Abstract
A regular-grid volume-integration algorithm has been previously developed for solving non-homogeneous versions of the Laplace and the elasticity equations. This note demonstrates that the same approach can be successfully adapted to the case of non-homogeneous, incompressible Stokes flow. The key observation is that the Stokeslet (Green’s function) can be written as \(\mathcal {U}=\mu \nabla ^{2}\mathcal {H}\), where \(\mathcal {H}\) has a simple analytical expression. As a consequence, the volume integral can be reformulated as an easily evaluated boundary integral, together with a remainder domain integral that can be computed using a regular cuboid grid covering the domain.
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Acknowledgments
The authors are grateful to Prof. B. Quaife for kindly pointing out several important references. L. J. Gray gratefully acknowledges an MTS Visiting Professorship Grant at the University of Minnesota, and he would like to thank Profs. S. Mogilevskaya, J. Labuz, and S. Crouch for the hospitality at the Department of Civil Engineering. The participation of J. Jakowski was facilitated by J. Williams and Dr. D. Pickel of the Mathematics Department, Oak Ridge High School. M. N. J. Moore acknowledges support from the Simmons Foundation, Grant 524259.
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Communicated by: Jon Wilkening
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Gray, L.J., Jakowski, J., Moore, M.N.J. et al. Boundary integral analysis for non-homogeneous, incompressible Stokes flows. Adv Comput Math 45, 1729–1734 (2019). https://doi.org/10.1007/s10444-019-09699-5
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DOI: https://doi.org/10.1007/s10444-019-09699-5