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Adaptive Meshing

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Thierry Coupez – One of the best experts on this subject based on the ideXlab platform.

  • anisotropic Adaptive Meshing and monolithic variational multiscale method for fluid structure interaction
    Computers & Structures, 2013
    Co-Authors: Elie Hachem, Stephanie Feghali, Ramon Codina, Thierry Coupez

    Abstract:

    This paper presents a monolithic formulation framework combined with an anisotropic mesh adaptation for fluid-structure interaction (FSI) applications with complex geometry. The fluid-solid interfaces are captured using a level-set method. A new a posteriori error estimate, based on the length distribution tensor approach and the associated edge based error analysis, is then used to ensure an accurate capturing of the discontinuities at the fluid-solid interface. It enables to calculate a stretching factor providing a new edge length distribution, its associated tensor and the corresponding metric. The optimal stretching factor field is obtained by solving an optimization problem under the constraint of a fixed number of edges in the mesh. The presence of the structure will be taken into account by means of an extra stress tensor in the Navier-Stokes equations. The system is solved using a stabilized three-field, stress, velocity and pressure finite element (FE) formulation. It consists in the decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales and also in the efficient enrichment of the extra constraint. We assess the accuracy of the proposed formulation by simulating 2D and 3D time-dependent numerical examples such as: falling disk in a channel, turbulent flows behind an airfoil profile and flow behind an immersed vehicle.

  • 3D Anisotropic Adaptive Meshing and Stabilised Finite Element Methods for Multiphase Flows at Low and High Reynolds Number
    , 2011
    Co-Authors: Elie Hachem, Stephanie Feghali, Hong Chau Nguyen, Hugues Digonnet, Thierry Coupez

    Abstract:

    This paper presents a stabilized finite element method for the solution of incompressible multiphase flow problems in three dimensions using a level set method with anisotropic Adaptive Meshing. A recently developed stabilized finite element solver which draws upon features of solving general fluid-structure interactions is presented. The proposed method is developed in the context of the monolithic formulation and the Immersed Volume Method. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure (e.g. rigid or elastic) in the fluid. The distinctive feature of the Variational MultiScale approach is not only the decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales but also the possible efficient enrichment of the extra constraint. This choice of decomposition is shown to be favorable for simulating multiphase flows at low or high Reynolds number. The interface between the phases is resolved using a convected level set approach developed. This approach enables first to restrict convection resolution to the neighbourhood of the interface and second to replace the reinitialisation steps by an advective reinitialisation. This enables an efficient resolution and accurate computations of flows even with large density and viscosity differences. The level set function is discretized using a stabilized upwind Petrov-Galerkin method and can be coupled to a direct anisotropic mesh adaptation process enhancing the interface representation. Therefore, we propose to build a metric field directly at the nodes of the mesh for a direct use in the Meshing tools. In addition, we show that we obtain an optimal stretching factor field by solving an optimization problem under the constraint of a fixed number of edges in the mesh. The capability of the resultant algorithm is demonstrated with three dimensional time-dependent numerical examples such as: the complex fluid buckling phenomena, the water waves propagations, and the rigid bodies motion in incompressible flows.

  • Stabilized Finite Element Methods vs LES modelling for fluid-strucure interaction with anisotropic Adaptive Meshing
    , 2011
    Co-Authors: Elie Hachem, Stephanie Feghali, Thierry Coupez

    Abstract:

    This paper presents a stabilised finite element method for the solution of incompressible multiphase flow problems in three dimensions using an immersed volume method with anisotropic Adaptive Meshing. A recently developed stabilised finite element solver which draws upon features of solving general fluid-structure interactions is presented. The proposed method is developed in the context of the monolithic formulation. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations coming from the presence of the structure in the fluid. The distinctive feature of the Variational MultiScale approach is not only the decomposition for both the velocity and the pressure fields into coarse/resolved scales and fine/unresolved scales but also the possible efficient enrichment of the extra constraint. This choice of decomposition is shown to be favorable for simulating multiphase flows at high Reynolds number. We assess the behaviour and accuracy of the proposed formulation coupled to the levelset method approximation in the simulation of 2D and 3D time-dependent numerical examples such as : vortex shedding behind an obstacle, conjugate heat transfer inside industrial furnaces and the rigid bodies motion in incompressible flows. See http://hal.archives-ouvertes.fr/docs/00/59/26/96/ANNEX/r_Q1R43125.pdf

M Ortiz – One of the best experts on this subject based on the ideXlab platform.

  • error estimation and Adaptive Meshing in strongly nonlinear dynamic problems
    Computer Methods in Applied Mechanics and Engineering, 1999
    Co-Authors: Raul Radovitzky, M Ortiz

    Abstract:

    We present work aimed at developing a general framework for mesh adaption in strongly nonlinear, possibly dynamic, problems. We begin by showing that the solutions of the incremental boundary value problem for a wide class of materials, including nonlinear elastic materials, compressible Newtonian fluids and viscoplastic solids, obey a minimum principle, provided that the constitutive updates are formulated appropriately. This minimum principle can be taken as a basis for asymptotic error estimation. In particular, we chose to monitor the error of a lower-order projection of the finite element solution. The optimal mesh size distribution then follows from a posteriori error indicators which are purely local, i.e. can be computed element-by-element. We demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application.

  • modelling and simulation of high speed machining
    International Journal for Numerical Methods in Engineering, 1995
    Co-Authors: T D Marusich, M Ortiz

    Abstract:

    A Lagrangian finite element model of orthogonal high-speed machining is developed. Continuous reMeshing and Adaptive Meshing are the principal tools which we employ for sidestepping the difficulties associated with deformation-induced element distortion, and for resolving fine-scale features in the solution. The model accounts for dynamic effects, heat conduction, mesh-on-mesh contact with friction, and full thermo-mechanical coupling. In addition, a fracture model has been implemented which allows for arbitrary crack initiation and propagation in the regime of shear localized chips. The model correctly exhibits the observed transition from continuous to segmented chips with increasing tool speed.

  • Adaptive mesh refinement in strain localization problems
    Computer Methods in Applied Mechanics and Engineering, 1991
    Co-Authors: M Ortiz, J J Quigley

    Abstract:

    An Adaptive Meshing method tailored to problems of strain localization is given. The adaption strategy consists of equi-distributing the variation of the velocity field over the elements of the mesh. A heuristic justification for the use of variations as indicators is advanced, and possible connections with interpolation error bounds are discussed. Meshes are constructed by Delaunay triangulation. It is shown how the Hu-Washizu principle determines a consistent transfer operator for the state variables. Examples of application are given which demonstrate the versatility of the method.

Ki Youn Kwon – One of the best experts on this subject based on the ideXlab platform.

  • An optimal design system for spot welding locations
    Finite Elements in Analysis and Design, 2002
    Co-Authors: Soo Won Chae, Ki Youn Kwon

    Abstract:

    An optimal design system using Adaptive meshes for spot welding locations in shell structures has been developed. In order to find out the optimal spot welding locations, iterative finite element analysis is necessary. The optimization process also requires that every mesh employed should be as uniform as possible in its quality. For this purpose an h-version of Adaptive Meshing scheme based on a background mesh has been proposed. The background meshes ares constructed with quadrilateral elements on three-dimensional surfaces by using a domain decomposition method. Sample problems are solved to demonstrate the effectiveness and capability of the developed system.