Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
by R. J. LeVeque and Z. Li SIAM J. Sci. Comput 18(1997), p.. 709-735.

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.

Keywords. Stokes flow, creeping flow, interface tracking, discontinuous coefficients, immersed interface methods, Cartesian grids, bubbles

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bibtex entry:

@Article{rjl-li:stokes,
  author =       "R. J. LeVeque and Z. Li",
  title =        "Immersed interface methods for {S}tokes flow with
                 elastic boundaries or surface tension",
  journal =      "SIAM J. Sci. Comput.",
  year =         "1997",
  volume =       "18",
  pages =        "709--735",
}