On the Stokes flow computation algorithm based on woodbury formula
https://doi.org/10.17586/2220-8054-2015-6-1-140-145
Abstract
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.
Supporting agencies: This work was partially nancially supported by the Government of the Russian Federation (grant 074-U01), by the Ministry of Science and Education of the Russian Feder-ation (GOSZADANIE 2014/190, Project 14.Z50.31.0031), by grant MK-5001.2015.1 of the President of the Russian Federation.
About the Authors
A. I. Popov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy 49, 197101, St. Petersburg
I. S. Lobanov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy 49, 197101, St. Petersburg
I. Yu. Popov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy 49, 197101, St. Petersburg
T. V. Gerya
Institute of Geophysics, Department of Earth Sciences, Swiss Federal Institute of Technology Zurich (ETH)
Switzerland
Switzerland
5 Sonnegstrasse, CH-8092 Zurich
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Review
For citations:
Popov A.I., Lobanov I.S., Popov I.Yu., Gerya T.V. On the Stokes flow computation algorithm based on woodbury formula. Nanosystems: Physics, Chemistry, Mathematics. 2015;6(1):140-145. https://doi.org/10.17586/2220-8054-2015-6-1-140-145
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