Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces

  • Authors:

  • J. Thomas Beale;John Strain

  • Affiliations:

  • Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, United States;Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, CA 94720-3840, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2008

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Abstract

We present a new method for computing two-dimensional Stokes flow with moving interfaces that respond elastically to stretching. The interface is moved by semi-Lagrangian contouring: a distance function is introduced on a tree of cells near the interface, transported by a semi-Lagrangian time step and then used to contour the new interface. The velocity field in a periodic box is calculated as a potential integral resulting from interfacial and body forces, using a technique based on Ewald summation with analytically derived local corrections. The interfacial stretching is found from a surprisingly natural formula. A test problem with an exact solution is constructed and used to verify the speed, accuracy and robustness of the approach.