Semi-implicit surface tension formulation with a Lagrangian surface mesh on an Eulerian simulation grid

  • Authors:

  • Craig Schroeder;Wen Zheng;Ronald Fedkiw

  • Affiliations:

  • Stanford University, 353 Serra Mall Room 207, Stanford, CA 94305, United States;Stanford University, 353 Serra Mall Room 207, Stanford, CA 94305, United States;Stanford University, 353 Serra Mall Room 207, Stanford, CA 94305, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

We present a method for applying semi-implicit forces on a Lagrangian mesh to an Eulerian discretization of the Navier Stokes equations in a way that produces a sparse symmetric positive definite system. The resulting method has semi-implicit and fully-coupled viscosity, pressure, and Lagrangian forces. We apply our new framework for forces on a Lagrangian mesh to the case of a surface tension force, which when treated explicitly leads to a tight time step restriction. By applying surface tension as a semi-implicit Lagrangian force, the resulting method benefits from improved stability and the ability to take larger time steps. The resulting discretization is also able to maintain parasitic currents at low levels.