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

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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.

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References

  1. Donea J, Huerta A (2003) Finite element method for flow problems. Wiley, Chichester

    Book  Google Scholar 

  2. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics, theory and application to non-spherical stars. R Astron Soc 181:375–389

    Article  MATH  Google Scholar 

  3. Monaghan JJ (1988) An introduction to SPH. Comput Phys Commun 48:89–96

    Article  MATH  Google Scholar 

  4. Harlow FH (1955) A machine calculation method for hydrodynamic problems. Los Alamos Scientific Laboratory Report LAMS-1956

  5. Harlow FH, Welch J (1965) Numerical calculation of time dependent viscous incompressible flow of fluid with free surface. Phys Fluids 8(12):2182–2189

    Article  MathSciNet  MATH  Google Scholar 

  6. Wieckowsky Z (2004) The material point method in large strain engineering problems. Comput Methods Appl Mech Eng 193(39):4417–4438

    Article  MATH  Google Scholar 

  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 61:964–989

    Article  MathSciNet  MATH  Google Scholar 

  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 217–220:168–185

    Article  MathSciNet  MATH  Google Scholar 

  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):197–222

    Article  Google Scholar 

  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, Argentina

  11. Idelsohn S, Oñate E, Nigro N, Becker P, Gimenez JM (2015) Lagrangian versus Eulerian integration errors. Comput Methods Appl Mech Eng 293:191–206

    Article  MathSciNet  Google Scholar 

  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 Litoral

  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):103–116

    Article  Google Scholar 

  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):621–644

    Article  MathSciNet  Google Scholar 

  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 284:186–205

    Article  MathSciNet  MATH  Google Scholar 

  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):1091–1104

    Article  MathSciNet  MATH  Google Scholar 

  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 Fluids

  18. Chorin A (1968) Numerical solution of the Navier–Stokes equations. Math Comput 22:745–762

    Article  MathSciNet  MATH  Google Scholar 

  19. Thomson DJ (1988) Random walk models of turbulent dispersion. Ph.D. Thesis, Department of Mathematics and Statistics, Brunel University

  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 63:2436–2449

    Article  Google Scholar 

  21. Fabbroni N (2009) Numerical simulations of passive tracers dispersion in the sea. Ph.D. Thesis, Alma Mater Studiorum Università di Bologna

  22. Graham DI, James PW (1996) Turbulent dispersion of particles using eddy interaction models. Int J Multiph Flow 22:157175

    Google Scholar 

  23. Gimenez JM, Nigro NM, Idelsohn SR (2012) Improvements to solve diffusion-dominant problems with PFEM-2. Mecánica Comput 31:137–155

    Google Scholar 

  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):451–457

    Article  Google Scholar 

  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)

  26. Shiono K, Teixeira EC (2000) Turbulent characteristics in a baffled contact tank. J Hydraul Res 38(6):403–416

  27. Wilson J, Venayagamoorthy S (2010) Evaluation of hydraulic efficiency of disinfection systems based on residence time distribution curves. Environ Sci Technol 44(24):9377–9382

    Article  Google Scholar 

  28. Smagorisnky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99–164

    Article  Google Scholar 

  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 33:267–318

    Article  Google Scholar 

  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 9397

  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 34:4106–4122

    Article  MathSciNet  MATH  Google Scholar 

  32. Sirrell B, Holliday M, Campbell J (1996) Benchmark testing the flow and solidification modeling of AI castings. JOM 48(3):20–23

    Article  Google Scholar 

  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, England

  34. Codina R (2001) Pressure stability in fractional step finite element methods for incompressible flows. J Comput Phys 170:112140

    Article  MathSciNet  Google Scholar 

  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):10911104

    Article  MathSciNet  MATH  Google Scholar 

Download references

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.

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Authors and Affiliations

  1. Centro de Investigación de Métodos Computacionales (CIMEC) - UNL/CONICET, Santa Fe, Argentina

    Juan M. Gimenez, Damián E. Ramajo, Santiago Márquez Damián & Norberto M. Nigro

  2. Facultad de Ingeniería y Ciencias Hídricas, Universidad Nacional del Litoral, Santa Fe, Argentina

    Juan M. Gimenez, Damián E. Ramajo & Norberto M. Nigro

  3. Departamento de Ingeniería Mecánica, Universidad Tecnológica Nacional, Facultad Regional Santa Fe, Santa Fe, Argentina

    Santiago Márquez Damián

  4. International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio R. Idelsohn

  5. Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

    Sergio R. Idelsohn

Authors
  1. Juan M. Gimenez
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  2. Damián E. Ramajo
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  3. Santiago Márquez Damián
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  4. Norberto M. Nigro
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  5. Sergio R. Idelsohn
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Correspondence to Juan M. Gimenez.

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Gimenez, J.M., Ramajo, D.E., Márquez Damián, S. et al. An assessment of the potential of PFEM-2 for solving long real-time industrial applications. Comp. Part. Mech. 4, 251–267 (2017). https://doi.org/10.1007/s40571-016-0135-2

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  • DOI: https://doi.org/10.1007/s40571-016-0135-2

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