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

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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. © 2007 Elsevier Inc. All rights reserved.






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Beale, JT, and J Strain (2008). Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces. Journal of Computational Physics, 227(8). pp. 3896–3920. 10.1016/j.jcp.2007.11.047 Retrieved from https://hdl.handle.net/10161/6958.

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