NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (1), P. 140-145
ON THE STOKES FLOW COMPUTATION ALGORITHM BASED ON WOODBURY FORMULA
A. I. Popov – ITMO University, Kronverkskiy 49, 197101, St. Petersburg, Russia; popov239@gmail.com
I. S. Lobanov – ITMO University, Kronverkskiy 49, 197101, St. Petersburg, Russia
I.Yu. Popov – ITMO University, Kronverkskiy 49, 197101, St. Petersburg, Russia
T. V. Gerya – Institute of Geophysics, Department of Earth Sciences, Swiss Federal Institute of Technology Zurich (ETH), 5 Sonnegstrasse, CH-8092 Zurich, Switzerland; taras.gerya@erdw.ethz.ch
The Stokes approximation is used for the description of flow in nanostructures. An algorithm for Stokes flow 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 diculties of the finite-di fference 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.
Keywords: nanotube, Stokes flow, finite-di fference method.
PACS 47.10.ad, 47.11.Fg
DOI 10.17586/2220-8054-2015-6-1-140-145
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