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The Far-field Green’s Integral in Stokes Flow from the Boundary Integral Formulation

E.A. Chadwick1
1 University of Salford, UK.

Computer Modeling in Engineering & Sciences 2013, 96(3), 177-184.


In boundary integral methods for Stokes flow, the far-field Green’s integral is usually taken to be zero without proof. However, this is not obviously the case, the reason being that Stokes flow is a near-field approximation and breaks down in the far-field. Here, we show that it is zero as expected by matching it to a far-field Green’s integral in Oseen flow. Hence, there are similarities to the matched asymptotic procedure matching a near-field Stokes flow to a far-field Oseen flow, except in this case a different and new procedure is required to deal with the Green’s integrals. In particular, the velocity is represented in the near-field by an integral distribution of stokeslets, and in the far-field by an integral distribution of oseenlets, and the two integral distributions are matched together by equating the stokeslets with the oseenlets in the matching region. A boundary integral representation is then obtained which holds throughout the whole flow region, enabling the velocity in the boundary integral scheme to be determined everywhere in the flow region.


Stokes flow, Green’s integral, Boundary Integral, matching preparation.

Cite This Article

Chadwick, E. (2013). The Far-field Green’s Integral in Stokes Flow from the Boundary Integral Formulation. CMES-Computer Modeling in Engineering & Sciences, 96(3), 177–184.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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