Journal of Scientific Computing

, Volume 19, Issue 1, pp 573–594

An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface

Authors

  • Jian-Jun Xu
    • Department of MathematicsUniversity of California
  • Hong-Kai Zhao
    • Department of MathematicsUniversity of California
Article

DOI: 10.1023/A:1025336916176

Cite this article as:
Xu, J. & Zhao, H. Journal of Scientific Computing (2003) 19: 573. doi:10.1023/A:1025336916176

Abstract

In this paper we study an Eulerian formulation for solving partial differential equations (PDE) on a moving interface. A level set function is used to represent and capture the moving interface. A dual function orthogonal to the level set function defined in a neighborhood of the interface is used to represent some associated quantity on the interface and evolves according to a PDE on the moving interface. In particular we use a convection diffusion equation for surfactant concentration on an interface passively convected in an incompressible flow as a model problem. We develop a stable and efficient semi-implicit scheme to remove the stiffness caused by surface diffusion.

moving interfaceslevel set methodsurface convection and diffusionsurfactantsemi-implicit method

Copyright information

© Plenum Publishing Corporation 2003