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• A simple shock-capturing technique for high-order discontinuous Galerkin methods

  A. Huerta, E. Casoni, J. Peraire

  Int. J. Numer. Meth. Fluids (2012). Vol. 69 (10), pp. 1614-1632

  
  

  Abstract

  This article presents a novel shock-capturing technique for the discontinuous Galerkin (DG) method. The technique is designed for compressible flow problems, which are usually characterized by the presence of strong shocks and discontinuities. The inherent structure of standard DG methods seems to suggest that they are especially adapted to capture shocks because of the numerical fluxes based on suitable approximate Riemann solvers, which, in practice, introduces some stabilization. However, the usual numerical fluxes are not sufficient to stabilize the solution in the presence of shocks for large high-order elements. Here, a new basis of shape functions is introduced. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization because of numerical fluxes. Large high-order elements can therefore be used and shocks captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Several numerical examples for transonic and supersonic flows are studied to demonstrate the applicability of the proposed approach.

  Abstract
  This article presents a novel shock-capturing technique for the discontinuous Galerkin (DG) method. The technique is designed for compressible flow problems, which are usually [...]

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• One-dimensional shock-capturing for high-order discontinuous Galerkin methods

  E. Casoni, J. Peraire, A. Huerta

  Int. J. Numer. Meth. Fluids (2012). Vol. 71 (6), pp. 737-755

  
  

  Abstract

  Discontinuous Galerkin methods have emerged in recent years as an alternative for nonlinear conservation equations. In particular, their inherent structure (a numerical flux based on a suitable approximate Riemann solver introduces some stabilization) suggests that they are specially adapted to capture shocks. However, numerical fluxes are not sufficient to stabilize the solution in the presence of shocks. Thus, slope limiter methods, which are extensions of finite volume methods, have been proposed. These techniques require, in practice, mesh adaption to localize the shock structure. This is is more obvious for large elements typical of high-order approximations. Here, a new approach based on the introduction of artificial diffusion into the original equations is presented. The order is not systematically decreased to one in the presence of the shock, large high-order elements can be used, and several linear and nonlinear tests demonstrate the efficiency of the proposed methodology.

  Abstract
  Discontinuous Galerkin methods have emerged in recent years as an alternative for nonlinear conservation equations. In particular, their inherent structure (a numerical flux [...]

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• Are High-order and Hybridizable Discontinuous Galerkin methods competitive?

  A. Huerta, A. Angeloski, X. Roca, J. Peraire

  Oberwolfach Reports (2012). Vol. 9 (1), pp. 485-487

  
  

  Abstract

  The talk covered several issues motivated by a practical engineering wave propagation problem: real-time evaluation of wave agitation in harbors. The first part, presented the application of a reduced order model in the framework of a Helmholtz equation with non-constant coefficients in an unbounded domain. This problem requires large numbers of degrees of freedom (ndof) because relatively high frequencies with small (compared with the domain size) geometric features must be considered

  Abstract
  The talk covered several issues motivated by a practical engineering wave propagation problem: real-time evaluation of wave agitation in harbors. The first part, presented [...]

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• Interactive simulation on a smart Phone

  E. Cueto, A. Huerta, F. Chinesta

  Benchmark (2012). Vol. January 12, pp. 12-14

  
  

  Abstract

  Traditionally, Simulationbased Engineering Sciences (SBES) made use of static data inputs to perform the simulations. Namely parameters of the model, boundary conditions, etc. were traditionally obtained by experimentation and could not be modified during the course of the simulation. More recently, large efforts have been invested in developing dynamic datadriven application systems (DDDAS): systems in which measurements and simulations are continuously influencing each other in a symbiotic manner. It should be understood that measurements should be incorporated in real time to the simulations, while simulations could eventually control the way in which measurements are done.

  Abstract
  Traditionally, Simulationbased Engineering Sciences (SBES) made use of static data inputs to perform the simulations. Namely parameters of the model, boundary conditions, [...]

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• Proper generalized decomposition based dynamic data-driven control of material forming processes

  C. Ghnatios, F. Masson, A. Huerta, A. Leygue, E. Cueto, F. Chinesta

  Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213-216, pp. 29-41

  
  

  Abstract

  Dynamic Data-Driven Application Systems—DDDAS—appear as a new paradigm in the field of applied sciences and engineering, and in particular in Simulation-based Engineering Sciences. By DDDAS we mean a set of techniques that allow to link simulation tools with measurement devices for real-time control of systems and processes. In this paper a novel simulation technique is developed with an eye towards its employ in the field of DDDAS. The main novelty of this technique relies in the consideration of parameters of the model as new dimensions in the parametric space. Such models often live in highly multidimensional spaces suffering the so-called curse of dimensionality. To avoid this problem related to mesh-based techniques, in this work an approach based upon the Proper Generalized Decomposition—PGD—is developed, which is able to circumvent the redoubtable curse of dimensionality. The approach thus developed is composed by a marriage of DDDAS concepts and a combination of PGD “off-line” computations, linked to “on-line” post-processing. In this work we explore some possibilities in the context of process control, malfunctioning identification and system reconfiguration in real time, showing the potentialities of the technique in real engineering contexts.

  Abstract
  Dynamic Data-Driven Application Systems—DDDAS—appear as a new paradigm in the field of applied sciences and engineering, and in particular in Simulation-based [...]

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• NURBS-Enhanced Finite Element Method (NEFEM)

  R. Sevilla, S. Fernández-Méndez, A. Huerta

  Archives of Comp. Meths. Engng. (2011). Vol. 18 (4), pp. 441-484

  
  

  Abstract

  The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.

  Abstract
  The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain [...]

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• 3D NURBS-enhanced finite element method (NEFEM)

  R. Sevilla, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Engng. (2011). Vol. 88 (12) pp. 109-125

  
  

  Abstract

  This paper presents the extension of the recently proposed NURBS-enhanced finite element method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the computational domain by means of its CAD boundary representation with non-uniform rational B-splines (NURBS) surfaces. Specific strategies for interpolation and numerical integration are presented for those elements affected by the NURBS boundary representation. For elements not intersecting the boundary, a standard finite element rationale is used, preserving the efficiency of the classical FEM. In 3D NEFEM special attention must be paid to geometric issues that are easily treated in the 2D implementation. Several numerical examples show the performance and benefits of NEFEM compared with standard isoparametric or cartesian finite elements. NEFEM is a powerful strategy to efficiently treat curved boundaries and it avoids excessive mesh refinement to capture small geometric features.

  Abstract
  This paper presents the extension of the recently proposed NURBS-enhanced finite element method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the [...]

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• Comparison of high-order curved finite elements

  R. Sevilla, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Engng. (2011). Vol. 87 (8), pp. 719-734

  
  

  Abstract

  Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two-dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS-enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p-FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations.

  Abstract
  Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation [...]

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• Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

  A. Montlaur, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Fluids (2010). Vol. 64 (5), pp. 549-564

  
  

  Abstract

  An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high-order piecewise divergence-free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods.

  Abstract
  An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. [...]

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• A new least-squares approximation of affine mappings for sweep algorithms

  X. Roca, J. Sarrate, A. Huerta

  Engineering with computers (2010). Vol. 26 (3), pp. 327-337

  
  

  Abstract

  This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep path. From the computational point of view, sweep methods based on a least-squares approximation of an affine mapping are the fastest alternative to compute these projections. Several functionals have been introduced to perform the least-squares approximation. However, for very simple and typical geometrical configurations they may generate low-quality projected meshes. For instance, they may induce skewness and flattening effects on the projected discretizations. In addition, for these configurations the minimization of these functionals may lead to a set of normal equations with singular system matrix. In this work we analyze previously defined functionals. Based on this analysis we propose a new functional and show that its minimization overcomes these drawbacks. Finally, we present several examples to assess the properties of the proposed functional.

  Abstract
  This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting [...]

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