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• PFEM–DEM for particle-laden flows with free surface

  A. Franci, I. de-Pouplana, G. Casas, M. Celigueta, J. González-Usúa, E. Oñate

  Computational Particle Mechanics (2020). Vol. 7, pp. 101-120

  
  

  Abstract

  This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element method (PFEM), while the solid particles embedded in the fluid are modeled with the discrete element method (DEM). The coupling between the implicit PFEM and the explicit DEM is performed through a sub-stepping staggered scheme. This work only considers suspended spherical particles that are assumed not to affect the fluid motion. Several tests are presented to validate the formulation. The PFEM–DEM results show very good agreement with analytical solutions, laboratory tests and numerical results from alternative numerical methods.

  Abstract
  This work proposes a fully Lagrangian formulation for the numerical modeling of free-surface particle-laden flows. The fluid phase is solved using the particle finite element [...]

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• A finite element reduced order model based on adaptive mesh refinement and artificial neural networks

  J. Baiges, R. Codina, I. Castañar, E. Castillo

  Comput. Methods Appl. Mech. Engrg., (2019). (prepint) pp. 1-14

  
  

  Abstract

  In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh, and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to non-linear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.

  Abstract
  In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The [...]

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• Variational multi-scale approximation of the one-dimensional forced Burguers' equation: the role of orthogonal sub-grid scales in turbulence modelling

  C. Bayona, J. Baiges, R. Codina

  Int. J. Numer. Meth. Fluids (2018). Vol. 86, pp. 313-328

  
  

  Abstract

  A numerical approximation for the one-dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS-VMS) method. We evaluate the role of the variational subscales in describing the Burgers “turbulence” phenomena. Particularly, we seek to clarify the interaction between the subscales and the resolved scales when the former are defined to be orthogonal to the finite-dimensional space. Direct numerical simulation is used to evaluate the resulting OSGS-VMS energy spectra. The comparison against a large eddy simulation model is presented for numerical discretizations in which the grid is not capable of solving the small scales. An accurate approximation to the phenomena of turbulence is obtained with the addition of the purely dissipative numerical terms given by the OSGS-VMS method without any modification of the continuous problem

  Abstract
  A numerical approximation for the one-dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS-VMS) method. We [...]

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• Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows

  O. Guasch, R. Codina

  Comput. Methods Appl. Mech. Engrg., (2013). Vol. 261-262, pp. 145-166

  
  

  Abstract

  Abstract Numerical simulations have proved that Variational Multiscale Methods (VMM) perform well as pure numerical large eddy simulation (LES) models. In this paper we focus on the orthogonal subgrid scale (OSS) finite element method and make an analysis of the statistical behavior of its stabilization terms in the quasi static approximation. This is done by resorting to results from classical statistical fluid mechanics concerning two point velocity, pressure and combined correlation functions of various orders. Given a fine enough mesh with characteristic element size h in the inertial subrange of a turbulent flow, it is shown that the rate of transfer of subgrid kinetic energy provided by the OSS stabilization terms does not depend on h and that it equals the molecular physical dissipation rate (up to a dimensionless constant that only depends on the finite element shapes) for a proper redesign of the standard parameters of the formulation. This is a noteworthy fact taking into account that the subgrid stabilization terms do not arise from physical considerations, but from the mathematical necessity to allow equal interpolation for the pressure and velocity fields, as well as to control convection. Therefore, the obtained results contribute somehow to the line of reasoning supporting that pure numerical approaches (i.e., without introducing additional physical models) could probably suffice in the LES simulation of turbulent flows

  Abstract
  Abstract Numerical simulations have proved that Variational Multiscale Methods (VMM) perform well as pure numerical large eddy simulation (LES) models. In this paper we focus [...]

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• A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form

  O. Zienkiewicz, K. Morgan, B. Sai, R. Codina, M. Vasquez

  Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 887-913

  
  

  Abstract

  The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks.

  Abstract
  The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent [...]

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• A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields

  O. Jou Devesa, M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

  Computational Particle Mechanics (2019). Vol. 6 (4), pp 739–765

  
  

  Abstract

  This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce the most frequently encountered ice infested scenarios, the main characteristics of ice-breaking ships and the predicted failure modes of floe-ice depending on the loading conditions, the structure type and the ice feature dimensions and thickness. For the simulations, a local bonded discrete element method (DEM) is used to model sea ice and its fractures. The packing of bonded spherical particles which reproduce the ice continuum can break due to ship–ice interactions and the failure modes are studied. A set of validation simulations are first carried out. A level ice sheet breaking against an installed ice-breaking cone with different slope angles is studied, and the results are compared with other DEM simulations. Then, a group of bonded DEM simulations are performed to predict the different failure modes produced when an ice-breaking ship bow contacts with ice cakes and floe-ice of different dimensions and thickness, typical in broken ice fields. Finally, the study of breaking a continuous level ice sheet is carried out by modeling with the bonded DEM an “infinite” large domain of sea ice and loaded by a single-degree-of-freedom model of an ice-breaking ship.

  Abstract
  This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce [...]

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• Chebyshev spectral collocation method approximations of the Stokes eigenvalue problem based on penalty techniques

  Ö. Türk, R. Codina

  Applied Numerical Mathematics (2019). (preprint) Vol. 145, pp. 188-200

  
  

  Abstract

  Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method approach can successfully be adapted for the eigenproblem to rectify the associated problems such as the existence of zero diagonal entries in the resulting algebraic system. Two different schemes, namely, the standard penalisation with a small penalty parameter, and the iterative penalisation that enables relatively large parameters, are implemented. The employment of the latter leads to a so-called inhomogeneous generalised eigenvalue problem which requires a special attention. A feasible solution strategy is presented which is adapted from a procedure based on Newton's method proposed for the corresponding standard (inhomogeneous) eigenvalue problems. Concerning the spatial discretisation, among other possible options, the Chebyshev spectral collocation method based on expanding the unknown fields in tensor product of Chebyshev polynomials is employed. It is shown that the method constitutes a novel way of efficiently examining the approximate eigensolutions of the Stokes operator with the use of Chebyshev spectral collocation method directly, without a decoupling of velocity and pressure.

  Abstract
  Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method [...]

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• Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation

  L. Moreno García, R. Codina, J. Baiges, E. Castillo

  Comput. Methods Appl. Mech. Engrg., (2019). Vol. 354, pp. 706-731

  
  

  Abstract

  The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.

  Abstract
  The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers [...]

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• Dynamic term-by-term stabilized finite element formulation using orthogonal subgrid-scales for the incompressible Navier–Stokes problem

  E. Castillo, R. Codina

  Comput. Methods Appl. Mech. Engrg., (2019). Vol. 349, pp. 701-721

  
  

  Abstract

  In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for the Navier–Stokes problem that can be viewed as a variational multiscale (VMS) method under some assumptions. The essential point of the formulation is the time dependent nature of the subscales and, contrary to residual-based formulations, the introduction of two velocity subscale components. They represent the components of the convective and the pressure gradient terms, respectively, of the momentum equation that cannot be captured by the finite element mesh. A key idea of the proposed method is that the convective subscale is close to a solenoidal field and the pressure gradient subscale is close to a potential field. The method ensures stability in anisotropic space–time discretizations, which is proved using numerical analysis for a linearized problem and demonstrated in classical numerical tests. The work includes a detailed description of the proposed formulation and several numerical examples that serve to justify our claims.

  Abstract
  In this paper, we propose and analyze the stability and the dissipative structure of a new dynamic term-by-term stabilized finite element formulation for [...]

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• Time-dependent semidiscrete analysis of the viscoelastic fluid flow problem using a variational multiscale stabilized formulation

  G. Barrenechea, E. Castillo, R. Codina

  Journal of Numerical Analysis (2019). Vol. 39 (2), pp. 792-819

  
  

  Abstract

  In this article we analyse a stabilized finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and robustness in the different benchmarks tested in the viscoelastic framework, and permitting the use of equal interpolation of the unknown fields. We first present results about a linearized subproblem, for which well-posedness and stability results can be proved. Then, the semidiscrete nonlinear time-dependent case is addressed using a fixed point theorem, which allows us to prove existence of a semidiscrete solution, along with error estimates.

  Abstract
  In this article we analyse a stabilized finite element formulation recently proposed to approximate viscoelastic fluid flows. The formulation has shown to have accuracy and [...]

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