International Journal for Numerical Methods in Fluids

Cover image for Vol. 75 Issue 6

30 June 2014

Volume 75, Issue 6

Pages 385–465

  1. Research Articles

    1. Top of page
    2. Research Articles
    1. Improving the accuracy of discontinuous Galerkin schemes at boundary layers (pages 385–402)

      Florian J. Hindenlang, Gregor J. Gassner and Claus-Dieter Munz

      Version of Record online: 4 MAR 2014 | DOI: 10.1002/fld.3898

      Thumbnail image of graphical abstract

      The upper plot shows the boundary layer solution for a DG scheme of polynomial degree N = 4 on a stretched grid (line with symbols). We also plot the Jacobian of the elements J * . In the figure, we show the approximation error (u − uex), which is reduced by an order of magnitude when replacing the linear element mapping ( Ng = 1, constant Jacobian) by a high order mapping Ng > 1. This is due to the distributed resolution inside the grid cells, which is reflected in the smoothed Jacobian.

    2. A spectral quadrilateral multidomain penalty method model for high Reynolds number incompressible stratified flows (pages 403–425)

      J.A. Escobar-Vargas, P.J. Diamessis and T. Sakai

      Version of Record online: 13 MAR 2014 | DOI: 10.1002/fld.3899

      Thumbnail image of graphical abstract

      A two-dimensional quadrilateral spectral multidomain penalty method model is presented for the simulation of high Reynolds number incompressible stratified flows. Details on the space/time discretization are presented, as well as the challenges faced with the stabilization of the numerical solution and the efficient solution of the pressure Poisson equation. Performance of the multidomain model is assessed through its application to three standard benchmark cases and the propagation of a nonlinear internal wave of depression.

    3. A mode split, Godunov-type model for nonhydrostatic, free surface flow (pages 426–445)

      Scott F. Bradford

      Version of Record online: 18 MAR 2014 | DOI: 10.1002/fld.3901

      Thumbnail image of graphical abstract

      A new model is proposed for simulating wave transformation including breaking. It utilizes mode splitting in which the external (barotropic) mode is computed by solving a Riemann problem, whereas the internal (baroclinic) mode employs the traditional velocity-based upwind discretization. Model predictions are as accurate as a nonsplit model but require significantly less computational effort for four or more vertical layers of cells. The succeeding text shows surface predictions for a wave shoaling over a bar for different lateral grid resolutions.

    4. Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem (pages 446–465)

      M. Tayachi, A. Rousseau, E. Blayo, N. Goutal and V. Martin

      Version of Record online: 19 MAR 2014 | DOI: 10.1002/fld.3902

      Thumbnail image of graphical abstract

      In this work, we proceed to the mathematical analysis and proof of convergence of an iterative coupling strategy between models with different horizontal dimensions. The coupling of a 1D-2D toy model is fully investigated, while heuristics for more complicated non-linear models are provided.