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• Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

  M. Mier-Torrecilla, A. Geyer, J. Phillips, S. Idelsohn, E. Oñate

  Int. J. Numer. Meth. Fluids (2012). Vol. 69 (5), pp. 1016-1030

  
  

  Abstract

  Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems.

  Abstract
  Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows [...]

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• A family of residual‐based stabilized finite element methods for Stokes flows

  E. Oñate, P. Nadukandi, S. Idelsohn, J. García-Espinosa, C. Felippa

  Int. J. Numer. Meth. Fluids (2011). Vol. 65 (1-3), pp. 106-134

  
  

  Abstract

  We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub‐scales (OSS) method are recovered from the general residual‐based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual‐based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.

  Abstract
  We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known [...]

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• A finite point method for adaptive three‐dimensional compressible flow calculations

  E. Ortega, E. Oñate, S. Idelsohn

  Int. J. Numer. Meth. Fluids (2008). Vol. 60 (9), pp. 937-971

  
  

  Abstract

  The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. 

  Abstract
  The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation [...]

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• The violation of objectivity in Laplace formulations of the Navier–Stokes equations

  A. Limache, S. Idelsohn, R. Rossi, E. Oñate

  Int. J. Numer. Meth. Fluids (2007). Vol. 54 (6-8), pp. 639-664

  
  

  Abstract

  The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations. 

  Abstract
  The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural [...]

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• Fractures prediction in concrete structures combining the finite and discrete element methods

  F. Zarate, E. Oñate

  Hormigón y Acero (2018). (prepint) 69, Supl 1, pp. 53-69

  
  

  Abstract

  This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation of fractures in concrete structures. The calculation of the structure, modeled as a continuum, begins with the FEMand the DEM is used to start and grow the cracks that may appear in the structure. This methodology has been proposed by the authors in two andthree dimensions. Recently, the use of one-dimensional steel elements embedded in the continuum has been added to model the reinforcement inconcrete structures. The work presents different examples of application to the study of the breakage of parts and structures of concrete in massand armed, as well as the multiple breakage of a historic structure of masonry due to an earthquake.

  Abstract
  This paper presents the basic concepts and application of the strategy that combines finite element methods (FEM) and discrete elements (DEM)for the study of the propagation [...]

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• Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction

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

  Comput. Methods Appl. Mech. Engrg., (2017). Vol. 315, pp. 1080-1097

  
  

  Abstract

  We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements described in terms of displacements. The novelty of the model consists in the use of the explicit streamline integration for predicting the end-of-step configuration of the fluid domain. It is shown that this prediction considerably alleviates the time step size restrictions faced by the former Lagrangian models due to the possibility of an element inversion within one time step. The method is validated and compared with conventional approaches using three numerical examples. Time step size and corresponding Courant numbers leading to optimal behavior in terms of computational efficiency are identified.

  Abstract
  We propose here a displacement-based updated Lagrangian fluid model developed to facilitate a monolithic coupling with a wide range of structural elements [...]

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• A finite point method in computational mechancis. Applications to convective transport and fluid flow.

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

  Int. J. Numer. Meth. Engng. (1996). Vol. 39 (22), pp. 3839-3866

  
  

  Abstract

  The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non‐self adjoint equations typical of convective‐diffusive transport and also to the analysis of compressible fluid mechanics problem are presented.

  Abstract
  The paper presents a fully meshless procedure fo solving partial differential equations. The approach termed generically the ‘finite point method’ is based on [...]

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• A formulation for the study, by the method of finite elements, of the deformation of marine pipes during their installation

  J. Oliver, E. Oñate

  Revista de Obras Públicas (1983). Vol. 130 (3218), pp. 747-763

  
  

  Abstract

  La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la necesidad de conocer los esfuerzos y deformaciones que se producen en el tendido de tuberías submarinas, a cuyo estudio, mediante elementos finitos en diversas condiciones de instalación, se dedica este artículo, que permite la obtención de ábacos de cálculo o formulas sencillas aplicables en los distintos casos.

  Abstract
  La ejecución de emisarios submarinos para saneamiento y la instalación de tuberías para transporte de productos petrolíferos son ejemplos de la [...]

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• A finite element method for solving the incompressible Navier-Stokes equations at low and high Reynolds numbers using finite calculus. Application to fluid-structure interaction

  H. Lynga, E. Oñate

  Monograph CIMNE (2007). M104

  
  

  Abstract

  The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus (FIC), which is a methodology developed by E. On˜ate and co-workers at CIMNE (International Center for Numerical Methods in Engineering),  flows with a wide range of Reynolds numbers can be modeled. The secondary objective is to test the applicability of the FIC/FEM model to fluid-structure interaction (FSI) emphasizing aero-elasticity. The implementation of the model is carried out within KRATOS, a finite element code for solving multi-physics problems developed at CIMNE.

  Abstract
  The main objective of this monograph is to develop a stabilized finite element method (FEM) for solving the incompressible Navier-Stokes equations. Using Finite Calculus [...]

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• Formulaciones tangentes y secantes en análisis no lineal de vigas Cosserat

  A. Morán, E. Oñate, J. Miquel

  Monograph CIMNE (2007). M103

  
  

  Abstract

  En este trabajo se han dedicado cinco capítulos a la exposición y discretización de un modelo clásico no lineal de viga Cosserat por medio del método de elementos finitos, utilizando las formulaciones Tangente y Secante.

  Abstract
  En este trabajo se han dedicado cinco capítulos a la exposición y discretización de un modelo clásico no lineal de viga Cosserat por medio del [...]

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