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• A fractional step method for computational aeroacoustics using weak imposition of Dirichlet boundary conditions

  S. Parada, J. Baiges, R. Codina

  Computers and Fluids (2020). Vol. 197, pp. 104374:1-104374:17

  
  

  Abstract

  In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow scales at once. After space and time discretizations have been chosen, it is very convenient from the computational point of view to design fractional step schemes in time so as to permit a segregated calculation of the problem unknowns. While these segregation schemes are well established for incompressible flows, much less is known in the case of isentropic flows. We discuss this issue in this article and, furthermore, we study the way to weakly impose Dirichlet boundary conditions via Nitsche’s method. In order to avoid spurious reflections of the acoustic waves, Nitsche’s method is combined with a non-reflecting boundary condition. Employing a purely algebraic approach to discuss the problem, some of the boundary contributions are treated explicitly and we explain how these are included in the different steps of the final algorithm. Numerical evidence shows that this explicit treatment does not have a significant impact on the convergence rate of the resulting time integration scheme. The equations of the formulation are solved using a subgrid scale technique based on a term-by-term stabilization.

  Abstract
  In this work we consider the approximation of the isentropic Navier–Stokes equations. The model we present is capable of taking into account acoustic and flow [...]

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• Pseudoplastic fluid flows for different Prandtl numbers: steady and time-dependent solutions

  A. Aguirre, E. Castillo, M. Cruchaga, R. Codina, J. Baiges

  International Journal for Numerical Methods in Engineering (2019). Vol. 145, pp. 106022-1/106022-17

  
  

  Abstract

  In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6

  Abstract
  In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated [...]

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• An oil sloshing study: adaptive fixed-mesh ALE analysis and comparison with experiments

  E. Castillo, M. Cruchaga, J. Baiges, J. Flores

  Computational Mechanics (2019). Vol. 63 (5), pp. 985-998 (Preprint)

  
  

  Abstract

  We report in this work a numerical analysis of the sloshing of a squared tank partially filled with a domestic vegetable oil. The tank is subject to controlled motions with a shake table. The free-surface evolution is captured using ultrasonic sensors and an image capturing method. Only confirmed data within the error range is reported. Filling depth, imposed amplitude and frequency effects on the sloshing wave pattern are specifically evaluated. The experiments also reveal the nonlinear wave behavior. The numerical model is based on a stabilized finite element method of the variational multi-scale type. The free-surface is captured using a level set technique developed to be used with adaptive meshes in Arbitrary Lagrangian–Eulerian framework. The numerical results are compared with the experiments for different sloshing conditions near the first sloshing mode. The simulations satisfactorily match the experiments, providing a reliable tool for the analysis of this kind of problems.

  Abstract
  We report in this work a numerical analysis of the sloshing of a squared tank partially filled with a domestic vegetable oil. The tank is subject to controlled motions with [...]

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• A dynamic spring element model for the prediction of longitudinal failure of polymer composites

  R. Tavares, F. Otero, J. Baiges, A. Turon, P. Camanho

  Computational Materials Science (2019). Vol. 160, pp. 42-52

  
  

  Abstract

  A spring element model that takes into account the dynamic effects associated with fibre failure in composite materials is presented. The model is implemented in a parallel environment to allow a better performance in the prediction of the complex mechanisms associated with longitudinal tensile failure. The model is used to identify the changes in the stress fields around a broken fibre representing fibre failure as a dynamic phenomenon. In light of these changes in the stress fields, the cluster formation and failure development is analysed and the results are compared with the static spring element model. It is observed that the stress redistribution around a broken fibre is strongly dependent on the dynamic effects and it varies with the material in study, specially if the matrix is considered linear elastic. The changes in local stress redistribution are seen to affect the materials tensile behaviour and cluster formation, being this changes higher for a material with an elastic matrix

  Abstract
  A spring element model that takes into account the dynamic effects associated with fibre failure in composite materials is presented. The model is implemented in a parallel [...]

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• Large-scale stochastic topology optimization using adaptive mesh refinement and coarsening through a two-level parallelization scheme

  J. Baiges, J. Martínez-Frutos, D. Herrero-Pérez, F. Otero, A. Ferrer

  Computer Methods in Applied Mechanics and Engineering (2019). Vol. 343, pp. 186-206

  
  

  Abstract

  Topology optimization under uncertainty of large-scale continuum structures is a computational challenge due to the combination of large finite element models and uncertainty propagation methods. The former aims to address the ever-increasing complexity of more and more realistic models, whereas the latter is required to estimate the statistical metrics of the formulation. In this work, the computational burden of the problem is addressed using a sparse grid stochastic collocation method, to calculate the statistical metrics of the topology optimization under uncertainty formulation, and a parallel adaptive mesh refinement method, to efficiently solve each of the stochastic collocation nodes. A two-level parallel processing scheme (TOUU-PS2) is proposed to profit from parallel computation on distributed memory systems: the stochastic nodes are distributed through the distributed memory system, and the efficient computation of each stochastic node is performed partitioning the problem using a domain decomposition strategy and solving each subdomain using an adaptive mesh refinement method. A dynamic load-balancing strategy is used to balance the workload between subdomains, and thus increasing the parallel performance by reducing processor idle time. The topology optimization problem is addressed using the topological derivative concept in combination with a level-set method. The performance and scalability of the proposed methodology are evaluated using several numerical benchmarks and real-world applications, showing good performance and scalability up to thousands of processors

  Abstract
  Topology optimization under uncertainty of large-scale continuum structures is a computational challenge due to the combination of large finite element models [...]

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• Refficientlib: an efficient load-rebalanced adaptive mesh refinement algorithm for high-performance computational physics meshes

  J. Baiges, C. Bayona

  SIAM journal on scientific computing (2017). Vol. 39 (2), pp. C65-C95 (Preprint)

  
  

  Abstract

  In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. Some of the main features of the algorithm presented in this paper are its capability of handling multiple types of elements in two and three dimensions (triangular, quadrilateral, tetrahedral, and hexahedral), the small amount of memory required per processor, and the parallel scalability up to thousands of processors. The presented algorithm is also capable of dealing with nonbalanced hierarchical refinement, where multirefinement level jumps are possible between neighbor elements. An algorithm for dealing with load rebalancing is also presented, which allows us to move the hierarchical data structure between processors so that load unbalancing is kept below an acceptable level at all times during the simulation. A particular feature of the proposed algorithm is that arbitrary renumbering algorithms can be used in the load rebalancing step, including both graph partitioning and space-filling renumbering algorithms. The presented algorithm is packed in the Fortran 2003 object oriented library \textttRefficientLib, whose interface calls which allow it to be used from any computational physics code are summarized. Finally, numerical experiments illustrating the performance and scalability of the algorithm are presented. No separate or additional fees are collected for access to or distribution of the work

  Abstract
  In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed [...]

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• Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches

  S. Kollmannsberger, A. Özcan, J. Baiges, M. Ruess, E. Rank, A. Reali

  International Journal for Numerical Methods in Engineering (2015). Vol. 101 (9), pp. 670-699 (Preprint)

  
  

  Abstract

  We present a parameter-free domain sewing approach for low-order as well as high-order finite elements. Its final form contains only primal unknowns; that is, the approach does not introduce additional unknowns at the interface. Additionally, it does not involve problem-dependent parameters, which require an estimation. The presented approach is symmetry preserving; that is, the resulting discrete form of an elliptic equation will remain symmetric and positive definite. It preserves the order of the underlying discretization, and we demonstrate high-order accuracy for problems of non-matching discretizations concerning the mesh size h as well as the polynomial degree of the order of discretization p. We also demonstrate how the method may be used to model material interfaces, which may be curved and for which the interface does not coincide with the underlying mesh. This novel approach is presented in the context of the p-version and B-spline version of the finite cell method, an embedded domain method of high order, and compared with more classical methods such as the penalty method or Nitsche's method.

  Abstract
  We present a parameter-free domain sewing approach for low-order as well as high-order finite elements. Its final form contains only primal unknowns; that is, the approach [...]

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• A scalable parallel finite element framework for growing geometries: application to metal additive manufacturing

  E. Neiva, S. Badia, A. Martín, M. Chiumenti

  International Journal for Numerical Methods in Engineering (2019). Vol. 119 (11), pp. 1098-1125

  
  

  Abstract

  This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time.

  Abstract
  This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known [...]

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• Scalable solvers for complex electromagnetics problems

  S. Badia, A. Martín, M. Olm

  Finite elements in analysis and design (2019). Vol. 161, pp. 16-31

  
  

  Abstract

  In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce the continuity across subdomains of the method, we use a partition of the interface objects (edges and faces) into sub-objects determined by the variation of the physical coefficients of the problem. For multi-material problems, a constant coefficient condition is enough to define this sub-partition of the objects. For arbitrarily heterogeneous problems, a relaxed version of the method is defined, where we only require that the maximal contrast of the physical coefficient in each object is smaller than a predefined threshold. Besides, the addition of perturbation terms to the preconditioner is empirically shown to be effective in order to deal with the case where the two coefficients of the model problem jump simultaneously across the interface. The new method, in contrast to existing approaches for problems in curl-conforming spaces does not require spectral information whilst providing robustness with regard to coefficient jumps and heterogeneous materials. A detailed set of numerical experiments, which includes the application of the preconditioner to 3D realistic cases, shows excellent weak scalability properties of the implementation of the proposed algorithms.

  Abstract
  In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations [...]

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• Maximum-principle preserving space–time isogeometric analysis

  J. Bonilla, S. Badia

  Computer Methods in Applied Mechanics and Engineering (2019). Vol. 354, pp. 422-440

  
  

  Abstract

  In this work we propose a nonlinear stabilization technique for convection–diffusion–reaction and pure transport problems discretized with space–time isogeometric analysis. The stabilization is based on a graph-theoretic artificial diffusion operator and a novel shock detector for isogeometric analysis. Stabilization in time and space directions are performed similarly, which allow us to use high-order discretizations in time without any CFL-like condition. The method is proven to yield solutions that satisfy the discrete maximum principle (DMP) unconditionally for arbitrary order. In addition, the stabilization is linearity preserving in a space–time sense. Moreover, the scheme is proven to be Lipschitz continuous ensuring that the nonlinear problem is well-posed. Solving large problems using a space–time discretization can become highly costly. Therefore, we also propose a partitioned space–time scheme that allows us to select the length of every time slab, and solve sequentially for every subdomain. As a result, the computational cost is reduced while the stability and convergence properties of the scheme remain unaltered. In addition, we propose a twice differentiable version of the stabilization scheme, which enjoys the same stability properties while the nonlinear convergence is significantly improved. Finally, the proposed schemes are assessed with numerical experiments. In particular, we considered steady and transient pure convection and convection–diffusion problems in one and two dimensions. -

  Abstract
  In this work we propose a nonlinear stabilization technique for convection–diffusion–reaction and pure transport problems discretized with space–time [...]

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