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• Multi-fluid flows with the particle finite element method

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

  Comput. Methods Appl. Mech. Engrg., (2009). vol. 198, pp. 2750–2767

  
  

  Abstract

  Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal forces applied on it. In this paper the Particle Finite Element Method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density. To evaluate the external applied forces to each particle, the incompressible Navier–Stokes equations are solved at each time step using a Lagrangian formulation. All the information in the fluid is transmitted via the particles. All kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free-surfaces, breaking waves and fluid separations may be easily solved with this methodology. 

  Abstract
  Particle methods are those in which the problem is represented by a discrete number of particles. Each particle moves accordingly with its own mass and the external/internal [...]

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• Large time-step explicit integration method for solving problems with dominant convection

  S. Idelsohn, N. Nigro, A. Limache, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2012). Vol. 217-220, pp. 168-185

  
  

  Abstract

  An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated by convection, independently of the spatial discretization. The idea is to use the information existing at time t=tn in the velocity streamlines as well as in the acceleration streamlines to update the particle position as well as the velocity in an updated Lagrangian frame. The method may be used with moving or fixed meshes.

  Abstract
  An explicit time integrator without the CFL < 1 restriction for the momentum equation is presented. This allows stable large time-steps in problems dominated [...]

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• A compressible Lagrangian framework for the simulation of the underwater implosion of large air bubbles

  K. Kamran, R. Rossi, E. Oñate, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2013). Vol. 255 (1), pp. 210-225

  
  

  Abstract

  A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is verified by several benchmarks which evaluate the behavior of the numerical scheme for severe compression and expansion cases. This model is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. We observe that the conditions within the bubble are nearly uniform until the converging pressure wave is strong enough to create very large pressures near the center of the bubble. These bubble dynamics occur on very small spatial (0.3 mm), and time (0.1 ms) scales. During the final stage of the collapse Rayleigh–Taylor instabilities appear at the interface and then disappear when the rebounce starts. At the end of the rebounce phase the bubble radius reaches 50% of its initial value and the bubble recover its circular shape. It is when the second collapse starts, with higher mode shape instabilities excited at the bubble interface, that leads to the rupture of the bubble. Several graphs are presented and the pressure pulse detected in the water is compared by experiment.

  Abstract
  A fully Lagrangian compressible numerical framework for the simulation of underwater implosion of a large air bubble is presented. Both air and water are considered compressible [...]

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• Lagrangian formulations to solve free surface incompressible inviscid fluid flows

  S. Idelsohn, M. Storti, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2001). Vol. 191 (6–7), pp. 583-593

  
  

  Abstract

  A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used in "meshless" approximations and the time integration is introduced in a semi-implicit way by a fractional step method. In this manner, both classical stabilization terms used in incompressible Euler equations are unnecessary: numerical diffusion for convective terms are unnecessary due to the Lagrangian formulation, and stabilization of pressure due to the incompressibility constraint for equal order interpolations is eliminated using the fractional step method.

  Abstract
  A particle method is presented for the solution of the incompressible inviscid fluid flow equation using a Lagrangian formulation. The interpolated function are those used [...]

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• To mesh or not to mesh. That is the question. . .

  S. Idelsohn, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 4681–4696

  
  

  Abstract

  In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification for numerical formulations may be to separate the methods that make use of a standard finite element mesh (such as those made of tetrahedra or hexahedra), from those that do not need a standard mesh, namely the meshless methods. For solving a partial different equation by a numerical method, a possible alternative may be either to use a mesh method or a meshless method. This paper discusses this issue to show that this choice is not, in the large majorities of the cases, the right question.

  Abstract
  In the last decade a family of methods called meshless methods has been developed both for structural and fluid mechanics problems. After these ideas, a possible classification [...]

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• A stabilized finite point method for analysis of fluid mechanics problems

  E. Oñate, S. Idelsohn, O. Zienkiewicz, R. Taylor, C. Sacco

  Comput. Methods Appl. Mech. Engrg., (1996). Vol. 195, pp. 6750-6777

  
  

  Abstract

  flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation integrals. Some examples of application to convective trasport and compressible flow problems are presented.

  Abstract
  flow type problems is presented. The method is based on the use of a weighted least square interpolation procedure together with point collocation for evaluating the approximation [...]

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• Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus

  E. Oñate, F. Zarate, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (13-16), pp. 1793–1825

  
  

  Abstract

  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.

  Abstract
  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]

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• Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion

  F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

  Fire and Materials (2015). Vol. 39 (6), pp. 570-584

  
  

  Abstract

  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classifi cations d ue to the  competing ef fects of gasifica ti on, charring, flame inhibition and melt flow/dripping. For numerical investigation, the particle finite element method (PFEM) is used. Its capability to model the complex fire behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efficie nt p lasticiser; adding PTFE p reve nts dripping  by causing a flo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasification and dripping. The thermal impact of both the burner and the flame is approximated taking into account flame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the fire behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi fi cations and t he exti nc tion times are well predicted.

  Abstract
  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol [...]

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• Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows

  E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

  Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (19-20), pp. 1777–1800

  
  

  Abstract

  We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.

  Abstract
  We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]

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• P1/P0+ elements for incompressible flows with discontinuous material properties

  E. Oñate, P. Nadukandi, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 293, pp. 191-206

  
  

  Abstract

  We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant pressure field'' and ''a prescribed linear field'' that satisfies the steady state momentum equations for a constant body force. The elements are termed P1/P0+ as the “effective” pressure field is linear, although the unknown pressure field is piecewise constant within each element. The elements have an excellent behaviour for incompressible viscous flow problems with discontinuous material properties formulated in either Eulerian or Lagrangian descriptions. The necessary numerical stabilization for dealing with the inf-sup condition imposed by the incompressibility constraint and high convective effects (in Eulerian flows) is introduced via the Finite Calculus (FIC) approach. For the sake of clarity, the element derivation is presented first for the simpler Stokes equations written in the standard Eulerian frame. The extension of the formulation to the Navier-Stokes equations written in the Eulerian and Lagrangian frameworks is straightforward and is presented in the second part of the paper. The efficiency and accuracy of the new P1/P0+ triangle is verified by solving a set of incompressible multifluid flow problems using a Lagrangian approach and a classical Eulerian description. The excellent performance of the new triangular element in terms of mass conservation and general accuracy for analysis of fluids with discontinuous material properties is highlighted.

  Abstract
  We present a 3-noded triangle and a 4-noded tetrahedra with a continuous linear velocity and a discontinuous linear pressure field formed by the sum of an unknown ''constant [...]

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