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Computational Particle Mechanics

, Volume 4, Issue 3, pp 251–267 | Cite as

An assessment of the potential of PFEM-2 for solving long real-time industrial applications

  • Juan M. Gimenez
  • Damián E. Ramajo
  • Santiago Márquez Damián
  • Norberto M. Nigro
  • Sergio R. Idelsohn
Article
  • 229 Downloads

Abstract

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.

Keywords

Particle methods PFEM-2 Large time-steps Multiphase flows 

Notes

Acknowledgments

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.

References

  1. 1.
    Donea J, Huerta A (2003) Finite element method for flow problems. Wiley, ChichesterCrossRefGoogle Scholar
  2. 2.
    Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics, theory and application to non-spherical stars. R Astron Soc 181:375–389CrossRefzbMATHGoogle Scholar
  3. 3.
    Monaghan JJ (1988) An introduction to SPH. Comput Phys Commun 48:89–96CrossRefzbMATHGoogle Scholar
  4. 4.
    Harlow FH (1955) A machine calculation method for hydrodynamic problems. Los Alamos Scientific Laboratory Report LAMS-1956Google Scholar
  5. 5.
    Harlow FH, Welch J (1965) Numerical calculation of time dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8(12):2182–2189MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Wieckowsky Z (2004) The material point method in large strain engineering problems. Comput Methods Appl Mech Eng 193(39):4417–4438CrossRefzbMATHGoogle Scholar
  7. 7.
    Idelsohn SR, Oñate E, Del Pin F (2004) The particle finite element method a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods 61:964–989MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Idelsohn SR, Nigro NM, Limache A, Oñate E (2012) Large time-step explicit integration method for solving problems with dominant convection. Comput Methods Appl Mech Eng 217–220:168–185MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Idelsohn SR, Nigro NM, Gimenez JM, Rossi R, Marti J (2013) A fast and accurate method to solve the incompressible Navier–Stokes equations. Eng Comput 30(2):197–222CrossRefGoogle Scholar
  10. 10.
    Gimenez JM (2015) Enlarging time-steps for solving one and two phase flows using the particle finite element method. Ph.D. Thesis, Universidad Nacional del Litoral, Santa Fe, ArgentinaGoogle Scholar
  11. 11.
    Idelsohn S, Oñate E, Nigro N, Becker P, Gimenez JM (2015) Lagrangian versus Eulerian integration errors. Comput Methods Appl Mech Eng 293:191–206MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gimenez JM (2014) Implementacin del mtodo PFEM sobre arquitecturas paralelas, Facultad de Ingeniería y Ciencias Hídricas, Centro de Investigación de Métodos Computacionales, Universidad Nacional del LitoralGoogle Scholar
  13. 13.
    Gimenez JM, Nigro NM, Idelsohn SR (2014) Evaluating the performance of the particle finite element method in parallel architectures. J Comput Part Mech 1(1):103–116CrossRefGoogle Scholar
  14. 14.
    Idelsohn SR, Marti J, Becker P, Oñate E (2014) Analysis of multifluid flows with large time steps using the particle finite element method. Int J Numer Methods Fluids 75(9):621–644MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gimenez JM, Gonzlez LM (2015) An extended validation of the last generation of particle finite element method for free surface flows. J Comput Phys 284:186–205MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Becker P, Idelsohn SR, Oñate E (2014) A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the particle finite element method with fixed mesh. Comput Mech 55(6):1091–1104MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Gimenez JM, Nigro N, Oñate E, Idelsohn S (2016) Surface tension problems solved with the particle finite element method using large time-steps. Comput FluidsGoogle Scholar
  18. 18.
    Chorin A (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745–762MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Thomson DJ (1988) Random walk models of turbulent dispersion. Ph.D. Thesis, Department of Mathematics and Statistics, Brunel UniversityGoogle Scholar
  20. 20.
    Le Moullec Y, Potier O, Gentric C (2008) Flow field and residence time distribution simulation of a cross-flow gasliquid wastewater treatment reactor using CFD. Chem Eng Sci 63:2436–2449CrossRefGoogle Scholar
  21. 21.
    Fabbroni N (2009) Numerical simulations of passive tracers dispersion in the sea. Ph.D. Thesis, Alma Mater Studiorum Università di BolognaGoogle Scholar
  22. 22.
    Graham DI, James PW (1996) Turbulent dispersion of particles using eddy interaction models. Int J Multiph Flow 22:157175Google Scholar
  23. 23.
    Gimenez JM, Nigro NM, Idelsohn SR (2012) Improvements to solve diffusion-dominant problems with PFEM-2. Mecánica Comput 31:137–155Google Scholar
  24. 24.
    Hryb D, Cardozo M, Ferro S, Goldschmit M (2009) Particle transport in turbulent flow using both Lagrangian and Eulerian formulations. Int Commun Heat Mass Transf 36(5):451–457CrossRefGoogle Scholar
  25. 25.
    Gualtieri C (2006) Numerical simulation of flow and tracer transport in a disinfection contact tank. In: Conference: third biennial meeting: international congress on environmental modelling and software (iEMSs 2006)Google Scholar
  26. 26.
    Shiono K, Teixeira EC (2000) Turbulent characteristics in a baffled contact tank. J Hydraul Res 38(6):403–416Google Scholar
  27. 27.
    Wilson J, Venayagamoorthy S (2010) Evaluation of hydraulic efficiency of disinfection systems based on residence time distribution curves. Environ Sci Technol 44(24):9377–9382CrossRefGoogle Scholar
  28. 28.
    Smagorisnky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
  29. 29.
    Norberto N, Gimenez JM, Idelsohn S (2014) Recent advances in the particle finite element method towards more complex fluid flow applications. Numer Simul Coupled Probl Eng 33:267–318CrossRefGoogle Scholar
  30. 30.
    Schmid M, Klein F (1995) Fluid flow in die-cavities: experiments and numerical simulation. In: The 18th international die casting congress and exposition, Indianapolis, Indiana, USA, p 9397Google Scholar
  31. 31.
    Pang S, Chen L, Zhang M, Yin Y, Chen T, Zhou J, Liao D (2010) Numerical simulation two phase flows of casting filling process using SOLA particle level set method. Appl Math Model 34:4106–4122MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Sirrell B, Holliday M, Campbell J (1996) Benchmark testing the flow and solidification modeling of AI castings. JOM 48(3):20–23CrossRefGoogle Scholar
  33. 33.
    Atherton W (2005) An experimental investigation of bund wall overtopping and dynamic pressures on the bund wall following catastrophic failure of a storage vessel. Research Report, Liverpool John Moores University, EnglandGoogle Scholar
  34. 34.
    Codina R (2001) Pressure stability in fractional step finite element methods for incompressible flows. J Comput Phys 170:112140MathSciNetCrossRefGoogle Scholar
  35. 35.
    Becker P, Idelsohn S, Oñate E (2015) A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the particle finite element method with fixed mesh. Comput Mech 55(6):10911104MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© OWZ 2016

Authors and Affiliations

  1. 1.Centro de Investigación de Métodos Computacionales (CIMEC) - UNL/CONICETSanta FeArgentina
  2. 2.Facultad de Ingeniería y Ciencias HídricasUniversidad Nacional del LitoralSanta FeArgentina
  3. 3.Departamento de Ingeniería MecánicaUniversidad Tecnológica NacionalSanta FeArgentina
  4. 4.International Center for Numerical Methods in Engineering (CIMNE)BarcelonaSpain
  5. 5.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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