Published in Acta Geotechnica Vol. 1 (4), pp. 237-252, 2006
doi: 10.1007/s11440-006-0019-3

Abstract

We present a general formulation for modeling bed erosion in free surface flows using the particle finite element method (PFEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in domains containing fluid and solid subdomains. Nodes are viewed as material points (called particles) which can freely move and even separate from the fluid and solid subdomains representing, for instance, the effect of water drops or soil/rock particles. A mesh connects the nodes defining the discretized domain in the fluid and solid regions where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the nonlinear transient coupled fluid-structure problem is described. The erosion mechanism is modeled by releasing the material adjacent to the bed surface according to the frictional work generated by the fluid shear stresses. The released bed material is subsequently transported by the fluid flow. Examples of application of the PFEM to solve a number of bed erosion problems involving large motions of the free surface and splashing of waves are presented.

R. Rossi, A. Larese, P. Dadvand, E. Oñate. An efficient edge-based level set finite element method for free surface flow problems. Int. J. Numer. Meth. Fluids 71(6) (2012) DOI 10.1002/fld.3680

E. Oñate, A. Franci, J. Carbonell. Lagrangian formulation for finite element analysis of quasi-incompressible fluids with reduced mass losses. Int. J. Numer. Meth. Fluids 74(10) (2014) DOI 10.1002/fld.3870

Y. Abdelhamid, U. El Shamy. Pore-scale modeling of surface erosion in a particle bed. Int. J. Numer. Anal. Meth. Geomech. 38(2) (2013) DOI 10.1002/nag.2201

J. Tejchman, W. Wu. FE-investigation of shear localization in granular bodies under high shear rate. Granular Matter 11(2) (2009) DOI 10.1007/s10035-009-0128-4

H. Teufelsbauer, Y. Wang, M. Chiou, W. Wu. Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment. Granular Matter 11(4) (2009) DOI 10.1007/s10035-009-0142-6

H. Harshani, S. Galindo-Torres, A. Scheuermann, H. Muhlhaus. Micro-mechanical analysis on the onset of erosion in granular materials. Philosophical Magazine 95(28-30) (2015) DOI 10.1080/14786435.2015.1049237

J. Rodriguez, J. Carbonell, J. Cante, J. Oliver. The particle finite element method (PFEM) in thermo-mechanical problems. Int. J. Numer. Meth. Engng 107(9) (2016) DOI 10.1002/nme.5186

M. Cerquaglia, G. Deliége, R. Boman, V. Terrapon, J. Ponthot. Free-slip boundary conditions for simulating free-surface incompressible flows through the particle finite element method. Int. J. Numer. Meth. Engng 110(10) (2016) DOI 10.1002/nme.5439

Y. Young, J. White, H. Xiao, R. Borja. Liquefaction potential of coastal slopes induced by solitary waves. Acta Geotech. 4(1) (2009) DOI 10.1007/s11440-009-0083-6

H. Zhu, L. Zhang. Field investigation of erosion resistance of common grass species for soil bioengineering in Hong Kong. Acta Geotech. 11(5) (2015) DOI 10.1007/s11440-015-0408-6

E. Oñate, J. García-Espinosa, S. Idelsohn, B. Serván-Camas. Ship Hydrodynamics. (2017) DOI 10.1002/9781119176817.ecm2070

C. de Saracibar, R. Boman, P. Bussetta, J. Cajas, M. Cervera, M. Chiumenti, A. Coll, P. Dadvand, J. Hernández Ortega, G. Houzeaux, M. de Riera, J. Ponthot. Numerical Methods. (2016) DOI 10.1002/9783527693566.ch7

A. Larese. A Lagrangian PFEM approach for non-Newtonian viscoplastic materials. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 33(3-4) DOI 10.1016/j.rimni.2016.07.002

J. Carbonell, E. Oñate, B. Suárez. Modeling of Ground Excavation with the Particle Finite-Element Method. J. Eng. Mech. 136(4) DOI 10.1061/(asce)em.1943-7889.0000086

E. Oñate, S. Idelsohn, M. Celigueta, B. Suárez. The Particle Finite Element Method (PFEM). An Effective Numerical Technique for Solving Marine, Naval and Harbour Engineering Problems. DOI 10.1007/978-94-007-6143-8_4

F. Salazar, E. Oñate, R. Morán. Numerical modeling of landslides in reservoirs using the Particle Finite Element Method (PFEM). (2012) DOI 10.1201/b11588-39

A. Franci. Unified Stabilized Formulation for Quasi-incompressible Materials. (2016) DOI 10.1007/978-3-319-45662-1_3

E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, S. Latorre. Possibilities of the Particle Finite Element Method in Computational Mechanics. DOI 10.1007/978-3-642-05241-5_15

E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, J. Marti, J. Carbonell, P. Ryzhakov, B. Suárez. Advances in the Particle Finite Element Method (PFEM) for Solving Coupled Problems in Engineering. (2011) DOI 10.1007/978-94-007-0735-1_1

E. Oñate, M. Celigueta, S. Latorre, G. Casas, R. Rossi, J. Rojek. Lagrangian analysis of multiscale particulate flows with the particle finite element method. Comp. Part. Mech. 1(1) (2014) DOI 10.1007/s40571-014-0012-9

M. Celigueta, K. Deshpande, S. Latorre, E. Oñate. A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores. Comp. Part. Mech. 3(2) (2015) DOI 10.1007/s40571-015-0090-3

F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate. Air demand estimation in bottom outlets with the particle finite element method. Comp. Part. Mech. 4(3) (2016) DOI 10.1007/s40571-016-0117-4

R. Bravo, P. Becker, P. Ortiz. Numerical simulation of evolutionary erodible bedforms using the particle finite element method. Comp. Part. Mech. 4(3) (2016) DOI 10.1007/s40571-016-0121-8

A. Franci, I. de-Pouplana, G. Casas, M. Celigueta, J. González-Usúa, E. Oñate. PFEM–DEM for particle-laden flows with free surface. Comp. Part. Mech. 7(1) (2019) DOI 10.1007/s40571-019-00244-1

F. Salazar, J. San-Mauro, M. Celigueta, E. Oñate. Shockwaves in spillways with the particle finite element method. Comp. Part. Mech. 7(1) (2019) DOI 10.1007/s40571-019-00252-1

R. Bravo, P. Ortiz, S. Idelsohn, P. Becker. Sediment transport problems by the particle finite element method (PFEM). Comp. Part. Mech. 7(1) (2019) DOI 10.1007/s40571-019-00255-y

E. Oñate, A. Franci, J. Carbonell. A Particle Finite Element Method (PFEM) for Coupled Thermal Analysis of Quasi and Fully Incompressible Flows and Fluid-Structure Interaction Problems. (2014) DOI 10.1007/978-3-319-06136-8_6

J. Rodríguez, J. Carbonell, P. Jonsén. Numerical Methods for the Modelling of Chip Formation. Arch Computat Methods Eng 27(2) (2018) DOI 10.1007/s11831-018-09313-9

E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suárez. Possibilities of the particle finite element method for fluid–soil–structure interaction problems. Comput Mech 48(3) (2011) DOI 10.1007/s00466-011-0617-2

E. Oñate, A. Franci, J. Carbonell. A particle finite element method for analysis of industrial forming processes. Comput Mech 54(1) (2014) DOI 10.1007/s00466-014-1016-2

J. Rodriguez Prieto, J. Carbonell, J. Cante, J. Oliver, P. Jonsén. Generation of segmental chips in metal cutting modeled with the PFEM. Comput Mech 61(6) (2017) DOI 10.1007/s00466-017-1442-z