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• Lagrangian versus Eulerian integration errors

  S. Idelsohn, E. Oñate, N. Nigro, P. Becker

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191–206; (preprint)

  
  

  Abstract

  The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible fluids and also for solving multi-fluid problems [28-30]. The strategy used by the authors was named Particle Finite Element Method second generation (PFEM-2). The objective of this paper is to demonstrate in which circumstances the use of a Lagrangian frame with particles is more accurate than a classical Eulerian finite element method, and when large time-steps and/or coarse meshes may be used.

  Abstract
  The possibility to use a Lagrangian frame to solve problems with large time-steps was successfully explored previously by the authors for the solution of homogeneous incompressible [...]

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• Surface tension problems solved with the Particle Finite Element Method using large time-steps

  J. Giménez, N. Nigro, S. Idelsohn, E. Oñate

  Computers and Fluids (2016). (preprint) Vol. 141, pp. 90-104

  
  

  Abstract

  In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology which uses X-IVS [3] to treat convection terms allowing large time-steps was validated for problems where the gravity forces and/or the inertial forces dominate the flow. Although that is the target range of problems to solve with PFEM-2, most of real problems that fall in these categories also includes other flow regimes in certain regions of the domain. Maybe the most common secondary regime is when the surface tension dominates, as an example when drops or bubbles are released from the main flow, and this feature must be taken into account in any complete numerical strategy. Attending to that, in this work the treatment of the surface tension to PFEM-2 is included. An implicit CSF methodology is employed together with a coupling between the marker function with a Level Set function to obtain a smooth representation of the normal of the interface which allows an accurate curvature calculation. Examples for curvature calculation and isolated bubbles and drops are presented where the accuracy and the computational efficiency are analyzed and contrasted with other numerical methodologies. Finally, a simulation of a jet atomization is analyzed. This case presents the above mentioned features: it is a inertia-dominant flow with a surface tension phenomena on drops and ligaments break up that can not be neglected.

  Abstract
  In previous works [1,2], the authors have presented a highly efficient extension of the Particle Finite Element Method, called PFEM-2, to solve two-phase flows. The methodology [...]

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• Possibilities of the particle finite element method for fluid-soil-structure interaction problems

  E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

  (2011). Research Report, Nº PI357

  
  

  Abstract

  We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.

  Abstract
  We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction [...]

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• Time domain simulation of coupled sloshing-seakeeping problems by coupling PFEM-2 and SeaFEM

  J. Colom Cobb, B. Servan Camas, P. Becker, J. García-Espinosa, S. Idelsohn

  Presentations to the VII International Conference on Computational Methods in Marine Engineering (Marine 2017).

  
  

  Abstract

  The aim of this work is to be able to cope with complex sloshing-seakeeping problems in an effective manner. For this purpose, two different solvers will be integrated into one coupled tool to take advantage of their characteristics. The Particle Finite Element Method is a versatile framework for the analysis of fluid-structure interaction problems. The latest development within the framework of the PFEM is the X-IVAS (eXplicit Integration along the Velocity and Acceleration Streamlines) scheme. It is a semi-implicit scheme built over a Semi-Lagrangian (SL) formulation. This new scheme was named PFEM-2 and will be used in this work to solve the fluid dynamics (sloshing) inside the tanks. The PFEM-2 will be coupled in the time domain with SeaFEM, a solver developed for seakeeping problems. SeaFEM solves the second-order diffraction-radiation equations by using the Finite Element Method (FEM) and will be used in this work to simulate the interaction between waves and a floating body. The coupling of the two tools will be accomplished by using an effective coupling algorithm and a communication technique that allows simulations to be computed without affecting the global compute time and the accuracy of the solvers. This new tool has been validated against experimental benchmarks carried out in a model basin at model scale.

  Abstract
  The aim of this work is to be able to cope with complex sloshing-seakeeping problems in an effective manner. For this purpose, two different solvers will be integrated into [...]

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• Particle Methods in Coupled Problems

  S. Idelsohn, J. Gimenez, N. Nigro, P. Becker

  Videos of Plenary Lectures presented at the VI International Conference on Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2015).

  
  

  Abstract

  One of the main drawbacks of all the time integration algorithms using an Eulerian formulations in Coupled Problems is the restricted time-step to be used to have acceptable results. For the case of fluid-structure interactions (FSI) with or without free-surfaces or for the case of fluid with moving internal interfaces (multi-fluids), it is well known that in the explicit integrations, the time-step to be used in the solution is stable only for time-step smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and the Fourier number. The first one is concerning with the convective terms and the second one with the diffusive ones. Both numbers must be less than one to have stable algorithms. For convection dominant problems the condition CFL<1 becomes crucial and limit the use of explicit methods or outdistance its to be efficient. On the other hand, implicit integrations using Eulerian formulations are restricted in the time-step size due to the lack of convergence of the non-linear terms. Both time integrations, explicit or implicit are, in most cases, limited to CFL no much larger than one. In this lecture we will present a Particle Method to solve coupled problems like FSI or multi-fluid problems that use in all the domain (solid and fluid) a Lagrangian formulation with explicit or implicit time integration without the CFL<1 restriction. This allows large time-steps, independent of the spatial discretization, having equal or better precision that an Eulerian integration. The proposal will be tested numerically for FSI and multi-fluid flows problems using the Particle Finite Element Method second generation (PFEM2). The results show than this Particle Method is largely more efficient compared as well in accuracy as in computing time with other more standard Eulerian formulations.

  Abstract
  One of the main drawbacks of all the time integration algorithms using an Eulerian formulations in Coupled Problems is the restricted time-step to be used to have acceptable [...]

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