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

✍ Scribed by J. Thomas Beale; John Strain

• Book ID: 104021751
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 610 KB
• Volume: 227
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2007.11.047

✦ Synopsis

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.