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

  • Authors:

  • Jian-Jun Xu;Hong-Kai Zhao

  • Affiliations:

  • Department of Mathematics, University of California, Irvine, California 92697. jxu@math.uci.edu;Department of Mathematics, University of California, Irvine, California 92697. zhao@math.uci.edu.

  • Venue:
  • Journal of Scientific Computing
  • Year:
  • 2003

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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.