, Spain.

General Information

• Location: Technical University of Catalonia (UPC), Barcelona, Spain.
• Date: 28 - 30 September 2015
• Secretariat: International Center for Numerical Methods in Engineering (CIMNE).

External Links

• Particles 2015 Official Website of the Conference.
• CIMNE Multimedia Channel

References

[1] Idelsohn, S., Oñate, E., Nigro, N., Becker, P., and Gimenez, J. (2015). Lagrangian versus eulerian integration errors. Computer Methods in Applied Mechanics and Engineering. http://dx.doi.org/10.1016/j.cma.2015.04.003.

[2] Idelsohn, S. R., Oñate, E., and Pin, F. D. (2004). The particle finite element method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. International journal for numerical methods in engineering, 61(7); 964; 989.

[3] Idelsohn, S., Nigro, N., Gimenez, J., Rossi, R., and Marti, J. (2013). A fast and accurate method to solve the incompressible navier-stokes equations. Engineering Computations, 30(2): 2;2.

[4] Idelsohn, S., Nigro, N., Limache, A. and Oñate, E. (2012). Large time-step explicit integration method for solving problems with dominant convection. Computer Methods in Applied Mechanics and Engineering, 217:168; 185.