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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

  Computational Mechanics (2011). Vol. 48 (3), pp. 307-318

  
  

  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 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 [...]

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• On the analysis of heterogeneous fluids with jumps in the viscosity using a discontinuous pressure field

  S. Idelsohn, M. Mier-Torrecilla, N. Nigro, E. Oñate

  Computational Mechanics (2010). Vol. 46 (1), pp. 115-124

  
  

  Abstract

  Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure fields. We show the importance of using discontinuous pressure fields to avoid errors in the incompressibility condition near the interface.

  Abstract
  Heterogeneous incompressible fluid flows with jumps in the viscous properties are solved with the particle finite element method using continuous and discontinuous pressure [...]

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• A monolithic Lagrangian approach for fluid–structure interaction problems

  P. Ryzhakov, R. Rossi, S. Idelsohn, E. Oñate

  Computational Mechanics (2010). Vol. 46 (6), pp. 883-899

  
  

  Abstract

  Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique presented is based upon the utilization of a Lagrangian description for both the fluid and the structure. A linear displacement–pressure interpolation pair is used for the fluid whereas the structure utilizes a standard displacement-based formulation. A slight fluid compressibility is assumed that allows to relate the mechanical pressure to the local volume variation. The method described features a global pressure condensation which in turn enables the definition of a purely displacement-based linear system of equations. A matrix-free technique is used for the solution of such linear system, leading to an efficient implementation. The result is a robust method which allows dealing with FSI problems involving arbitrary variations in the shape of the fluid domain. The method is completely free of spurious added-mass effects.

  Abstract
  Current work presents a monolithic method for the solution of fluid–structure interaction problems involving flexible structures and free-surface flows. The technique [...]

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• Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the PFEM

  S. Idelsohn, J. Marti, A. Souto-Iglesias, E. Oñate

  Computational Mechanics (2008). Vol. 43 (1), pp. 125-132

  
  

  Abstract

  The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular case for which experimental results are not much reported. This is the case of FSI including free surface flows. The possibilities of the Particle Finite Element Method (PFEM) for the simulation of free surface flows is also tested. The simulations are run using the same scale as the experiment in order to minimize errors due to scale effects. Different scenarios are simulated by changing the boundary conditions for reproducing flows with the desired characteristics. Details of the input data for all the examples studied are given. The aim is to identifying benchmark problems for FSI including free surface flows for future comparisons between different numerical approaches.

  Abstract
  The paper aims to introduce new fluid–structure interaction (FSI) tests to compare experimental results with numerical ones. The examples have been chosen for a particular [...]

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• An improved finite point method for tridimensional potential flows

  E. Ortega, E. Oñate, S. Idelsohn

  Computational Mechanics (2007). Vol. 40 (6), pp. 949-963

  
  

  Abstract

  At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical approximation built on the former. In this article we develop the second condition and present an alternative procedure to obtain shape functions and their derivatives from a given cloud of points regardless of its geometrical features. This procedure, based on a QR factorization and an iterative adjust of local approximation parameters, allows obtaining a satisfactory minimization problem solution, even in the most difficult cases where usual approaches fail. It is known that high-order meshless constructions need to include a large number of points in the local support zone and this fact turns the approximation more dependent on the size, shape and spatial distribution of the local cloud of points. The proposed procedure also facilitates the construction of high-order approximations on generic geometries reducing their dependence on the geometrical support where they are based. Apart from the alternative solution to the minimization problem, the behaviour of high-order Finite Point approximations and the overall performance of the proposed methodology are shown by means of several numerical tests.

  Abstract
  At the local level, successful meshless techniques such as the Finite Point Method must have two main characteristics: a suitable geometrical support and a robust numerical [...]

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• Fractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEM

  R. Aubry, E. Oñate, S. Idelsohn

  Computational Mechanics (2006). Vol. 38 (4-5), pp. 294-309

  
  

  Abstract

  The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505–526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.

  Abstract
  The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian [...]

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• A mesh-free finite point method for advective-diffusive transport and fluid flow problems

  E. Oñate, S. Idelsohn

  Computational Mechanics (1998). Vol. 21 (4-5), pp. 283-292

  
  

  Abstract

  The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation for evaluating the approximation integrals. In the paper, details of a procedure for stabilizing the numerical solution for advective-diffusive transport and fluid flow problems using the FPM are given. The method is based on a consistent introduction of the stabilizing terms in the governing differential equations. One example showing the applicability of the FPM is given.

  Abstract
  The finite point method (FPM) is a gridless numerical procedure based on the combination of weighted least square interpolations on a cloud of points with point collocation [...]

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• Improving mass conservation in simulation of incompressible flows

  P. Ryzhakov, E. Oñate, R. Rossi, S. Idelsohn

  Int. J. Numer. Meth. Engng. (2012). Vol. 90 (12), pp. 1435-1451

  
  

  Abstract

  We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian fluid formulation, where the mass loss effects are particularly apparent. However, the methodology is general and could be used for fixed grid approaches. The idea consists in reflecting the incompressibility condition already in the intermediate velocity. This is achieved by predicting the end‐of‐step pressure and using this prediction in the fractional momentum equation. The resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme. In turn, the predicted pressure can be used as the boundary condition necessary for the solution of the pressure Poisson equation in case a continuous Laplacian matrix is employed. Using this approximation of the end‐of‐step incompressible pressure as the essential boundary condition considerably improves the conservation of mass, specially for the free surface flows of fluids with low viscosity. The pressure prediction does not require the resolution of any additional equations system. The efficiency of the method is shown in two examples. The first one shows the performance of the method with respect to mass conservation. The second one tests the method in a challenging fluid–structure interaction benchmark, which can be naturally resolved by using the presented approach.

  Abstract
  We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian [...]

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• Combined Eulerian–PFEM approach for analysis of polymers in fire situations

  J. Marti, P. Ryzhakov, S. Idelsohn, E. Oñate

  Int. J. Numer. Meth. Engng. (2012). Vol. 92 (9), pp. 782-801

  
  

  Abstract

  In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose here a technique that aims at minimizing the computational cost. This is basically achieved by using the immersed boundary‐like approach, combining the particle finite element method for the polymer with an Eulerian formulation for the ambience. The polymer and ambience domains interact over the interface boundary. The boundary is explicitly defined by the position of the Lagrangian domain (polymer) within the background Eulerian mesh (ambience). This allows to solve the energy equation for both subdomains on the Eulerian mesh with different thermal properties. Radiative transport equation is exclusively considered for the ambience, and the heat exchange at the interface is modeled by calculating the radiant heat flux and imposing it as a natural boundary condition.

  Abstract
  In this paper, we present a computational algorithm for solving an important practical problem, namely, the thermoplastic polymer melting under fire conditions. We propose [...]

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• Consistent pressure Laplacian stabilization for incompressible continua via higher‐order finite calculus

  E. Oñate, S. Idelsohn, C. Felippa

  Int. J. Numer. Meth. Engng. (2011). Vol. 87 (1-5), pp. 171-195

  
  

  Abstract

  We present a stabilized numerical formulation for incompressible continua based on a higher‐order Finite Calculus (FIC) approach and the finite element method. The focus of the paper is on the derivation of a stabilized form for the mass balance (incompressibility) equation. The simpler form of the momentum equations neglecting the non‐linear convective terms, which is typical for incompressible solids, Stokes flows and Lagrangian flows is used for the sake of clarity. The discretized stabilized mass balance equation adds to the standard divergence of velocity term a pressure Laplacian and an additional boundary term. The boundary term is relevant for the accuracy of the numerical solution, especially for free surface flow problems. The Laplacian and boundary stabilization terms are multiplied by non‐linear parameters that have an extremely simple expression in terms of element sizes, the pressure and the discrete residuals of the incompressibility equation and the momentum equations, thus ensuring the consistency of the method. The stabilized formulation allows solving the incompressible problem iteratively using an equal‐order interpolation for the velocities (or displacements) and the pressure, which are the only unknowns. The use of additional pressure gradient projection variables, typical of many stabilized methods, is unnecessary. The formulation is particularly useful for heterogeneous incompressible materials with discontinuous material properties, as it allows computing all the stabilization matrices at the element level. Details of the finite element formulation are given. The good behaviour of the new pressure Laplacian stabilization (PLS) technique is shown in simple but demonstrative examples of application. A very accurate solution was obtained in all cases in 2–3 iterations. Copyright © 2010 John Wiley & Sons, Ltd.

  Abstract
  We present a stabilized numerical formulation for incompressible continua based on a higher‐order Finite Calculus (FIC) approach and the finite element method. The focus [...]

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