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Daniel Broc - One of the best experts on this subject based on the ideXlab platform.

  • homogenisation method for the modal analysis of tube bundle with fluid structure interaction modelling
    Finite Elements in Analysis and Design, 2008
    Co-Authors: Jean François Sigrist, Daniel Broc
    Abstract:

    The present paper is concerned with the modal analysis of a two-dimensional tube bundle with fluid-structure interaction (FSI) modelling. The numerical modelling of FSI effects is performed with a homogenisation approach, using a method whose principles have been presented in a previous paper for the modal analysis of a nuclear reactor with internal structures and FSI modelling [J.F. Sigrist, D. Broc, Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid structure-interaction coupling, Nucl. Eng. Des. 237 (2007) 431-440]. The method is adapted here in the case of tube bundle and compared with the classical approach, based on a direct finite Element Discretisation of the coupled problem with all tubes modelling. The theoretical background of the method is recalled, the numerical implementation in a finite Element code is exposed and a comparison of the ''homogenisation'' and ''coupled'' methods is proposed in the case of a 10x10 tube bundle. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed; it is concluded that: (i) the computational time is significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects. Extension of the method to a three-dimensional case can now be considered; implementation of the method in a commercial finite Element code is also currently investigated.

  • dynamic analysis of a tube bundle with fluid structure interaction modelling using a homogenisation method
    Computer Methods in Applied Mechanics and Engineering, 2008
    Co-Authors: Jean François Sigrist, Daniel Broc
    Abstract:

    Abstract The present paper is concerned with the dynamic analysis of a tube bundle with fluid–structure interaction (FSI) modelling. Modelling of FSI is performed with a homogenisation approach which is compared with the classical coupled approach; this latter is based on a direct finite Element Discretisation of the coupled problem with all tubes modelling, while the former lies on a description of the fluid–tubes system through an equivalent continuous medium, characterised by a set of dynamic equations which describe the behaviour of the tubes and the fluid from a global point of view. Theoretical background of the method is recalled, numerical implementation in a finite Element code is exposed and comparison of the “homogenisation” and “coupled” method is proposed in the case of a 10 × 10 tube bundle, in 2D and 3D configurations. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed, as well as the dynamic response of the coupled system subjected to seismic loading. It is concluded that: (i) the computational time are significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects: no significant discrepancies are reported in the modal and dynamic analysis, when performed with the homogenisation and the coupled approaches, which makes the proposed method of practical interest for future engineering applications.

Jean François Sigrist - One of the best experts on this subject based on the ideXlab platform.

  • homogenisation method for the modal analysis of tube bundle with fluid structure interaction modelling
    Finite Elements in Analysis and Design, 2008
    Co-Authors: Jean François Sigrist, Daniel Broc
    Abstract:

    The present paper is concerned with the modal analysis of a two-dimensional tube bundle with fluid-structure interaction (FSI) modelling. The numerical modelling of FSI effects is performed with a homogenisation approach, using a method whose principles have been presented in a previous paper for the modal analysis of a nuclear reactor with internal structures and FSI modelling [J.F. Sigrist, D. Broc, Homogenisation method for the modal analysis of a nuclear reactor with internal structures modelling and fluid structure-interaction coupling, Nucl. Eng. Des. 237 (2007) 431-440]. The method is adapted here in the case of tube bundle and compared with the classical approach, based on a direct finite Element Discretisation of the coupled problem with all tubes modelling. The theoretical background of the method is recalled, the numerical implementation in a finite Element code is exposed and a comparison of the ''homogenisation'' and ''coupled'' methods is proposed in the case of a 10x10 tube bundle. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed; it is concluded that: (i) the computational time is significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects. Extension of the method to a three-dimensional case can now be considered; implementation of the method in a commercial finite Element code is also currently investigated.

  • dynamic analysis of a tube bundle with fluid structure interaction modelling using a homogenisation method
    Computer Methods in Applied Mechanics and Engineering, 2008
    Co-Authors: Jean François Sigrist, Daniel Broc
    Abstract:

    Abstract The present paper is concerned with the dynamic analysis of a tube bundle with fluid–structure interaction (FSI) modelling. Modelling of FSI is performed with a homogenisation approach which is compared with the classical coupled approach; this latter is based on a direct finite Element Discretisation of the coupled problem with all tubes modelling, while the former lies on a description of the fluid–tubes system through an equivalent continuous medium, characterised by a set of dynamic equations which describe the behaviour of the tubes and the fluid from a global point of view. Theoretical background of the method is recalled, numerical implementation in a finite Element code is exposed and comparison of the “homogenisation” and “coupled” method is proposed in the case of a 10 × 10 tube bundle, in 2D and 3D configurations. Calculation of eigenmode shapes, frequencies and effective masses with the two methods is performed, as well as the dynamic response of the coupled system subjected to seismic loading. It is concluded that: (i) the computational time are significantly lowered when using the homogenisation method instead of the coupled method, since the problem size is reduced by 90%; (ii) the tube bundle dynamic is described in a space-averaged manner, which is sufficient to account for the main inertial coupling effects: no significant discrepancies are reported in the modal and dynamic analysis, when performed with the homogenisation and the coupled approaches, which makes the proposed method of practical interest for future engineering applications.

Colin J Cotter - One of the best experts on this subject based on the ideXlab platform.

  • higher order compatible finite Element schemes for the nonlinear rotating shallow water equations on the sphere
    Journal of Computational Physics, 2018
    Co-Authors: Jemma Shipton, Thomas H Gibson, Colin J Cotter
    Abstract:

    Abstract We describe a compatible finite Element Discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity and layer depth, the Discretisation has a diagnostic potential vorticity that satisfies a stable upwinded advection equation through a Taylor–Galerkin scheme; this provides a mechanism for dissipating enstrophy at the gridscale whilst retaining optimal order consistency. We also use upwind discontinuous Galerkin schemes for the transport of layer depth. These transport schemes are incorporated into a semi-implicit formulation that is facilitated by a hybridisation method for solving the resulting mixed Helmholtz equation. We demonstrate that our Discretisation achieves the expected second order convergence and provide results from some standard rotating sphere test problems.

  • a variational boldsymbol h rm div finite Element discretization approach for perfect incompressible fluids
    Ima Journal of Numerical Analysis, 2018
    Co-Authors: Andrea Natale, Colin J Cotter
    Abstract:

    We propose a finite Element Discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite Element method that arises from a nonholonomic variational principle and an appropriately defined Lagrangian, where finite Element H(div) vector fields are identified with advection operators; this is the first successful extension of the structure-preserving Discretisation of Pavlov et al. (2009) to the finite Element setting. The resulting algorithm coincides with the energy-conserving scheme presented in Guzman et al. (2016). Through the variational derivation, we discover that it also satisfies a discrete analogous of Kelvin's circulation theorem. Further, we propose an upwind-stabilised version of the scheme which dissipates enstrophy whilst preserving energy conservation and the discrete Kelvin's theorem. We prove error estimates for this version of the scheme, and we study its behaviour through numerical tests.

Jemma Shipton - One of the best experts on this subject based on the ideXlab platform.

  • higher order compatible finite Element schemes for the nonlinear rotating shallow water equations on the sphere
    Journal of Computational Physics, 2018
    Co-Authors: Jemma Shipton, Thomas H Gibson, Colin J Cotter
    Abstract:

    Abstract We describe a compatible finite Element Discretisation for the shallow water equations on the rotating sphere, concentrating on integrating consistent upwind stabilisation into the framework. Although the prognostic variables are velocity and layer depth, the Discretisation has a diagnostic potential vorticity that satisfies a stable upwinded advection equation through a Taylor–Galerkin scheme; this provides a mechanism for dissipating enstrophy at the gridscale whilst retaining optimal order consistency. We also use upwind discontinuous Galerkin schemes for the transport of layer depth. These transport schemes are incorporated into a semi-implicit formulation that is facilitated by a hybridisation method for solving the resulting mixed Helmholtz equation. We demonstrate that our Discretisation achieves the expected second order convergence and provide results from some standard rotating sphere test problems.

Oliver Junge - One of the best experts on this subject based on the ideXlab platform.

  • higher order finite Element approximation of the dynamic laplacian
    Mathematical Modelling and Numerical Analysis, 2020
    Co-Authors: Nathanael Schilling, Gary Froyland, Oliver Junge
    Abstract:

    The dynamic Laplace operator arises from extending problems of isoperimetry from fixed manifolds to manifolds evolved by general nonlinear dynamics. Eigenfunctions of this operator are used to identify and track finite-time coherent sets, which physically manifest in fluid flows as jets, vortices, and more complicated structures. Two robust and efficient finite-Element Discretisation schemes for numerically computing the dynamic Laplacian were proposed in Froyland and Junge [SIAM J. Appl. Dyn. Syst. 17 (2018) 1891–1924]. In this work we consider higher-order versions of these two numerical schemes and analyse them experimentally. We also prove the numerically computed eigenvalues and eigenvectors converge to the true objects for both schemes under certain assumptions. We provide an efficient implementation of the higher-order Element schemes in an accompanying Julia package.