COLLECTIONS

Documents published in Scipedia

• Improving the k-compressibility of Hyper Reduced Order Models with moving sources: Applications to welding and phase change problems

  A. Cosimo, A. Cardona, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2014). Vol. 274, pp. 237-263

  
  

  Abstract

  The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising alternative for real-time simulations. In this work, we study the design of HROMs for non-linear problems with a moving source. Applications to nonlinear phase change problems with temperature dependent thermophysical properties are particularly considered; however, the techniques developed can be applied in other fields as well. A basic assumption in the design of HROMs is that the quantities that will be hyper-reduced are k-compressible in a certain basis in the sense that these quantities have at most k non-zero significant entries when expressed in terms of that basis. To reach the computational speed required for a real-time application, k must be small. This work examines different strategies for addressing hyper-reduction of the nonlinear terms with the objective of obtaining k-compressible signals with a notably small k. To improve performance and robustness, it is proposed that the different contributing terms to the residual are separately hyper-reduced. Additionally, the use of moving reference frames is proposed to simulate and hyper-reduce cases that contain moving heat sources. Two application examples are presented: the solidification of a cube in which no heat source is present and the welding of a tube in which the problem posed by a moving heat source is analysed.

  Abstract
  The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising [...]

  • 12
  •  read

• A domain decomposition strategy for reduced order models. Application to the incompressible Navier–Stokes equations

  J. Baiges, R. Codina, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2013). Vol. 267, pp. 23-42

  
  

  Abstract

  In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions to the nodes belonging to each of the subdomains into which the physical domain is partitioned. An extension of the proposed domain decomposition strategy to a hybrid full-order/reduced-order model is then described. The general domain decomposition approach is particularized for the reduced-order finite element approximation of the incompressible Navier–Stokes equations with hyper-reduction. When solving the reduced incompressible Navier–Stokes equations, instabilities in the form of large gradients of the recovered reduced-order unknown at the subdomain interfaces may appear, which is the motivation for the design of additional stability terms giving rise to penalty matrices. Numerical examples illustrate the behavior of the proposed method for the simulation of the reduced-order systems, showing the capability of the approach to adapt to configurations which are not present in the original snapshot set.

  Abstract
  In this work, a domain decomposition strategy for non-linear hyper-reduced-order models is presented. The basic idea consists of restricting the reduced-order basis functions [...]

  • 28
  •  read

• Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations

  A. Limache, R. Sánchez, L. Dalcín, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (49–50), pp. 4180-4192

  
  

  Abstract

  Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.

  Abstract
  Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given [...]

  • 27
  •  read

• All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision

  N. Calvo, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3–4), pp. 371-378

  
  

  Abstract

  The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples.

  Abstract
  The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner [...]

  • 10
  •  read

• The DNL absorbing boundary condition: applications to wave problems

  M. Storti, J. D'ELIA, R. Bonet Chaple, N. Nigro, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2000). Vol. 182 (3–4), pp. 483-498

  
  

  Abstract

  A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference equations that arise from partial discretization in the directions transversal to the artificial boundary followed by discretization on a constant step 1D grid in the direction normal to the boundary. This leads to an eigenvalue problem of the size of the number of degrees of freedom in the lateral discretization. The eigenvalues are classified as right- or left-going and the absorbing boundary condition consists in imposing a null value for the ingoing modes, leaving free the outgoing ones. Whereas the classification is straightforward for operators with definite sign, like the Laplace operator, a virtual dissipative mechanism has to be added in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation. The main advantage of the method is that it can be implemented as a black-box routine, taking as input the coefficients of the linear system, obtained from standard discretization (FEM or FDM) packages and giving on output the absorption matrix. We present the application of the DNL methodology to typical wave problems, like Helmholtz equations and potential flow with free surface (the ship wave resistance and sea-keeping problems).

  Abstract
  A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference [...]

  • 12
  •  read

• Physics based GMRES preconditioner for compressible and incompressible Navier-Stokes equations

  N. Nigro, M. Storti, S. Idelsohn, T. Tezduyar

  Comput. Methods Appl. Mech. Engrg., (1998). Vol. 154 (3–4), pp. 203-228

  
  

  Abstract

  This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations using an SUPG finite element formulation and GMRES implicit solver. During the last years a lot of effort has been dedicated to finding a unified approach for compressible and incompressible flow in order to treat fluid dynamic problems with a very wide range of Mach and Reynolds numbers [10,26,37]. On the other hand, SUPG finite element formulation and GMRES implicit solver is one of the most robust combinations to solve state of the art CFD problems [1,6,9,22,29,30,31]. The selection of a good preconditioner and its performance on parallel architecture is another open problem in CFD community. The local feature of the preconditioner presented here means that no communication among processors is needed when working on parallel architectures. Due to these facts we consider that this research can make some contributions towards the development of a unified fluid dynamic model with high rates of convergence for any combination of Mach and Reynolds numbers, being very suitable for massively parallel computations. Finally, it is important to remark that while this kind of preconditioning produces stabilized results in nearly incompressible regimes the standard version exhibits some numerical drawbacks that lead to solutions without physical meaning.

  Abstract
  This paper presents the implementation of a local physics preconditioning mass matrix [8] for an unified approach of 3D compressible and incompressible Navier-Stokes equations [...]

  • 22
  •  read

• Equal-order interpolations: a unified approach to stabilize the incompressible and advective effects

  M. Storti, N. Nigro, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1997). Vol. 143 (3–4), pp. 317-331

  
  

  Abstract

  In this paper we present a new SUPG formulation for compressible and near incompressible Navier-Stokes equations [5]. It introduces an extension of the exact solution for one-dimensional systems to the multidimensional case, in a similar way to that arising in the scalar problem. It is important to note that this formulation satisfies both the one-dimensional advective-diffusive system limit case and the advection-dominated multidimensional system case presented by Mallet et al. Another interesting feature of this formulation is that it introduces naturally a stabilizing term for the incompressibility condition, in a similar way to that found by other authors [1–4]. However, in our formulation the stabilization is introduced to the whole system of equations, while other authors introduce a term to stabilize the incompressibility condition and another one for the advective term. In Section 1 we present Navier-Stokes equations for compressible flow and, then, we pass to detail several topics related to the numerical discretization of such advective-diffusive multidimensional systems of PDEs, in the Petrov-Galerkin context. The method is applicable and described for the general Re > 0 laminar flow, but the nature of the stabilizing effect of the artificial diffusion matrix introduced is discussed in depth for the simpler Stokes (Re = 0) flow. Several numerical results are shown in Section 5, taking the well-known test problem of the square-cavity and a variant of this, namely a multiply connected square-cavity, as a validation for this code

  Abstract
  In this paper we present a new SUPG formulation for compressible and near incompressible Navier-Stokes equations [5]. It introduces an extension of the exact solution for [...]

  • 14
  •  read

• A Petrov-Galerkin formulation for advection-reaction-diffusion problems

  S. Idelsohn, N. Nigro, M. Storti, G. Buscaglia

  Comput. Methods Appl. Mech. Engrg., (1996). Vol. 136 (1–2), pp. 27-46

  
  

  Abstract

  In this work we present a new method called (SU + C)PG to solve advection-reaction-diffusion scalar equations by the Finite Element Method (FEM). The SUPG (for Streamline Upwind Petrov-Galerkin) method is currently one of the most popular methods for advection-diffusion problems due to its inherent consistency and efficiency in avoiding the spurious oscillations obtained from the plain Galerkin method when there are discontinuities in the solution. Following this ideas, Tezduyar and Park treated the more general advection-reaction-diffusion problem and they developed a stabilizing term for advection-reaction problems without significant diffusive boundary layers. In this work an SUPG extension for all situations is performed, covering the whole plane represented by the Peclet number and the dimensionless reaction number. The scheme is based on the extension of the super-convergence feature through the inclusion of an additional perturbation function and a corresponding proportionality constant. Both proportionality constants (that one corresponding to the standard perturbation function from SUPG, and the new one introduced here) are selected in order to verify the ‘super-convergence’ feature, i.e. exact nodal values are obtained for a restricted class of problems (uniform mesh, no source term, constant physical properties). It is also shown that the (SU + C)PG scheme verifies the Discrete Maximum Principle (DMP), that guarantees uniform convergence of the finite element solution. Moreover, it is shown that super-convergence is closely related to the DMP, motivating the interest in developing numerical schemes that extend the super-convergence feature to a broader class of problems.

  Abstract
  In this work we present a new method called (SU + C)PG to solve advection-reaction-diffusion scalar equations by the Finite Element Method (FEM). The SUPG (for Streamline [...]

  • 15
  •  read

• Steady state incompressible flows using explicit schemes with an optimal local preconditioning

  M. Storti, N. Nigro, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1995). Vol. 124 (3), pp. 231-252

  
  

  Abstract

  Solving large systems of equations from CFD problems by the explicit pseudo-temporal scheme requires a very low amount of memory and is highly parallelizable, but the CPU time largely depends on the conditioning of the system. For advective systems it is shown that the rate of convergence depends on a condition number defined as the ratio of the maximum and the minimum group velocities of the continuum system. If the objective is to reach the steady state, the temporal term can be modified in order to reduce this condition number. Another possibility consists in the addition of a local preconditioning mass matrix. In this paper an optimal preconditioning for incompressible flow is presented, also applicable to compressible ones with locally incompressible zones, like stagnation points, in contrast with the artificial compressibility method. The preconditioned system has a rate of convergence independent from Mach number. Moreover, the discrete solution is highly improved, eliminating spurious oscillations frequently encountered in incompressible flows.

  Abstract
  Solving large systems of equations from CFD problems by the explicit pseudo-temporal scheme requires a very low amount of memory and is highly parallelizable, but the CPU [...]

  • 12
  •  read

• A Petrov-Galerkin technique for the solution of transonic and supersonic flows

  C. Baumann, M. Storti, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (1992). Vol. 95 (1), pp. 49-70

  
  

  Abstract

  This paper is both the description of a streamline-upwind/Petrov-Galerkin (SUPG) formulation and the documentation of the development of a code for the finite element solution of transonic and supersonic flows. The aim of this work is to present a formulation to be able to treat domains of any configuration and to use the appropriate physical boundary conditions, which are the major stumbling blocks of the finite difference schemes. The implemented code has the following features: the Hughes' SUPG-type formulation with an oscillation-free shock-capturing operator, adaptive refinement, explicit integration with local time-step and hourglassing control. An automatic scheme for dealing with slip boundary conditions and a boundary-augmented lumped mass matrix for speeding up convergence. The theoretical background of the SUPG formulation is described briefly. How the foregoing formulation was used in the finite element code and which are the appropriate boundary conditions to be used are also described. Finally some results obtained with this code are discussed.

  Abstract
  This paper is both the description of a streamline-upwind/Petrov-Galerkin (SUPG) formulation and the documentation of the development of a code for the finite element solution [...]

  • 15
  •  read