International Journal for Numerical Methods in Fluids

Cover image for Vol. 71 Issue 5

20 February 2013

Volume 71, Issue 5

Pages 537–670

  1. Research Articles

    1. Top of page
    2. Research Articles
    1. A simple SPH algorithm for multi-fluid flow with high density ratios (pages 537–561)

      J. J. Monaghan and Ashkan Rafiee

      Version of Record online: 29 MAR 2012 | DOI: 10.1002/fld.3671

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      In this paper, we show that problems involving two fluids, with density ratios up to at least 1000, can be simulated by means of a simple modification to standard SPH equations. The simulations treat liquids as slightly compressible with a Mach number of 0.1. Convergence is established for a wide variety of problems including themotion of an ellipsoid composed of two fluids, the Rayleigh-Taylor instability, interface waves, and gravity currents.

    2. Using symbolic computation software packages in production of multidimensional finite volume-based large eddy simulation codes (pages 562–583)

      A. Aprovitola and F. M. Denaro

      Version of Record online: 30 MAR 2012 | DOI: 10.1002/fld.3673

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      We illustrated an original multidimensional finite volume-based upwind method suitable for large eddy simulation. We also examined the local truncation errors in wave number space. The use of symbolic calculation software for developing the flux integration was illustrated in this paper. Furthermore, we tested the results for both analytical solutions and plane channel turbulent flow. Finally, we concluded that the use of dedicated symbolic software is suitable in developing and validating a large eddy simulation code.

    3. A novel multidimensional solution reconstruction and edge-based limiting procedure for unstructured cell-centered finite volumes with application to shallow water dynamics (pages 584–633)

      A. I. Delis and I. K. Nikolos

      Version of Record online: 17 APR 2012 | DOI: 10.1002/fld.3674

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      A novel geometrical approach for linear reconstruction and limiting of the numerical solution on cell-centered finite volume methods, which is independent of the (approximate) Riemann solver used, is presented. Within the proposed reconstruction, edge-based limiters can be applied in a multi-dimensional manner to control the oscillatory behavior of the solution, avoiding the procedure of solving any minimization problems or tuning parameters. Extensive convergence comparisons are presented for two different solution gradient computations, identifying the one that satisfies the good neighborhood property for limiting.

    4. An assessment of particle methods for approximating anisotropic dispersion (pages 634–651)

      Paulo A. Herrera and Roger D. Beckie

      Version of Record online: 18 APR 2012 | DOI: 10.1002/fld.3676

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      We derive a smoothed particle hydrodynamics (SPH) approximation for anisotropic dispersion and compare it with the particle strength exchange (PSE) formulation and a standard finite volume formulation. We show that, given an appropriate selection of numerical parameters and regular particle distribution, the new SPH approximation is comparable with the PSE and the finite volume approximations. We also show that the performance of the SPH and PSE approximations decreases as the degree of disorder of the particle increases; however, the accuracy and convergence properties of both particle methods can be improved by an appropriate choice of some numerical parameters such as kernel core size and kernel function.

    5. Third-order sensitivity analysis for robust aerodynamic design using continuous adjoint (pages 652–670)

      D. I. Papadimitriou and K. C. Giannakoglou

      Version of Record online: 12 APR 2012 | DOI: 10.1002/fld.3677

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      An objective function for robust design problems includes the mean value and standard deviation of the shape performance, that is first-order and second-order derivatives with respect to the environmental variables, if second-order Taylor expansion is used. Working with gradient-based methods, this function should be differentiated with respect to the design variables. A method, based on the continuous adjoint and direct differentiation, for computing these third-order mixed derivatives is presented with applications in ducts and turbomachinery cascades.