Javier Principe

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    Author Title Year Journal
    Badia, S.; Martín, A.F. & Principe, J. Multilevel balancing domain decomposition at extreme scales 2016 SIAM Journal on Scientific Computing
    Vol. 38 (1) , pp. C22-C52  
    BibTeX:
    @article{art007,
      author = {Santiago Badia and Alberto F. Martín and Javier Principe},
      title = {Multilevel balancing domain decomposition at extreme scales},
      journal = {SIAM Journal on Scientific Computing},
      year = {2016},
      volume = {38},
      number = {1},
      pages = {C22--C52},
      doi = {http://dx.doi.org/10.1137/15M1013511}
    }
    					
    Colomés, O.; Badia, S. & Principe, J. Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows 2016 Computer Methods in Applied Mechanics and Engineering
    Vol. 304 (1) , pp. 294-318  
    BibTeX:
    @article{Colomes2016,
      author = {Oriol Colomés and Santiago Badia and Javier Principe},
      title = {Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2016},
      volume = {304},
      number = {1},
      pages = {294--318},
      doi = {http://dx.doi.org/10.1016/j.cma.2016.02.026}
    }
    					
    Badia, S.; Martín, A.F. & Principe, J. On an overlapped coarse/fine implementation of balancing domain decomposition with inexact solvers 2015 Parallel Computing
    Vol. 50 , pp. 1-24  
    BibTeX:
    @article{art008,
      author = {Santiago Badia and Alberto F. Martín and Javier Principe},
      title = {On an overlapped coarse/fine implementation of balancing domain decomposition with inexact solvers},
      journal = {Parallel Computing},
      year = {2015},
      volume = {50},
      pages = {1--24},
      doi = {http://dx.doi.org/10.1016/j.parco.2015.09.004}
    }
    					
    Avila, M.; Codina, R. & Principe, J. Finite element dynamical subgrid-scale model for low Mach number flows with radiative heat transfer 2015 International Journal for Numerical Methods in Heat & Fluid Flow, Accepted
    Vol. 25 (6) , pp. 1361-1384  
    Abstract: Purpose - To present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative heat transfer. For high temperature ows this coupling can have strong e ects on the temperature and velocity elds. Design/methodology/approach - The basic numerical formulation has been proposed in previous works. It is based on the variational multiscale concept in which the unknowns of the problem are divided into resolved and subgrid parts which are modeled to consider their e ect into the former. The aim of the present article is to extend this modeling to the case in which the low Mach number equations are coupled with radiation, also introducing the concept of subgrid scales for the radiation equations. Findings - As in the non-radiative case, an important improvement in the accuracy of the numerical scheme is observed when the nonlinear e ects of the subgrid scales are taken into account. Besides it is possible to show global conservation of thermal energy. Originality/value - The original contribution of the work is the proposal of keeping the variational multiscale splitting into the nonlinear coupling between the low Mach number and the radiative transport equations, its numerical evaluation and the description of its properties.
    BibTeX:
    @article{Avila2015,
      author = {Matias Avila and Ramon Codina and Javier Principe},
      title = {Finite element dynamical subgrid-scale model for low Mach number flows with radiative heat transfer},
      journal = {International Journal for Numerical Methods in Heat & Fluid Flow, Accepted},
      year = {2015},
      volume = {25},
      number = {6},
      pages = {1361--1384},
      doi = {http://dx.doi.org/10.1108/HFF-07-2014-0238}
    }
    					
    Codina, R.; Principe, J.; noz, C.M. & Baiges, J. Numerical modeling of chlorine concentration in water storage tanks 2015 International Journal for Numerical Methods in Fluids
    Vol. 79 , pp. 84-107  
    Abstract: In this paper we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution of chlorine concetration. The mathematical model contains several ingredients particularly designed for this problem, namely, a boundary condition to model falling jets on free surfaces, an arbitrary Lagrangian-Eulerian formulation to account for the motion of the free surface due to demand and supply of water, and a coupling of the hydroynamics with a convection-diffusion-reaction equation modeling the time evolution of chlorine. From the numerical point of view, the equations resulting from the mathematical model are approximated using a finite element formulation, with linear continuous interpolations on tetrahedra for all the unknowns. To make it possible, and also to be able to deal with convection dominated flows, a stabilized formlulation is used. In order to capture the sharp gradients present in the chlorine concentration, particularly near the injection zone, a discontinuity capturing technique is employed.
    BibTeX:
    @article{Codina2015,
      author = {Ramon Codina and Javier Principe and Christian Muñoz and Joan Baiges},
      title = {Numerical modeling of chlorine concentration in water storage tanks},
      journal = {International Journal for Numerical Methods in Fluids},
      year = {2015},
      volume = {79},
      pages = {84--107},
      doi = {http://dx.doi.org/10.1002/fld.4044}
    }
    					
    Colomés, O.; Badia, S.; Codina, R. & Principe, J. Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows 2015 Computer Methods in Applied Mechanics and Engineering
    Vol. 285 , pp. 32-63  
    Abstract: In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor-Green vortex problem and the turbulent flow in a channel. We compare the results obtained using the different VMS models and against a classical LES scheme based on filtering and the Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these results, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.
    BibTeX:
    @article{Colomes2015,
      author = {Oriol Colomés and Santiago Badia and Ramon Codina and Javier Principe},
      title = {Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2015},
      volume = {285},
      pages = {32--63},
      note = {2},
      doi = {http://dx.doi.org/10.1016/j.cma.2014.10.041}
    }
    					
    Avila, M.; Codina, R. & Principe, J. Large eddy simulation of low Mach number flows using dynamic and orthogonal subgrid scales 2014 Computers & Fluids
    Vol. 99 (0) , pp. 44 - 66  
    Abstract: Objective: In this article we study the approximation to thermal turbulence from a strictly numerical point of view, without the use of any physical model. The main goal is to analyze the behavior of our numerical method in the large eddy simulation (LES) of thermally coupled turbulent flows at low Mach number. Methods: Our numerical method is 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 as LES model) depends on the particular subscale 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. Another important contribution of this work is the extension of the orthogonal subgrid scale method widely tested for incompressible flows to variable density flows, using a density-weighted L 2 product to define the orthogonality of the subscales and the finite element spaces. Results: Referring to numerical testing, we present numerical results for a laminar testcase validation that shows the dissipative behavior of the different stabilized methods. Then, we present results of the numerical simulation of two turbulent flow problems, the turbulent channel flow with large temperature differences in the wall normal direction at Re τ = 180 , and the turbulent thermally driven cavity with aspect ratio 4. The behavior of the method is evaluated by comparison against results available in the literature obtained using LES and direct numerical simulation (DNS). They are explained based on a careful analysis of the dissipative structure of the method, showing the physical interpretation of the subgrid scale method presented. conclusion: The material presented here is a clear indication of the potential of the method to model all kinds of turbulent thermally coupled flows. The formulation is the same in laminar and turbulent regimes.
    BibTeX:
    @article{Avila2014,
      author = {Matias Avila and Ramon Codina and Javier Principe},
      title = {Large eddy simulation of low Mach number flows using dynamic and orthogonal subgrid scales},
      journal = {Computers & Fluids},
      year = {2014},
      volume = {99},
      number = {0},
      pages = {44 - 66},
      doi = {http://dx.doi.org/10.1016/j.compfluid.2014.04.003}
    }
    					
    Badia, S.; Martín, A.F. & Principe, J. A highly scalable parallel implementation of balancing domain decomposition by constraints 2014 SIAM Journal on Scientific Computing
    Vol. 36 (2) , pp. C190-C218  
    Abstract: In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then re-scheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments, that includes weak scalability analyses, with structured and unstructured meshes, and exact and inexact solvers for the 3D Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-memory machines. This experimental study reveals remarkable weak scalability in the solution of problems with thousands of millions of unknowns on several tens of thousands of computational cores.
    BibTeX:
    @article{Badia2014,
      author = {Santiago Badia and Alberto F. Martín and Javier Principe},
      title = {A highly scalable parallel implementation of balancing domain decomposition by constraints},
      journal = {SIAM Journal on Scientific Computing},
      year = {2014},
      volume = {36},
      number = {2},
      pages = {C190-C218},
      doi = {http://dx.doi.org/10.1137/130931989}
    }
    					
    Badia, S.; Martín, A.F. & Principe, J. Implementation and scalability analysis of balancing domain decomposition methods 2013 Archives of Computational Methods in Engineering
    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 xed 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 eciency on current distributed-memory machines. Besides, for those scenarios where poor scalability is expected, the study precisely identi es, quanti es and justi es which are the main sources of inefficiency.
    BibTeX:
    @article{Badia2013,
      author = {Santiago Badia and Alberto F. Martín and Javier Principe},
      title = {Implementation and scalability analysis of balancing domain decomposition methods},
      journal = {Archives of Computational Methods in Engineering},
      year = {2013},
      volume = {20},
      number = {3},
      pages = {239-262},
      doi = {http://dx.doi.org/10.1007/s11831-013-9086-4}
    }
    					
    Badia, S.; Martín, A.F. & Principe, J. Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics 2013 International Journal for Numerical Methods in Engineering
    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 identi cation strategy that allows us to eciently compute the action of the pseudo-inverse via local inde nite solvers. We further show how, identifying a minimum set of degrees of freedom to be xed, an equivalent de nite system can be solved instead, even in the elastic case. On the other hand, we propose a simple modi cation 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.
    BibTeX:
    @article{Badia2013a,
      author = {Santiago Badia and Alberto F. Martín and Javier Principe},
      title = {Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics},
      journal = {International Journal for Numerical Methods in Engineering},
      year = {2013},
      volume = {96},
      number = {4},
      pages = {203-230},
      doi = {http://dx.doi.org/10.1002/nme.4541}
    }
    					
    Avila, M.; Codina, R. & Principe, J. Spatial approximation of the radiation transport equation using a subgrid-scale finite element method 2011 Computer Methods in Applied Mechanics and Engineering
    Vol. 200 (5-8) , pp. 425 - 438  
    Abstract: In this paper we present stabilized finite element methods to discretize in space the monochromatic radiation transport equation. These methods are based on the decomposition of the unknowns into resolvable and subgrid scales, with an approximation for the latter that yields a problem to be solved for the former. This approach allows us to design the algorithmic parameters on which the method depends, which we do here when the discrete ordinates method is used for the directional approximation. We concentrate on two stabilized methods, namely, the classical SUPG technique and the orthogonal subscale stabilization. A numerical analysis of the spatial approximation for both formulations is performed, which shows that they have a similar behavior: they are both stable and optimally convergent in the same mesh-dependent norm. A comparison with the behavior of the Galerkin method, for which a non-standard numerical analysis is done, is also presented.
    BibTeX:
    @article{Avila.etal.CMiAMaE.2011,
      author = {Matias Avila and Ramon Codina and Javier Principe},
      title = {Spatial approximation of the radiation transport equation using a subgrid-scale finite element method},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2011},
      volume = {200},
      number = {5-8},
      pages = {425 - 438},
      doi = {http://dx.doi.org/10.1016/j.cma.2010.11.003}
    }
    					
    Avila, M.; Principe, J. & Codina, R. A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations 2011 Journal of Computational Physics
    Vol. 230 (10-11) , 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 later, 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 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.
    BibTeX:
    @article{Avila2011,
      author = {Matias Avila and Javier Principe and Ramon Codina},
      title = {A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations},
      journal = {Journal of Computational Physics},
      year = {2011},
      volume = {230},
      number = {10-11},
      pages = {7988--8009},
      doi = {http://dx.doi.org/10.1016/j.jcp.2011.06.032}
    }
    					
    Schrefler, B.A.; Codina, R.; Pesavento, F. & Principe, J. Thermal coupling of fluid and structural response of a tunnel induced by fire 2011 International Journal for Numerical Methods in Engineering
    Vol. 87 , pp. 361-385  
    Abstract: In this work we present the progress in the development of an algorithm for the simulation of thermal fluid–structural coupling in a tunnel fire. The coupling strategy is based on a Dirichlet/Neumann non-overlapping domain decomposition of the problem, which is carried out by developing a master code that controls solvers dedicated to the fluid mechanics and to the solid mechanics simulation. The computational fluid dynamics formulation consists of a stabilized finite element approximation of the low Mach number equations based on the subgrid scale concept, that allows us to deal with convection-dominated problems and to use equal order interpolation of velocity and pressure. The thermo-structural model of the tunnel vault, that considers a multiphase porous material where pores are partly filled with liquid and partly by gas, is specially devised for the simulation of concrete at high temperatures and consists of balance equations for mass conservation of dry air, mass conservation of water species (both in the liquid and gaseous state), enthalpy conservation and linear momentum conservation taking phase changes into account. The developed algorithm is applied to the problem of the response of a tunnel to a fire. We consider the combustion process as a heat release which can vary usually from 1thinspaceMW for small car fires to 100 MW for catastrophic fires. The released heat is transferred to the concrete walls of the tunnel which could cause extensive and heavy damage of the structure.
    BibTeX:
    @article{Schrefler.etal.IJfNMiE.2011,
      author = {Bernhard A Schrefler and Ramon Codina and Francesco Pesavento and Javier Principe},
      title = {Thermal coupling of fluid and structural response of a tunnel induced by fire},
      journal = {International Journal for Numerical Methods in Engineering},
      year = {2011},
      volume = {87},
      pages = {361-385},
      doi = {http://dx.doi.org/10.1002/nme.3077}
    }
    					
    Codina, R.; Principe, J. & Ávila, M. Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling 2010 International Journal of Numerical Methods for Heat and Fluid Flow
    Vol. 20 , pp. 492-516  
    Abstract: Purpose - The purpose of this paper is to describe a variational multiscale finite element approximation for the incompressible Navier-Stokes equations using the Boussinesq approximation to model thermal coupling. Design/methodology/approach - The main feature of the formulation, in contrast to other stabilized methods, is that the subscales are considered as transient and orthogonal to the finite element space. These subscales are solution of a differential equation in time that needs to be integrated. Likewise, the effect of the subscales is kept, both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation. Findings - This strategy allows the approaching of the problem of dealing with thermal turbulence from a strictly numerical point of view and discussion important issues, such as the relationship between the turbulent mechanical dissipation and the turbulent thermal dissipation. Originality/value - The treatment of thermal turbulence from a strictly numerical point of view is the main originality of the work.
    BibTeX:
    @article{Codina.etal.IJNMH.2010,
      author = {Ramon Codina and Javier Principe and Matias Ávila},
      title = {Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling},
      journal = {International Journal of Numerical Methods for Heat and Fluid Flow},
      year = {2010},
      volume = {20},
      pages = {492-516},
      doi = {http://dx.doi.org/10.1108/09615531011048213}
    }
    					
    Principe, J. & Codina, R. On the stabilization parameter in the subgrid scale approximation of scalar convection-diffusion-reaction equations on distorted meshes 2010 Computer Methods in Applied Mechanics and Engineering
    Vol. 199 (21/22) , pp. 1386-1402  
    Abstract: In this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection-diffusion-reaction equation. The starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated. In order to incorporate the distortion of the mesh into this approximation, we transform the equation for the subgrid scale within each element to the shape-regular reference domain. The expression for the subgrid scale arises from an approximate Fourier analysis and the identification of the wave number direction where instabilities are most likely to occur. The final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation.
    BibTeX:
    @article{Principe.Codina.CMAM.2010,
      author = {Javier Principe and Ramon Codina},
      title = {On the stabilization parameter in the subgrid scale approximation of scalar convection-diffusion-reaction equations on distorted meshes},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2010},
      volume = {199},
      number = {21/22},
      pages = {1386-1402},
      doi = {http://dx.doi.org/10.1016/j.cma.2009.08.011}
    }
    					
    Principe, J.; Codina, R. & Henke, F. The dissipative structure of variational multiscale methods for incompressible flows 2010 Computer Methods in Applied Mechanics and Engineering
    Vol. 199 (13-16) , pp. 791-801  
    Abstract: In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.
    BibTeX:
    @article{Principe.etal.CMAM.2010,
      author = {Javier Principe and Ramon Codina and Florian Henke},
      title = {The dissipative structure of variational multiscale methods for incompressible flows},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2010},
      volume = {199},
      number = {13-16},
      pages = {791-801},
      doi = {http://dx.doi.org/10.1016/j.cma.2008.09.007}
    }
    					
    Codina, R.; Principe, J. & Baiges, J. Subscales on the element boundaries in the variational two-scale finite element method 2009 Computer Methods in Applied Mechanics and Engineering
    Vol. 198 (5-8) , pp. 838-852  
    Abstract: In this paper, we introduce a way to approximate the subscales on the boundaries of the elements in a variational two-scale finite element approximation to flow problems. The key idea is that the subscales on the element boundaries must be such that the transmission conditions for the unknown, split as its finite element contribution and the subscale, hold. In particular, we consider the scalar convection-diffusion-reaction equation, the Stokes problem and Darcy's problem. For these problems the transmission conditions are the continuity of the unknown and its fluxes through element boundaries. The former is automatically achieved by introducing a single valued subscale on the boundaries (for the conforming approximations we consider), whereas the latter provides the effective condition for approximating these values. The final result is that the subscale on the interelement boundaries must be proportional to the jump of the flux of the finite element component and the average of the subscale calculated in the element interiors.
    BibTeX:
    @article{Codina.etal.CMAM.2009,
      author = {Ramon Codina and Javier Principe and Joan Baiges},
      title = {Subscales on the element boundaries in the variational two-scale finite element method},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2009},
      volume = {198},
      number = {5-8},
      pages = {838-852},
      doi = {http://dx.doi.org/10.1016/j.cma.2008.10.020}
    }
    					
    Principe, J. & Codina, R. Mathematical models for thermally coupled low speed flows 2009 Advances in Theoretical and Applied Mechanics
    Vol. 2 (1-4) , pp. 93-112  
    Abstract: In this paper we review and clarify some aspects of the asymptotic analysis of the compressible Navier Stokes equations in the low Mach number limit. In the absence of heat exchange (the isentropic regime) this limit is well understood and rigorous results are available. When heat exchange is considered different simplified models can be obtained, the most famous being the Boussinesq approximation. Here a unified formal justification of these models is presented, paying special attention to the relation between the low Mach number and the Boussinesq approximations. Precise conditions for their validity are given for classical problems in bounded domains.
    BibTeX:
    @article{Principe.Codina.ATAM.2009,
      author = {Javier Principe and Ramon Codina},
      title = {Mathematical models for thermally coupled low speed flows},
      journal = {Advances in Theoretical and Applied Mechanics},
      year = {2009},
      volume = {2},
      number = {1-4},
      pages = {93-112},
      url = {http://www.m-hikari.com/atam/atam2009/atam1-4-2009/principeATAM1-4-2009.pdf}
    }
    					
    Principe, J. & Codina, R. A numerical approximation of the thermal coupling of fluids and solids 2009 International Journal for Numerical Methods in Fluids
    Vol. 59 , pp. 1181-1201  
    Abstract: In this article we analyze the problem of the thermal coupling of fluids and solids through a common interface. We state the global thermal problem in the whole domain, including the fluid part and the solid part. This global thermal problem presents discontinuous physical properties that depend on the solution of auxiliary problems on each part of the domain (a fluid flow problem and a solid state problem). We present a domain decomposition strategy to iteratively solve problems posed in both subdomains and discuss some implementation aspects of the algorithm. This domain decomposition framework is also used to revisit the use of wall function approaches used in this context.
    BibTeX:
    @article{Principe.Codina.IJNMF.2009,
      author = {Javier Principe and Ramon Codina},
      title = {A numerical approximation of the thermal coupling of fluids and solids},
      journal = {International Journal for Numerical Methods in Fluids},
      year = {2009},
      volume = {59},
      pages = {1181-1201},
      doi = {http://dx.doi.org/10.1002/fld.1856}
    }
    					
    Codina, R.; González-Ondina, J.M.; Díaz-Hernández, G. & Principe, J. Finite element approximation of the modified Boussinesq equations using a stabilized formulation 2008 International Journal for Numerical Methods in Fluids
    Vol. 57 (9) , pp. 1249-1268  
    Abstract: In this work, we present a finite element model to approximate the modified Boussinesq equations. The objective is to deal with the major problem associated with this system of equations, namely, the need to use stable velocity-depth interpolations, which can be overcome by the use of a stabilization technique. The one described in this paper is based on the splitting of the unknowns into their finite element component and the remainder, which we call the subgrid scale. We also discuss the treatment of high-order derivatives of the mathematical model and describe the time integration scheme.
    BibTeX:
    @article{Codina.etal.IJNMF.2008,
      author = {Ramon Codina and Jose M. González-Ondina and Gabriel Díaz-Hernández and Javier Principe},
      title = {Finite element approximation of the modified Boussinesq equations using a stabilized formulation},
      journal = {International Journal for Numerical Methods in Fluids},
      year = {2008},
      volume = {57},
      number = {9},
      pages = {1249-1268},
      doi = {http://dx.doi.org/10.1002/fld.1718}
    }
    					
    Houzeaux, G. & Principe, J. A variational subgrid scale model for transient incompressible flows 2008 International Journal of Computational Fluid Dynamics
    Vol. 22 , 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.
    BibTeX:
    @article{Houzeaux.Principe.IJCFD.2008,
      author = {Guillaume Houzeaux and Javier Principe},
      title = {A variational subgrid scale model for transient incompressible flows},
      journal = {International Journal of Computational Fluid Dynamics},
      year = {2008},
      volume = {22},
      pages = {135-152},
      doi = {http://dx.doi.org/10.1080/10618560701816387}
    }
    					
    Principe, J. & Codina, R. A stabilized finite element approximation of low speed thermally coupled flows 2008 International Journal of Numerical Methods for Heat and Fluid Flow
    Vol. 18 (7/8) , pp. 835-867  
    Abstract: Purpose - The purpose of this paper is to describe a finite element formulation to approximate thermally coupled flows using both the Boussinesq and the low Mach number models with particular emphasis on the numerical implementation of the algorithm developed. Design/methodology/approach - The formulation, that allows us to consider convection dominated problems using equal order interpolation for all the valuables of the problem, is based on the subgrid scale concept. The full Newton linearization strategy gives rise to monolithic treatment of the coupling of variables whereas some fixed point schemes permit the segregated treatment of velocity-pressure and temperature. A relaxation scheme based on the Armijo rule has also been developed. Findings - A full Newtown linearization turns out to be very efficient for steady-state problems and very robust when it is combined with a line search strategy. A segregated treatment of velocity-pressure and temperature happens to be more appropriate for transient problems. Research limitations/implications - A fractional step scheme, splitting also momentum and continuity equations, could be further analysed. Practical implications - The results presented in the paper are useful to decide the solution strategy for a given problem. Originality/value - The numerical implementation of a stabilized finite element approximation of thermally coupled flows is described. The implementation algorithm is developed considering several possibilities for the solution of the discrete nonlinear problem.
    BibTeX:
    @article{Principe.Codina.IJNMH.2009,
      author = {Javier Principe and Ramon Codina},
      title = {A stabilized finite element approximation of low speed thermally coupled flows},
      journal = {International Journal of Numerical Methods for Heat and Fluid Flow},
      year = {2008},
      volume = {18},
      number = {7/8},
      pages = {835-867},
      doi = {http://dx.doi.org/10.1108/09615530810898980}
    }
    					
    Codina, R.; Principe, J.; Guasch, O. & Badia, S. Time dependent subscales in the stabilized finite element approximation of incompressible flow problems 2007 Computer Methods in Applied Mechanics and Engineering
    Vol. 196 (21-24) , pp. 2413-2430  
    Abstract: In this paper we analyze a stabilized finite element approximation for the incompressible Navier-Stokes equations based on the subgrid-scale concept. The essential point is that we explore the properties of the discrete formulation that results allowing the subgrid-scales to depend on time. This apparently #natural# idea avoids several inconsistencies of previous formulations and also opens the door to generalizations.
    BibTeX:
    @article{Codina.etal.CMAM.2007,
      author = {Ramon Codina and Javier Principe and Oriol Guasch and Santiago Badia},
      title = {Time dependent subscales in the stabilized finite element approximation of incompressible flow problems},
      journal = {Computer Methods in Applied Mechanics and Engineering},
      year = {2007},
      volume = {196},
      number = {21-24},
      pages = {2413-2430},
      doi = {http://dx.doi.org/10.1016/j.cma.2007.01.002}
    }
    					
    Codina, R. & Principe, J. Dynamic subscales in the finite element approximation of thermally coupled incompressible flows 2007 International Journal for Numerical Methods in Fluids
    Vol. 54 (6-8) , pp. 707-730  
    Abstract: In this paper, we propose a variational multiscale finite-element approximation for the incompressible Navier-Stokes equations using the Boussinesq approximation to model thermal coupling. The main feature of the formulation in contrast to other stabilized methods is that we consider the subscales as transient. They are solution of a differential equation in time that needs to be integrated. Likewise, we keep the effect of the subscales both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation. Apart from presenting the main properties of the formulation, we also discuss some computational aspects such as the linearization strategy or the way to integrate in time the equation for the subscales.
    BibTeX:
    @article{Codina.Principe.IJNMF.2007,
      author = {Ramon Codina and Javier Principe},
      title = {Dynamic subscales in the finite element approximation of thermally coupled incompressible flows},
      journal = {International Journal for Numerical Methods in Fluids},
      year = {2007},
      volume = {54},
      number = {6-8},
      pages = {707-730},
      doi = {http://dx.doi.org/10.1002/fld.1481}
    }
    					
    Goldschmit, M.B.; Ferro, S.P.; Principe, J. & Coppola Owen, A.H. On the modelling of liquid steel processes. 2002 Latin American Applied research
    Vol. 32 , 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.
    BibTeX:
    @article{Goldschmit.etal.LAAR.2002,
      author = {Marcela B. Goldschmit and Sergio P. Ferro and Javier Principe and Angel H. Coppola Owen},
      title = {On the modelling of liquid steel processes.},
      journal = {Latin American Applied research},
      year = {2002},
      volume = {32},
      pages = {263-273},
      url = {http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327-07932002000300010&lng=en&nrm=iso}
    }
    					
    Ferro, S.P.; Principe, J. & Goldschmit, M.B. A new approach to the analysis of vessel residence time distribution curves 2001 Metallurgical and Materials Transactions B
    Vol. 32 , 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.
    BibTeX:
    @article{Ferro.etal.MMTB.2001,
      author = {Sergio P. Ferro and Javier Principe and Marcela B. Goldschmit},
      title = {A new approach to the analysis of vessel residence time distribution curves},
      journal = {Metallurgical and Materials Transactions B},
      year = {2001},
      volume = {32},
      pages = {1185-1193},
      doi = {http://dx.doi.org/10.1007/s11663-001-0106-7}
    }
    					
    Goldschmit, M.B.; Principe, J. & Koslowski, M. Applications of a (k-e) model for the analysis of continuous casting processes 1999 International Journal for Numerical Methods in Engineering
    Vol. 46 (9) , pp. 1097-0207  
    Abstract: The finite element solution of the turbulent Navier-Stokes equations developed via (k-e) turbulence models was addressed in previous publications [1-4], where a (k-L)-predictor/(e)-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.
    BibTeX:
    @article{Goldschmit.etal.IJNME.1999,
      author = {Marcela B. Goldschmit and Javier Principe and Marisol Koslowski},
      title = {Applications of a (k-e) model for the analysis of continuous casting processes},
      journal = {International Journal for Numerical Methods in Engineering},
      year = {1999},
      volume = {46},
      number = {9},
      pages = {1097-0207},
      doi = {http://dx.doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1505::AID-NME709>3.0.CO;2-3}
    }
    					

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