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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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• Validation of numerical flow simulations against in vitro phantom measurements in different type B aortic dissection scenarios

  E. Soudah, P. Rudenick, M. Bordone, D. García-Dorado, A. Evangelista, E. Oñate

  Computer Methods in Biomechanics and Biomedical Engineering (2015). Vol. 18 (8), pp. 805-815

  
  

  Abstract

  An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment and follow-up are clinical challenges due to the progressive aortic dilatation and potentially severe complications during follow-up. It is well known that the direction and rate of dilatation of the artery wall depend on haemodynamic parameters such as the local velocity profiles, intra-luminal pressures and resultant wall stresses. These factors act on the FL and true lumen, triggering remodelling and clinical worsening. In this study, we aimed to validate a computational fluid dynamic (CFD) tool for the haemodynamic characterisation of chronic (type B) ADs. We validated the numerical results, for several dissection geometries, with experimental data obtained from a previous in vitro study performed on idealised dissected physical models. We found a good correlation between CFD simulations and experimental measurements as long as the tear size was large enough so that the effect of the wall compliance was negligible.

  Abstract
  An aortic dissection (AD) is a serious condition defined by the splitting of the arterial wall, thus generating a secondary lumen [the false lumen (FL)]. Its management, treatment [...]

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• A locally extended finite element method for the simulation of multi-fluid flows using the particle level set method

  K. Kamran, R. Rossi, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2015). Vol. 294, pp. 1-18

  
  

  Abstract

  The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations. First of all, a spatial enrichment is employed to improve the approximation properties of the Eulerian mesh. This is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface. Then, the Lagrangian Particle Level Set (PLS) method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method. While the local enrichment can be understood in the general context of the XFEM, we employ an element-local variant, which allows preserving the matrix graph, and hence highly improving the computational efficiency.

  Abstract
  The simulation of immiscible two-phase flows on Eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface. This [...]

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• The intrinsic time for the streamline upwind Petrov-Galerkin formulation using quadratic elements

  R. Codina, E. Oñate, M. Cervera

  Comput. Methods Appl. Mech. Engrg., (1992). Vol. 94, pp. 239-262

  
  

  Abstract

  In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic elements. Some related issues such as the computation of the characteristic element length and the introduction of source terms in the one-dimensional model problem are also addressed.

  Abstract
  In this paper the functions of the Péclet number that appear in the intrinsic time of the streamline upwind/Petrov-Galerkin (SUPG) formulation are analyzed for quadratic [...]

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• A finite element formulation for incompressible flow problems using a generalized streamline operator

  M. Cruchaga, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143, pp. 49-67

  
  

  Abstract

  A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. Methods Appl. Mech. Engrg. (1986) 58 305-328) for compressible flows is adapted to the incompressible Navier-Stokes equations. This new methodology allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, the definition of the ‘upwinding tensor’ does not require parameters defined outside this model. This formulation has been checked in classical tests with satisfactory results. Finally, a moving surface problem (Cruchaga et al., Comput. Numer. Methods Engrg. (1986) 59: 85-99) is also presented. 

  Abstract
  A finite element formulation for solving incompressible flow problems is presented. In this paper, the generalized streamline operator presented by Hughes et al. (Comput. [...]

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• A hierarchical finite element method based on the partition of unity

  R. Taylor, O. Zienkiewicz, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (1998). Vol. 152, pp. 73-84

  
  

  Abstract

  In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added to base finite element interpolations which, for Co approximations, are a particular case of the partition of unity. We also show how the functions may be constructed to preserve the interpolation property of the base finite element functions. An application to linear elasticity is used to illustrate the properties and stability of the approximation. 

  Abstract
  In this paper we consider the application of hierarchical functions to base approximations which are a partition of unity. The particular hierarchical functions used are added [...]

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• A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem

  P. Nadukandi, E. Oñate, J. García-Espinosa

  Int. J. Numer. Meth. Engng. (2010). Vol. 199, pp. 525–546

  
  

  Abstract

  We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi /partial t + u partial phi /partial x - k partial^2 phi /partial x^2 +s phi -f where k; s > o = 0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov– Galerkin (CAU/PG) method [A.C. Galeão, E.G. Dutra do Carmo, A consistent approximate upwind Petrov– Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83–95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Oñate, Derivation of stabilized equations for numerical solution of advective–diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233–265; E. Oñate, J. Miquel, G. Hauke, Stabilized formulation for the advection–diffusion– absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926–3946] by an appropriate definition of the characteristic length. The prefix ‘high-resolution’ is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L2-projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u; k; s and f . Finally, some remarks are made on the extension of the HRPG method to multidimensions.

  Abstract
  We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi [...]

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• A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces

  M. Cruchaga, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (1999). Vol. 173, pp. 241-255

  
  

  Abstract

  In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this technique allows the use of equal order interpolation for the unknowns of the problem: velocity and pressure. In this context, stable and convergent solutions can be obtained without requiring tuning parameters defined outside this model. The tracking of moving surfaces is also included in the numerical model. This formulation has been checked in 21) and 3D tests.

  Abstract
  In the present work a generalized streamline finite element formulation able to deal with incompressible flow problems is presented. In the finite element framework, this [...]

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• Shape variable definition with C0 , C1 and C2 continuity functions

  G. Chiandussi, G. Bugeda, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 188, pp. 727-742

  
  

  Abstract

  The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of the analysed structure or to the original geometry without any previous knowledge of the analytical expression of the CAD defining surfaces. The proposed technique allows the surface continuity to be preserved during the geometry modification process to be defined a priori. This capability allows for the definition of shape variables suitable for every kind of discipline involved in the optimisation process (structural analysis, fluid-dynamic analysis, crash analysis, aerodynamic analysis, etc.).

  Abstract
  The present paper proposes a new technique for the definition of the shape design variables in 2D and 3D optimisation problems. It can be applied to the discrete model of [...]

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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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