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• New rotation-free finite element shell triangle accurately using geometrical data

  P. Fuentes, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2010). vol. 199, pp. 383–391

  
  

  Abstract

  A new triangle shell element is presented. The advantages of this element are threefold: simplicity, generality and geometrical accuracy. The formulation is free from rotation degrees of freedom. The triangle here presented can be used regardless of the mesh topology, thus generality is conserved for any meshrepresented surface. From an original first order approach we evolve to a third order geometric description. The higher degree geometric description is based on the Bézier triangles concept, a very well known geometry in the domain of CAGD [G. Farin, Curves and Surfaces for CAGD. A Practical Guide, fifth ed., Morgan Kaufmann Publishers, San Francisco, CA, 2002]. Using this concept we show the path to reconstruct a general third order interpolating surface using only the three coordinates at each node. This work takes as starting point the nodal implementation of a basic triangle shell element [E. Oñate, F. Zárate, Rotation-free triangular plate and shell elements, Int. J. Numer. Methods Engrg. 47 (2000) 557– 603]. In order to use an exact formula for the curvature, the normal directions at each node and the way to characterize them are proposed. Then, the geometrical properties and the mechanical behavior of the surface created are introduced. Finally, different examples are presented to depict the versatility and accuracy of the element.

  Abstract
  A new triangle shell element is presented. The advantages of this element are threefold: simplicity, generality and geometrical accuracy. The formulation is free from rotation [...]

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• A high-resolution Petrov-Galerkin method for the convection-diffusion-reaction problem. Part II-A multidimensional extension

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

  Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213-216, pp. 327-352

  
  

  Abstract

  A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions. This is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1D reaction–diffusion problem. The nondimensional element number is then defined using this fictitious reaction coefficient, the diffusion coefficient and an appropriate element size. Next, we introduce anisotropic element length vectors li and the stabilization parameters αi, βi are calculated along these li. Except for the modification to include the new dimensionless number that quantifies the characteristic layers, the definitions of αi, βi are a direct extension of their counterparts in 1D. Using αi, βiand li, objective characteristic tensors associated with the HRPG method are defined. The numerical artifacts across the characteristic layers are manifested as the Gibbs phenomenon. Hence, we treat them just like the artifacts formed across the parabolic layers in the reaction-dominant case. Several 2D examples are presented that support the design objective—stabilization with high-resolution

  Abstract
  A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies [...]

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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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• 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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