Journal of Scientific Computing

, Volume 19, Issue 1, pp 573-594

First online:

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

  • Jian-Jun XuAffiliated withDepartment of Mathematics, University of California
  • , Hong-Kai ZhaoAffiliated withDepartment of Mathematics, University of California

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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 interfaces level set method surface convection and diffusion surfactant semi-implicit method