A geometrical predictor-corrector advection scheme and its application to the volume fraction function

  • Authors:

  • A. Cervone;S. Manservisi;R. Scardovelli;S. Zaleski

  • Affiliations:

  • DIENCA-Lab. di Montecuccolino, Universití degli Studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy;DIENCA-Lab. di Montecuccolino, Universití degli Studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy;DIENCA-Lab. di Montecuccolino, Universití degli Studi di Bologna, Via dei Colli 16, 40136 Bologna, Italy;Institut Jean Le Rond d'Alembert (IJLRdA), UMR 7190, Université Pierre et Marie Curie - Paris 6 and CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

We present a multidimensional Eulerian advection method for interfacial and incompressible flows in two-dimensional Cartesian geometry. In the scheme we advect the grid nodes backwards along the streamlines to compute the pre-images of the grid lines. These pre-images are approximated by continuous, piecewise-linear lines. The enforcement of the discrete version of the incompressibility constraint is a very important issue to determine correctly the flux polygons and to reduce considerably the integration, discretization and interpolation numerical errors. The proposed method compares favorably with other previous multidimensional advection methods as long as the initial interface line is well reconstructed. Conversely, we show that when the interface is very fragmented the total numerical error is completely dominated by the reconstruction error and in these conditions it is very difficult to assess which advection scheme is the most reliable one.