Purpose: The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier-Stokes equations with very large time steps.\ud \ud Design/methodology/approach: The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.\ud \ud Findings: The authors have found that even though this method was originally designed to deal with heterogeneous or free-surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.\ud \ud Originality/value: With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in-house and commercial codes.Peer ReviewedPostprint (author's final draft

The behavior of the cable jacket in fire characterized by the tendency to melt and drip constitutes a major source of fire hazard. The reason is that the melted material may convey the flame from one point to another, expanding fire and contributing to the fire load. In this article, the capability of a new computational strategy based on the particle finite element method for simulating a bench-scale cables burning test is analyzed. The use bench-scale test has been previously used to simulate the full-scale test described in EN 50399. As the air effect is neglected, a simple combustion model is included. The samples selected are two cables consisting of a copper core and differently flame retarded thermoplastic polyurethane sheets. The key modeling parameters were determined from different literature sources as well as experimentally. During the experiment, the specimen was burned under the test set-up condition recording the process and measuring the temperature evolution by means of three thermocouples. Next, the test was reproduced numerically and compared with a real fire test. The numerical results show that the particle finite element method can accurately predict the evolution of the temperature and the melting of the jacket.

A semi-explicit Lagrangian scheme for the simulation of thermally coupled incompressible flow problems is presented. The model relies on combining an explicit multi-step solver for the momentum equation with an implicit heat equation solver. Computational cost of the model is reduced via application of an efficient strategy adopted for the solution of momentum/continuity system by the authors in their previous work. The applicability of the method to solving thermo-mechanical problems is studied via various numerical examples.