11

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

Download

Leave a Reply

Your email address will not be published. Required fields are marked *

*

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>