Computational Particle Mechanics

, Volume 4, Issue 3, pp 297–305 | Cite as

Numerical simulation of evolutionary erodible bedforms using the particle finite element method

  • Rafael Bravo
  • Pablo Becker
  • Pablo Ortiz


This paper presents a numerical strategy for the simulation of flows with evolutionary erodible boundaries. The fluid equations are fully resolved in 3D, while the sediment transport is modelled using the Exner equation and solved with an explicit Lagrangian procedure based on a fixed 2D mesh. Flow and sediment are coupled in geometry by deforming the fluid mesh in the vertical direction and in velocities with the experimental sediment flux computed using the Meyer Peter Müller model. A comparison with real experiments on channels is performed, giving good agreement.


Erodible beds FSI Sediment transport Updated Lagrangian formulation Convection PFEM-2 



R. Bravo and P. Ortiz were supported by the MICIIN Grant #BIA-2012-32918 and the MICIIN Grant #BIA-2015-64994-P (MINECO/FEDER). P. Becker was supported by the H2020-ERC-2014-PoC Grant 664910-FORECAST.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    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
  2. 2.
    Becker P, Nigro N, Idelsohn S (2012) Integración temporal explícita con grandes pasos de tiempo de la ecuación de transmisión del calor. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 28(4):187–197MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bravo R, Ortiz P, Pérez-Aparicio J (2014) Incipient sediment transport for non-cohesive landforms by the discrete element method (dem). Appl Math Model 38(4):1326–1337MathSciNetCrossRefGoogle Scholar
  4. 4.
    Camenen B, Larson M (2005) A general formula for non-cohesive bed load sediment transport. Estuar Coast Shelf Sci 63(1):249–260CrossRefGoogle Scholar
  5. 5.
    Casagrande MVS, Alves JLD, Silva CE, Alves FT, Elias RN, Coutinho ALGA (2016) A hybrid fem-dem approach to the simulation of fluid flow laden with many particles. Comput Part Mech 1–15Google Scholar
  6. 6.
    Castro-Diaz MJ, Fernandez-Nieto ED, Ferreiro AM (2008) Sediment transport models in shallow water equations and numerical approach by high order finite volume methods. Comput Fluids 37(3):299–316MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Celigueta MA, Deshpande KM, Latorre S, Oñate E (2016) A fem-dem technique for studying the motion of particles in non-newtonian fluids. application to the transport of drill cuttings in wellbores. Comput Part Mech 3(2):263–276CrossRefGoogle Scholar
  8. 8.
    Codina R (2001) Pressure stability in fractional step finite element methods for incompressible flows. J Comput Phys 170(1):112–140MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17(3):253–297CrossRefzbMATHGoogle Scholar
  10. 10.
    Donea J, Huerta A (2003) Finite element methods for flow problems. Wiley, New YorkCrossRefGoogle Scholar
  11. 11.
    Einstein HA (1949) Formulas for the transportation of bed load. Trans Am Soc Civ Eng 107:561–573Google Scholar
  12. 12.
    Engelund F, Fredsoe J (1976) A sediment transport model for straight alluvial channels. Nord Hydrol 125(5):293–306Google Scholar
  13. 13.
    Exner FM (1925) Uber die wechselwirkung zwischen wasser und geschiebe in flussen. Akad Wiss Wien Math Naturwiss 134:165–204Google Scholar
  14. 14.
    Idelsohn S, Marti J, Limache A, Oñate E (2008) Unified lagrangian formulation for elastic solids and incompressible fluids: application to fluid-structure interaction problems via the pfem. Comput Methods Appl Mech Eng 197(19–20):1762–1776MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Idelsohn S, Mier-Torrecilla M, Oñate E (2009) Multi-fluid flows with the particle finite element method. Comput Methods Appl Mech Eng 198(33–36):2750–2767CrossRefzbMATHGoogle Scholar
  16. 16.
    Idelsohn S, Nigro N, 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
  17. 17.
    Leclair S (2002) Preservation of cross-strata due to the migration of subaqueous dunes: an experimental investigation. Sedimentology 49(6):1157–1180CrossRefGoogle Scholar
  18. 18.
    Meyer-Peter E, Müller R (1948) Formulae for bedload transport. In: Proceedings of 3rd congress, international association of hydraulic research, Sweeden, pp. 39–64Google Scholar
  19. 19.
    Nielsen P (1992) Coastal bottom boundary layers and sediment trasport, Advanced series on ocean engineering, vol 4. World Scientific Publishing, SingaporeCrossRefGoogle Scholar
  20. 20.
    Oñate E, Celigueta MA, Idelsohn SR (2006) Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotechnica 1(4):237–252Google Scholar
  21. 21.
    Oñate E, Celigueta MA, Latorre S, Casas G, Rossi R, Rojek J (2014) Lagrangian analysis of multiscale particulate flows with the particle finite element method. Comput Part Mech 1(1):85–102Google Scholar
  22. 22.
    Ortiz P (2012) Non-oscilatory continuous fem for transport and shallow water flows. Comput Methods Appl Mech Eng 223–224:55–69CrossRefzbMATHGoogle Scholar
  23. 23.
    Ortiz P, Anguita J, Riveiro M (2015) Free surface flows over partially erodible beds by a continuous finite element method. Environ Earth Sci 74(11):7357–7370CrossRefGoogle Scholar
  24. 24.
    Ortiz P, Smolarkiewicz PK (2006) Numerical simulation of sand dune evolution in severe winds. Int J Numer Methods Fluids 50(10):1229–1246MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Ortiz P, Smolarkiewicz PK (2009) Coupling the dynamics of boundary layers and evolutionary dunes. Phys Rev E 79(4):041307-1-041307-11Google Scholar
  26. 26.
    Paola C, Voller VR (2005) A generalized exner equation for sediment mass balance. J Geophys Res 110(4):1–8Google Scholar
  27. 27.
    Pin FD, Idelsohn S, Oñate E, Aubry R (2007) The ale/lagrangian particle finite element method: a new approach to computation of free-surface flows and fluid-object interactions. Comput Fluids 36(1):27–38CrossRefzbMATHGoogle Scholar
  28. 28.
    Rijn LV (1984) Sediment transport. part i: bed load transport. J Hydraul Eng ASCE 110(10):1431–1456CrossRefGoogle Scholar
  29. 29.
    Rijn LV (1993) Principles of sediment transport in rivers, estuaries and coastal seas, vol 1006. Aqua publications, BlokzijlGoogle Scholar
  30. 30.
    Schwämmle V, Herrmann H (2004) Modelling transverse dunes. Earth Surface Process Landf 29(6):769–784CrossRefGoogle Scholar
  31. 31.
    Shields A (1936) Application of similarity principles and turbulence research to bed-load movement. Technical report laboratory for hydraulic water resourcesGoogle Scholar
  32. 32.
    Weng WS, Hunt JCR, Carruthers DJ, Warren A, Wiggs GFS, Livingstone I, Castro I (1991) Air flow and sand transport over sand-dunes, Acta Mechanica. Supplementa, vol. 2, 1 edn., chap. Air flow and sand transport over sand-dunes, Springer Vienna, Vienna, pp. 1–22Google Scholar
  33. 33.
    Wippermann FK, Gross G (1986) The wind-induced shaping and migration of an isolated dune: a numerical experiment. Bound Layer Meteorol 36(4):319–334CrossRefGoogle Scholar
  34. 34.
    Zienkiewicz OC, Nithiarasu P, Codina R, Vázquez M, Ortiz P (1999) An efficient and accurate algorithm for fluid mechanics problems. the characteristic based split procedure. Int J Numer Methods Fluids 31(1):359–392CrossRefzbMATHGoogle Scholar

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© OWZ 2016

Authors and Affiliations

  1. 1.University of GranadaGranadaSpain
  2. 2.International Center for Numerical Methods in Engineering (CIMNE)BarcelonaSpain

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