COLLECTIONS

Documents published in Scipedia

• Contaminación por lavado piezométrico a partir de vertederos enterrados: aplicación a un acuífero aluvial

  A. Navarro, J. Carrera, X. Sánchez-Vila

  Tecnología del agua (1992). Vol. 98, pp. 16-34

  
  

  Abstract

  El vertido incontrolado de residuos industriales y urbanos en acuíferos aluviales constituye una práctica frecuente en el entorno de áreas industrializadas y provoca la contaminación de las aguas subterráneas. En el proceso de contaminación juega un papel primordial el efecto producido por el ascenso y descenso de los niveles piezométricos que provoca un lavado de los residuos, generalmente enterrados en antiguas extracciones de áridos. La modelización de este fenómeno se ha realizado mediante el empleo de un modelo numérico de flujo-no lineal y transporte transitorios (TRNOCONF), que ha permitido reproducir la propagación del ión C1 desde las zonas de vertido. Los resultados obtenidos indican que junto al lavado piezométrico, los factores condicionantes en la formación de los penachos son la recarga procedente de avenidas y la existencia de una red de paleocanales que condiciona la geometría del fondo.

  Abstract
  El vertido incontrolado de residuos industriales y urbanos en acuíferos aluviales constituye una práctica frecuente en el entorno de áreas industrializadas [...]

  • 0
  •  read

• Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

  V. Tsiolakis, M. Giacomini, R. Sevilla, C. Othmer, A. Huerta

  Computer physics communications (2020). Vol 249, pp. 1-15

  
  

  Abstract

  The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.

  Abstract
  The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial [...]

  • 4
  •  read

• Fast solution of elliptic harbor agitation problems under frequency-direction input spectra by model order reduction and NURBS-enhanced FEM

  D. Modesto, B. Ye, S. Zlotnik, A. Huerta

  Coastal engineering (2020). Vol. 156, pp. 103618:1-103618:13

  
  

  Abstract

  Many harbor applications are based on the solution of linear elliptic agitation problems for many spectral conditions. One of the main goals consists in computing the linear combination of numerous simulations of the harbor agitation problem, using monochromatic waves of different spectral components (i.e. frequency and incoming wave direction). In practice, the standard strategy selects the number of wave components according to a prescribed discretization of the 2D input spectra. The main issue relies on some quantities of interest that are very sensitive to the level of refinement of the spectra, such as the significant wave height at every mesh point or the identification of resonance modes induced by long wave scattering. In many cases, achieving enough quality in these quantities may impose numerous simulations and, consequently, non-practical computer costs. This can drastically limit the final accuracy of results. To overcome this situation, here a new strategy is proposed to efficiently solve a large number of harbor agitation problems derived from dense discretizations of the 2D input spectra. The strategy is based on the combination of two different numerical approaches. Firstly, each required monochromatic simulation is solved via high order NURBS (non-uniform rational B-splines) enhanced finite elements (NEFEM). More precisely, NEFEM captures the exact harbor geometry using large mesh elements that produce accurate solutions and significant savings on the system size, particularly in long wave cases. Secondly, a model order reduction technique is used to approximate the original elliptic harbor model by a so-called surrogate model. The main advantage is that, once the surrogate model is constructed, it can be rapidly evaluated to provide simulations for any value of the spectral components within a range of interest, and without the need of solving any new harbor agitation problem (as the standard strategy does). Thus, this enables the possibility of using any desired discretization of the 2D input spectra with no additional computer cost. The construction of the surrogate model is performed using the proper generalized decomposition method with a novel incremental computation along the frequency dimension. The proposed strategy is discussed, and its superior performance with respect to standard strategies is demonstrated, on two harbor agitation examples with several applications.

  Abstract
  Many harbor applications are based on the solution of linear elliptic agitation problems for many spectral conditions. One of the main goals consists in computing the linear [...]

  • 2
  •  read

• Hybrid coupling of CG and HDG discretizations based on Nitsche’s method

  A. Spina, M. Giacomini, A. Huerta

  Computational mechanics (2020). Vol. 65 (2), pp. 311-330

  
  

  Abstract

  A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CG-HDG coupling exploits the definition of the numerical flux and the trace of the solution on the mesh faces to impose the transmission conditions between the CG and HDG subdomains. The con- tinuity of the solution is imposed in the CG problem via Nitsche’s method, whereas the equilibrium of the flux at the interface is naturally enforced as a Neumann con- dition in the HDG global problem. The proposed strategy does not affect the core structure of CG and HDG discretizations. In fact, the resulting formulation leads to a minimally-intrusive coupling, suitable to be integrated in existing CG and HDG libraries. Numerical experiments in two and three dimensions show optimal global convergence of the stress and superconvergence of the displacement field, locking-free approximation, as well as the potential to treat structural problems of engineering interest featuring multiple materials with compressible and nearly incompressible behaviors. This is a post-peer-review, pre-copyedit version of an article published in Computational mechanics.

  Abstract
  A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal [...]

  • 2
  •  read

• A second-order face-centred finite volume method for elliptic problems

  L. Vieira, M. Giacomini, R. Sevilla, A. Huerta

  Computer methods in applied mechanics and engineering (2020). Vol. 358, pp. 112655:1-112655:23

  
  

  Abstract

  A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving an element-by-element problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented

  Abstract
  A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed [...]

  • 3
  •  read

• Solution of geometrically parametrised problems within a CAD environment via model order reduction

  R. Sevilla, S. Zlotnik, A. Huerta

  Computer methods in applied mechanics and engineering (2020). Vol. 358, pp. 112631:1-112631:33

  
  

  Abstract

  The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows

  Abstract
  The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. [...]

  • 11
  •  read

• A regularised-adaptive Proper Generalised Decomposition implementation for coupled magneto-mechanical problems with application to MRI scanners

  G. Barroso, A. Ruiz, P. Ledger, M. Mallett, A. Huerta

  Computer methods in applied mechanics and engineering (2020). Vol. 358, pp. 112640:1-112640:28

  
  

  Abstract

  Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new cost-effective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electro-magneto-mechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the ill-conditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.

  Abstract
  Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose [...]

  • 3
  •  read

• Encapsulated PGD algebraic toolbox operating with high-dimensional data

  P. Diez, S. Zlotnik, A. Garcia, A. Huerta

  Archives of computational methods in engineering (2019).

  
  

  Abstract

  In its original conception, proper generalized decomposition (PGD) provides explicit parametric solutions, denoted as computational vademecums or digital abacuses, to parametric boundary value problems. The PGD approach is extended here to devise a set of algebraic tools enabling to operate with multidimensional tensor data. These tools are designed to store, compress and perform basic operations (in particular divisions) with tensors in separable format. These tools are directly producing the computational vademecums for the resulting high-dimensional tensor data. Thus, the general methodology enables performing nontrivial operations (storage, compression, division, solving linear systems of equations...) for multidimensional tensor data. The idea is based on the principle of the PGD separation, that produces a separable least squares approximation of any multidimensional function. The PGD compression is a particular case, extensively used in practice to compact the separable solution without loss of accuracy. Here, this concept is applied to algebraic tensor structures that are also seen as functions in multidimensional Cartesian domains. Moreover, a straightforward extension of this concept is devised to operate with multidimensional objects stored in the separable format. That allows creating a toolbox of PGD arithmetic operators that is publicly released at https://git.lacan.upc.edu/zlotnik/algebraicPGDtools. Numerical tests demonstrate the performance and efficiency of the toolbox, both for tensor data handling and operation and also in applications pertaining to the discretized version of boundary value problems.

  Abstract
  In its original conception, proper generalized decomposition (PGD) provides explicit parametric solutions, denoted as computational vademecums or digital abacuses, to parametric [...]

  • 3
  •  read

• Multiscale proper generalized decomposition based on the partition of unity

  R. Ibañez, A. Ammar, E. Cueto, J. Duval, F. Chinesta

  Int. J. Numer. Meths. Engng. (2019). Vol. 120 (6), pp. 727-747

  
  

  Abstract

  Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict accurately the response of the system. The proposed methodology is based on the standard proper generalized decomposition rationale; thus, the PDE is transformed into a nonlinear system that iterates between microscale and macroscale states, where the time coordinate could be viewed as a 2D time, representing the microtime and macrotime scales. The macroscale effects are taken into account because of an FEM-based macrodiscretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the domain. The proposed methodology can be seen as an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors.

  Abstract
  Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict [...]

  • 0
  •  read

• A local multiple proper generalized decomposition based on the partition of unity

  R. Ibañez, E. Abisset-Chavanne, F. Chinesta, A. Huerta, E. Cueto

  Int. J. Numer. Meths. Engng. (2019). Vol 120 (2), pp. 139-152

  
  

  Abstract

  It is well known that model order reduction techniques that project the solution of the problem at hand onto alow-dimensional subspace present difficulties when this solution lies on a non-linear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of non-linear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employing Proper Generalized Decompositions at each local patch.

  Abstract
  It is well known that model order reduction techniques that project the solution of the problem at hand onto alow-dimensional subspace present difficulties when this solution [...]

  • 4
  •  read