Recent Advances in the Particle Finite Element Method Towards More Complex Fluid Flow Applications

Abstract

This paper presents a state of the art in the Particle Finite Element Method, normally called PFEM, its emphasis in the new ideas oriented to extend its application not only to solve fluid structure interaction and multifluid problems, also bring new opportunities to shorten the gap between engineering design times and computational simulation times for general problems when Eulerian formulation were typically chosen. In order to reduce the long history of this method here the starting point begins with the reformulation of the method to solve academic and real problems in real time or at least in drastically reduced computational times. The main topics involved in this paper are around the stability and the accuracy of Lagrangian formulations against its Eulerian counterpart shown through several academic benchmarks and a deep analysis of the efficiency revealing that the original method needs some new features. The former brought out a new integration method called X-IVAS and the later has produced a new version of the method called PFEM in fixed Mesh. Once the method had shown its good performance and how the new features impact on the final efficiency the last developments had been done in extending the application of this new method in multifluids and other complex fluid mechanics problems like turbulence and reactive flows.