Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension

  • Authors:

  • Randall J. LeVeque;Zhilin Li

  • Affiliations:

  • -;-

  • Venue:
  • SIAM Journal on Scientific Computing
  • Year:
  • 1997

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Abstract

A second-order accurate interface tracking method for the solution of incompressible Stokes flow problems with moving interfaces on a uniform Cartesian grid is presented. The interface may consist of an elastic boundary immersed in the fluid or an interface between two different fluids. The interface is represented by a cubic spline along which the singularly supported elastic or surface tension force can be computed. The Stokes equations are then discretized using the second-order accurate finite difference methods for elliptic equations with singular sources developed in our previous paper [SIAM J. Numer. Anal., 31(1994), pp. 1019--1044]. The resulting velocities are interpolated to the interface to determine the motion of the interface. An implicit quasi-Newton method is developed that allows reasonable time steps to be used.