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Modeling bed erosion in free surface flows by the particle finite element method

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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.

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Acknowledgments

Thanks are given to Dr. R. Rossi and Ms M. de Mier for useful suggestions. This research was partially supported by the FP6 Programme of the European Commission on Global Change and Ecosystems through Project RAMWAS, Project no. FP6-037081. Dr. S.R. Idelsohn is an ICREA Professor at CIMNE.

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Correspondence to Eugenio Oñate.

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Oñate, E., Celigueta, M.A. & Idelsohn, S.R. Modeling bed erosion in free surface flows by the particle finite element method. Acta Geotech. 1, 237–252 (2006). https://doi.org/10.1007/s11440-006-0019-3

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  • DOI: https://doi.org/10.1007/s11440-006-0019-3

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