Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
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.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- April 2008
- DOI:
- 10.1016/j.jcp.2007.11.047
- Bibcode:
- 2008JCoPh.227.3896B