Short Note: On the properties and limitations of the height function method in two-dimensional Cartesian geometry

  • Authors:

  • G. Bornia;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;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:
  • 2011

Quantified Score

Hi-index 31.45

Visualization

Abstract

In this study we define the continuous height function to investigate the approximation of an interface line and its geometrical properties with the height function method. We show that in each mixed cell the piecewise linear interface reconstruction and the approximation of the derivatives and curvature based on three consecutive height function values are second-order accurate. We also discuss the quadratic reconstruction and fourth-order accurate expressions of the normal and curvature. We present a hierarchical algorithm to compute the normal vector and curvature of an interface line with the height function method that switches automatically between second- and fourth-order approximations and that can be applied also when the local radius of curvature is of the order of the grid spacing.