An assessment of the potential of PFEM-2 for solving long real-time industrial applications
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The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages in terms of robustness and efficiency over classical Eulerian methodologies when certain kind of flows are simulated, especially those where convection plays an important role. These situations are often encountered in real engineering problems, where very complex geometries and operating conditions require very large and long computations. The advantages that the parallelism introduced in the computational fluid dynamics making affordable computations with very fine spatial discretizations are well known. However, it is not possible to have the time parallelized, despite the effort that is being dedicated to use space–time formulations. In this sense, PFEM-2 adds a valuable feature in that its strong stability with little loss of accuracy provides an interesting way of satisfying the real-life computation needs. After having already demonstrated in previous publications its ability to achieve academic-based solutions with a good compromise between accuracy and efficiency, in this work, the method is revisited and employed to solve several nonacademic problems of technological interest, which fall into that category. Simulations concerning oil–water separation, waste-water treatment, metallurgical foundries, and safety assessment are presented. These cases are selected due to their particular requirements of long simulation times and or intensive interface treatment. Thus, large time-steps may be employed with PFEM-2 without compromising the accuracy and robustness of the simulation, as occurs with Eulerian alternatives, showing the potentiality of the methodology for solving not only academic tests but also real engineering problems.
KeywordsParticle methods PFEM-2 Large time-steps Multiphase flows
The authors wish to offer their thanks to the CONICET, the Universidad Nacional del Litoral, and the ANPCyT for their financial supports through Grants PIP-2012 GI 11220110100331, CAI+D 2011 501 201101 00435 LI, and PICT-2013 0830.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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