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• Fluid flows around turbomachinery using an explicit pseudo‐temporal Euler FEM

  N. Nigro, M. Storti, S. Idelsohn

  Commun. Numer. Meth. Engng (1995). Vol. 11 (3), pp. 199-211

  
  

  Abstract

  This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov–Galerkin) method, explicit forward Euler pseudo‐temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.

  Abstract
  This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline [...]

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• Multifluid flows with weak and strong discontinuous interfaces using an elemental enriched space

  S. Idelsohn, J. Gimenez, N. Nigro

  Int. J. Numer. Meth. Fluids (2018). Vol. 86 (12), pp. 750–769

  
  

  Abstract

  In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown function using a fixed mesh in which the jumps and kinks do not coincide with the interelement boundaries. In this previous publication, only scalar transport problems were solved (thermal problems). In the present work, these ideas are generalized to vectorial unknowns, in particular, the incompressible Navier‐Stokes equations for multifluid flows presenting internal moving interfaces. The advantage of the EFEM compared with global enrichment is the significant reduction in computing time when the internal interface is moving. In the EFEM, the matrix to be solved at each time step has not only the same amount of degrees of freedom (DOFs) but also the same connectivity between the DOFs. This frozen matrix graph enormously improves the efficiency of the solver. Another characteristic of the elemental enriched space presented here is that it allows a linear variation of the jump, thus improving the convergence rate, compared with other enriched spaces that have a constant variation of the jump. Furthermore, the implementation in any existing finite‐element code is extremely easy with the version presented here because the new shape functions are based on the usual finite‐element method shape functions for triangles or tetrahedrals, and once the internal DOFs are statically condensed, the resulting elements have exactly the same number of unknowns as the nonenriched finite elements.

  Abstract
  In a previous paper, the authors presented an elemental enriched space to be used in a finite‐element framework (EFEM) capable of reproducing kinks and jumps in an unknown [...]

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• Analysis of multifluid flows with large time steps using the particle finite element method

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

  Int. J. Numer. Meth. Fluids (2014). Vol. 75 (9), pp. 621-644

  
  

  Abstract

  Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity in the Navier–Stokes equations. For this reason, standard numerical methods require very small time steps in order to solve accurately the internal interface position. In a previous paper, the authors developed a particle‐based method (named particle finite element method (PFEM)) based on a Lagrangian formulation and FEM for solving the fluid mechanics equations for multifluids. PFEM was capable of achieving accurate results, but the limitation of small time steps was still present. In this work, a new strategy concerning the time integration for the analysis of multifluids is developed allowing time steps one order of magnitude larger than the previous method. The advantage of using a Lagrangian solution with PFEM is shown in several examples. All kind of heterogeneous fluids (with different densities or viscosities), multiphase flows with internal interfaces, breaking waves, and fluid separation may be easily solved with this methodology without the need of small time steps.

  Abstract
  Multifluids are those fluids in which their physical properties (viscosity or density) vary internally and abruptly forming internal interfaces that introduce a large nonlinearity [...]

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• Application of the finite point method to high‐Reynolds number compressible flow problems

  R. Ortega, E. Oñate, S. Idelsohn, R. Flores

  Int. J. Numer. Meth. Fluids (2014). Vol. 74 (10), pp. 732-748

  
  

  Abstract

  In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications focusing on two main aspects: the easiness and automation of the meshless discretization of viscous layers and the construction of a robust numerical approximation in the highly stretched clouds of points resulting in such domain areas. The flow solution scheme adopts an upwind‐biased scheme to solve the averaged Navier–Stokes equations in conjunction with an algebraic turbulence model. The numerical applications presented involve different attached boundary layer flows and are intended to show the performance of the numerical technique. The results obtained are satisfactory and indicative of the possibilities to extend the present meshless technique to more complex flow problems.

  Abstract
  In this work, the finite point method is applied to the solution of high‐Reynolds compressible viscous flows. The aim is to explore this important field of applications [...]

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• A meshless finite point method for three‐dimensional analysis of compressible flow problems involving moving boundaries and adaptivity

  R. Ortega, E. Oñate, S. Idelsohn, R. Flores

  Int. J. Numer. Meth. Fluids (2013). Vol. 73 (4), pp. 323-343

  
  

  Abstract

  A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased discretization of the Euler equations, written in arbitrary Lagrangian–Eulerian form and integrated in time by means of a dual‐time steeping technique. In order to exploit the meshless potential of the method, a domain deformation approach based on the spring network analogy is implemented, and h‐adaptivity is also employed in the computations. Typical movable boundary problems in transonic flow regime are solved to assess the performance of the proposed technique. In addition, an application to a fluid–structure interaction problem involving static aeroelasticity illustrates the capability of the method to deal with practical engineering analyses. The computational cost and multi‐core performance of the proposed technique is also discussed through the examples provided.

  Abstract
  A finite point method for solving compressible flow problems involving moving boundaries and adaptivity is presented. The numerical methodology is based on an upwind‐biased [...]

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• Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations

  J. Baiges, R. Codina, S. Idelsohn

  Int. J. Numer. Meth. Fluids (2013). Vol. 72 (12), pp. 1219-1243

  
  

  Abstract

  In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. The basic idea is to build a reduced‐order model based on a proper orthogonal decomposition and a Galerkin projection and treat all the terms in an explicit way in the time integration scheme, including the pressure. This is possible because the reduced model snapshots do already fulfill the continuity equation. The pressure field is automatically recovered from the reduced‐order basis and solution coefficients. The main advantage of this explicit treatment of the incompressible Navier–Stokes equations is that it allows for the easy use of hyper‐reduced order models, because only the right‐hand side vector needs to be recovered by means of a gappy data reconstruction procedure. A method for choosing the optimal set of sampling points at the discrete level in the gappy procedure is also presented. Numerical examples show the performance of the proposed strategy

  Abstract
  In this paper, we present an explicit formulation for reduced‐order models of the stabilized finite element approximation of the incompressible Navier–Stokes equations. [...]

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• A new enrichment space for the treatment of discontinuous pressures in multi‐fluid flows

  R. Ausas, G. Buscaglia, S. Idelsohn

  Int. J. Numer. Meth. Fluids (2011). Vol. 70 (7), pp. 829-850

  
  

  Abstract

  In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds two degrees of freedom per element that can be eliminated by means of static condensation. The new space is tested and compared with the classical P1 space and to the space proposed by Ausas et al (Comp. Meth. Appl. Mech. Eng., Vol. 199, 1019–1031, 2010) in several problems involving jumps in the viscosity and/or the presence of singular forces at interfaces not conforming with the element edges. The combination of this enrichment space with another enrichment that accommodates discontinuities in the pressure gradient has also been explored, exhibiting excellent results in problems involving jumps in the density or the volume forces.

  Abstract
  In this work, a new enrichment space to accommodate jumps in the pressure field at immersed interfaces in finite element formulations, is proposed. The new enrichment adds [...]

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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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