najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2015-6-1-140-145najo-1018Research ArticleCONTRIBUTED TALKSCONTRIBUTED TALKSOn the Stokes flow computation algorithm based on woodbury formulaPopovA. I.

Kronverkskiy 49, 197101, St. Petersburg

popov239@gmail.comLobanovI. S.

Kronverkskiy 49, 197101, St. Petersburg

PopovI. Yu.

Kronverkskiy 49, 197101, St. Petersburg

GeryaT. V.

5 Sonnegstrasse, CH-8092 Zurich

taras.gerya@erdw.ethz.chITMO UniversityRussian FederationInstitute of Geophysics, Department of Earth Sciences, Swiss Federal Institute of Technology Zurich (ETH)Switzerland20151508202561140145Copyright © Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V., 20252025Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V.Popov A.I., Lobanov I.S., Popov I.Y., Gerya T.V.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1018

The Stokes approximation is used for the description of flow in nanostructures. An algorithm for Stokes  ow computation in cases when there is great variation in the viscosity over a small spatial region is described. This method allows us to overcome computational dificulties of the  nite-dierence method. The background of the approach is using the Woodbury formula - a discrete analog of the Krein resolvent formula. The particular example of a rectangular domain is considered in detail. The inversion of the discrete Stokes operator is made in analytic form for the case of constant viscosity.

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The authors declare that there are no conflicts of interest present.