International Journal for Numerical Methods in Fluids

Cover image for Vol. 73 Issue 11

20 December 2013

Volume 73, Issue 11

Pages 927–1000

  1. Review Article

    1. Top of page
    2. Review Article
    3. Research Articles
    1. An efficient and stable finite element solver of higher order in space and time for nonstationary incompressible flow (pages 927–952)

      S. Hussain, F. Schieweck and S. Turek

      Version of Record online: 24 JUL 2013 | DOI: 10.1002/fld.3831

      Thumbnail image of graphical abstract

      In this paper, we present the numerical study of fully implicit continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time-stepping schemes for incompressible flow. In particular, we analyze numerically the higher order dG(1) and cGP(2) methods which are super-convergent of third, resp., fourth order in time, whereas for the space discretization, the well-known LBB-stable finite element pair inline image of third order accuracy is used. We perform nonstationary simulations for two benchmarking configurations to analyze the temporal accuracy and efficiency of the presented time discretization schemes w.r.t. CPU and numerical costs.

  2. Research Articles

    1. Top of page
    2. Review Article
    3. Research Articles
    1. A new weighted upwind finite volume element method based on non-standard covolume for time-dependent convection–diffusion problems (pages 953–975)

      Fuzheng Gao and Dong Liang

      Version of Record online: 22 JUL 2013 | DOI: 10.1002/fld.3830

      Thumbnail image of graphical abstract

      In this paper, based on non-standard covolume grids, we propose a new kind of high-order weighted upwind finite volume element method for the time-dependent convection–diffusion problems. For the proposed scheme, we strictly prove the stability and mass conservation in the discrete forms and optimal second-order error estimate in L 2-norm in spatial step. The scheme is effective for avoiding numerical diffusions and nonphysical oscillations and has a second-order accuracy.

    2. A depth-integrated non-hydrostatic finite element model for wave propagation (pages 976–1000)

      Zhangping Wei and Yafei Jia

      Version of Record online: 29 JUL 2013 | DOI: 10.1002/fld.3832

      Thumbnail image of graphical abstract

      We develop a finite element based depth-integrated non-hydrostatic wave model, which can properly handle linear and nonlinear dispersive waves, wave shoaling, diffraction, refraction and focusing. We derive a physically bounded, non-oscillatory and quasi second-order upwind scheme, which is applied to approximate advection terms in our wave model.

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