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• Implementation and Scalability Analysis of Balancing Domain Decomposition Methods

  S. Badia, A. Martín, J. Principe

  Archives of Comp. Meths. Engng. (2013). Vol. 20 (3), pp. 239-262

  
  

  Abstract

  In this paper we present a detailed description of a high-performance distributed-memory implementation of balancing domain decomposition preconditioning techniques. This coverage provides a pool of implementation hints and considerations that can be very useful for scientists that are willing to tackle large-scale distributed-memory machines using these methods. On the other hand, the paper includes a comprehensive performance and scalability study of the resulting codes when they are applied for the solution of the Poisson problem on a large-scale multicore-based distributed-memory machine with up to 4096 cores. Well-known theoretical results guarantee the optimality (algorithmic scalability) of these preconditioning techniques for weak scaling scenarios, as they are able to keep the condition number of the preconditioned operator bounded by a constant with fixed load per core and increasing number of cores. The experimental study presented in the paper complements this mathematical analysis and answers how far can these methods go in the number of cores and the scale of the problem to still be within reasonable ranges of efficiency on current distributed-memory machines. Besides, for those scenarios where poor scalability is expected, the study precisely identifies, quantifies and justifies which are the main sources of inefficiency.

  Abstract
  In this paper we present a detailed description of a high-performance distributed-memory implementation of balancing domain decomposition preconditioning techniques. This [...]

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• Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics

  S. Badia, A. Martín, J. Principe

  Int. J. Numer. Meth. Engng. (2013). (preprint) Vol. 96 (4), pp. 203-230

  
  

  Abstract

  In this work, we propose an enhanced implementation of balancing Neumann-Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing domain decomposition by constraints (BDDC) preconditioner. As model problems, we consider the Poisson and linear elasticity problems. On one hand, we propose a novel way to deal with singular matrices and pseudo-inverses appearing in local solvers. It is based on a kernel identication strategy that allows us to eciently compute the action of the pseudo-inverse via local indenite solvers. We further show how, identifying a minimum set of degrees of freedom to be xed, an equivalent denite system can be solved instead, even in the elastic case. On the other hand, we propose a simple modication of the preconditioned conjugate gradient (PCG) algorithm that reduces the number of Dirichlet solvers to only one per iteration, leading to similar computational cost as additive methods. After these improvements of the BNN PCG algorithm, we compare its performance against that of the BDDC preconditioners on a pair of large-scale distributed-memory platforms. The enhanced BNN method is a competitive preconditioner for three-dimensional Poisson and elasticity problems, and outperforms the BDDC method in many cases.

  Abstract
  In this work, we propose an enhanced implementation of balancing Neumann-Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing [...]

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• A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations

  M. Ávila, J. Principe, R. Codina

  Journal of Computational Physics (2011). Vol. 230 (22), pp. 7988-8009

  
  

  Abstract

  In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier–Stokes equations in the small Mach number regime. In contrast to the commonly used Boussinesq approximation, this model permits to take volumetric deformation into account. Although the former is more general than the latter, both systems have similar mathematical structure and their numerical approximation can suffer from the same type of instabilities. We propose a stabilized finite element approximation based on the variational multiscale method, in which a decomposition of the approximating space into a coarse scale resolvable part and a fine scale subgrid part is performed. Modeling the subscale and taking its effect on the coarse scale problem into account results in a stable formulation. The quality of the final approximation (accuracy, efficiency) depends on the particular model. The distinctive features of our approach are to consider the subscales as transient and to keep the scale splitting in all the nonlinear terms. The first ingredient permits to obtain an improved time discretization scheme (higher accuracy, better stability, no restrictions on the time step size). The second ingredient permits to prove global conservation properties. It also allows us to approach the problem of dealing with thermal turbulence from a strictly numerical point of view. Numerical tests show that nonlinear and dynamic subscales give more accurate solutions than classical stabilized methods.

  Abstract
  In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number [...]

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• A variational subgrid scale model for transient incompressible flows

  G. Houzeaux, J. Principe

  Int. J. Computational Fluid Dynamics (2008). Vol. 22 (3), pp. 135-152

  
  

  Abstract

  We introduce in this paper a variational subgrid scale model for the solution of the incompressible Navier-Stokes equations. With respect to classical multiscale-based stabilisation techniques, we retain the subgrid scale effects in the convective term and integrate the subgrid scale equation in time. The method is applied to the Navier-Stokes equations in an accelerating frame of reference and with Dirichlet (essential), Neumann (natural) and mixed boundary conditions. The concrete objective of the paper is to test a numerical algorithm for solving the non-linear subgrid scale equation and the introduction of the subgrid scale into the grid scale equation. The performance of the technique is demonstrated through the solution of two numerical examples: one to test the tracking of the subgrid scale in the convection term and the other to investigate the effects of considering the subgrid scale transient.

  Abstract
  We introduce in this paper a variational subgrid scale model for the solution of the incompressible Navier-Stokes equations. With respect to classical multiscale-based stabilisation [...]

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• On the modelling of liquid steel processes

  M. Goldschmit, S. Ferro, J. Principe, A. Coppola‐Owen

  Latin American Applied Research (2002). Vol. 32 (3), pp. 263-273

  
  

  Abstract

  An iterative (k-L)-predictor / (epsilon)- corrector algorithm that models turbulent flow was developed in previous publications. In this paper, the 3D finite element turbulent model was used to analyze the liquid steel movement produced by gravity force, inert gas stirring or electromagnetic force stirring.

  Abstract
  An iterative (k-L)-predictor / (epsilon)- corrector algorithm that models turbulent flow was developed in previous publications. In this paper, the 3D finite element turbulent [...]

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• A new approach to the analysis of vessel residence time distribution curves

  S. Ferro, J. Principe, M. Goldschmit

  Metallurgical and Materials Transactions B (2001). Vol. 32 (6), pp. 1185-1193

  
  

  Abstract

  Mathematical models for the evaluation of residence time distribution (RTD) curves on a large variety of vessels are presented. These models have been constructed by combination of different tanks or volumes. In order to obtain a good representation of RTD curves, a new volume (called convection diffusion volume) is introduced. The convection-diffusion volume allows the approximation of different experimental or numerical RTD curves with very simple models. An algorithm has been developed to calculate the parameters of the models for any given set of RTD curve experimental points. Validation of the models is carried out by comparison with experimental RTD curves taken from the literature and with a numerical RTD curve obtained by three-dimensional simulation of the flow inside a tundish.  

  Abstract
  Mathematical models for the evaluation of residence time distribution (RTD) curves on a large variety of vessels are presented. These models have been constructed by [...]

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• Applications of a (k–ϵ) model for the analysis of continuous casting processes

  M. Goldschmit, J. Principe, M. Koslowski

  Int. J. Numer. Meth. Engng. (1999). Vol. 46 (9), pp. 1505-1519

  
  

  Abstract

  The finite element solution of the turbulent Navier–Stokes equations developed via (k–ϵ) turbulence models was addressed in previous publications [1–4], where a (k–L)‐predictor/(ϵ)‐corrector iterative algorithm was developed. It was shown that the developed algorithm is robust and converges for the analyses of different flows without requiring the implementation of ad hoc numerical procedures. The turbulent convection–diffusion transport equations are solved by using the velocity distributions determined from the solution of the turbulent Navier–Stokes equations. The dispersion of a die in a turbulent flow can therefore be modelled and the obtained dispersion patterns are validated via flow visualizations in water models. In the present paper, the developed analysis capability is applied to the analysis of continuous casting processes.

  Abstract
  The finite element solution of the turbulent Navier–Stokes equations developed via (k–ϵ) turbulence models was addressed in previous publications [1–4], [...]

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• Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method

  L. Monforte, M. Arroyo, J. Carbonell, A. Gens

  Computers and Geotechnics (2018). Vol. 101, pp. 114-129

  
  

  Abstract

  This paper describes a computational framework for the numerical analysis of quasi-static soil-structure insertion problems in water saturated media. The Particle Finite Element Method is used to solve the linear momentum and mass balance equations at large strains. Solid-fluid interaction is described by a simplified Biot formulation using pore pressure and skeleton displacements as basic field variables. The robustness and accuracy of the proposal is numerically demonstrated presenting results from two benchmark examples. The first one addresses the consolidation of a circular footing on a poroelastic soil. The second one is a parametric analysis of the cone penetration test (CPTu) in a material described by a Cam-clay hyperelastic model, in which the influence of permeability and contact roughness on test results is assessed.

  Abstract
  This paper describes a computational framework for the numerical analysis of quasi-static soil-structure insertion problems in water saturated media. The Particle Finite [...]

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• Hydraulic conductivity from piezocone on-the-fly: a numerical evaluation

  L. Monforte, M. Arroyo, A. Gens, J. Carbonell

  Géotechnique Letters (2018). Vol. 8 (4), pp. 268-277

  
  

  Abstract

  Permeability is important in many geotechnical applications. The current (cone penetration test that gathers piezometer data (CPTu)) practice to obtain permeability values relies on dissipation tests, which are frequently slow and only linked to permeability through compressibility measures. On-the-fly methods offer an alternative approach in which permeability is directly linked to CPTu penetration measurements. Several on-the-fly methods have been proposed and their applicability and relative advantages are not fully clear. Numerical effective stress simulation of CPTu testing is used here to explore in a simplified but realistic setting the relative merits of different on-the-fly methods. It is found that for partly drained materials, the original simpler relation between cone metrics and normalised permeability works reasonably well. A continuous generalisation of Elsworth and Lee method to the full permeability range is proposed, noting the connection to the backbone normalised pore-pressure curve that describes the partly drained transition of cone penetration. The importance of an undrained limit beyond which the method produces large errors is emphasised.

  Abstract
  Permeability is important in many geotechnical applications. The current (cone penetration test that gathers piezometer data (CPTu)) practice to obtain permeability values [...]

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• Numerical Methods for the Modelling of Chip Formation

  J. Prieto, J. Carbonell, P. Jonsén

  Archives of Comp. Meths. Engng. (2018). Epub ahead of print

  
  

  Abstract

  The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction and material failure. During the last few decades, there has been significant progress in the development of numerical methods for modeling machining operations. Furthermore, the most relevant techniques have been implemented in the relevant commercial codes creating tools for the engineers working in the design of processes and cutting devices. This paper presents a review on the numerical modeling methods and techniques used for the simulation of machining processes. The main purpose is to identify the strengths and weaknesses of each method and strategy developed up-to-now. Moreover the review covers the classical Finite Element Method covering mesh-less methods, particle-based methods and different possibilities of Eulerian and Lagrangian approaches.

  Abstract
  The modeling of metal cutting has proved to be particularly complex due to the diversity of physical phenomena involved, including thermo-mechanical coupling, contact/friction [...]

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