A stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics

  • Authors:

  • Emilie Marchandise;Philippe Geuzaine;Nicolas Chevaugeon;Jean-François Remacle

  • Affiliations:

  • Université catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Fonds National de la Recherche Scientifique (FNRS), Rue d'Egmont 5, 10 ...;CENAERO, Multiphysics Group, Avenue Jean Mermoz 30, 6041 Gosselies, Belgium;Université catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium;Université catholique de Louvain, Department of Civil Engineering, Place du Levant 1, 1348 Louvain-la-Neuve, Belgium and Center for Systems Engineering and Applied Mechanics (CESAME), Univers ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

Quantified Score

Hi-index 31.50

Visualization

Abstract

A novel numerical method for solving three-dimensional two phase flow problems is presented. This method combines a quadrature free discontinuous Galerkin method for the level set equation with a pressure stabilized finite element method for the Navier Stokes equations. The main challenge in the computation of such flows is the accurate evaluation of surface tension forces. This involves the computation of the curvature of the fluid interface. In the context of the discontinuous Galerkin method, we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results. A more robust, second-order, least squares computation of the curvature that filters out the high frequencies and produces converged results is presented. This whole numerical technology allows to simulate a wide range of flow regimes with large density ratios, to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation.