International Journal for Numerical Methods in Fluids

Cover image for Vol. 74 Issue 7

10 March 2014

Volume 74, Issue 7

Pages 469–542

  1. Research Articles

    1. Top of page
    2. Research Articles
    1. Assessment of a discontinuous Galerkin method for the simulation of vortical flows at high Reynolds number (pages 469–493)

      C. Carton de Wiart, K. Hillewaert, M. Duponcheel and G. Winckelmans

      Version of Record online: 14 NOV 2013 | DOI: 10.1002/fld.3859

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      The Taylor–Green vortex at Re = 1600 is considered to assess a discontinuous Galerkin method for the direct numerical simulation of high Reynolds number flows. Grid convergence, order convergence and comparison with the fourth-order finite difference method are performed on hexahedral grids, showing the ability of discontinuous Galerkin method to capture the flow features using reasonably small resolution. Finally, the method is successfully applied on unstructured meshes composed of prismatic or tetrahedral elements. Although the energy spectrum is overpredicted on the high wavenumber range, the dissipation rate captured is not significantly impacted by the element type.

    2. A new matrix dissipation model for central scheme (pages 494–513)

      Xinrong Su and Satoru Yamamoto

      Version of Record online: 25 OCT 2013 | DOI: 10.1002/fld.3860

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      Based on the flow physics analysis about the Rankine-Hugoniot jump condition, this paper proposes a new matrix dissipation model for the widely used central scheme. Current method has better accuracy and improved vortical flow predictability. At the same time it preserves the excellent properties of original method, including shock capturing and convergence speed. A set of numerical examples verify the excellent performance of current method and its potential use in routine applications.

    3. Equivalence conditions between linear Lagrangian finite element and node-centred finite volume schemes for conservation laws in cylindrical coordinates (pages 514–542)

      D. De Santis, G. Geraci and A. Guardone

      Version of Record online: 27 NOV 2013 | DOI: 10.1002/fld.3862

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      Equivalence conditions relating the mass-lumped Bubnov–Galerkin finite element scheme for Lagrangian linear elements to node-centred finite volume schemes are derived for the first time for conservation laws in a three-dimensional cylindrical reference.

      The two-dimensional schemes for the polar and the axisymmetrical cases are also explicitly derived.

      Results from numerical simulations of expanding and converging shock problems and of the interaction of a converging shock waves with obstacles agree fairly well with one-dimensional simulations and simplified models.