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.
Published Version (Please cite this version)10.1016/j.jcp.2007.11.047
Publication InfoBeale, JT; & Strain, J (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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J. Thomas Beale
Professor Emeritus of Mathematics
Here are five recent papers:J. T. Beale, Solving partial differential equations on closed surfaces with planar Cartesian grids, SIAM J. Sci. Comput. 42 (2020), A1052-A1070 or arxiv.org/abs/1908.01796S. Tlupova and J. T. Beale, Regularized single and double layer integrals in 3D Stokes flow, J. Comput. Phys. 386 (2019), 568-584 or arxiv.org/abs/1808.02177J. T. Beale and W. Ying, Solution of the Dirichlet problem by a finite difference analog of the boundary integral
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