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A novel
regularization for higher accuracy in the solution of the
3-dimensional Stokes flow
J. Thomas Beale, Christina Jones, Jillian Reale and Svetlana Tlupova
Vol. 15 (2022), No. 3, 515–524
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Abstract |
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Many problems in fluid dynamics are effectively modeled as Stokes flows — slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the fluid velocity are the Stokeslet and stresslet. One of the main challenges in evaluating the boundary integrals is that the kernels become singular on the surface. A regularization method that eliminates the singularities and reduces the numerical error through correction terms for both the Stokeslet and stresslet integrals was developed by Tlupova and Beale (J. Comput. Phys. 386 (2019), 568–584). In this work we build on the previously developed method to introduce a new stresslet regularization that is simpler and results in higher accuracy when evaluated on the surface. Our regularization replaces a seventh-degree polynomial that results from an equation with two conditions and two unknowns with a fifth-degree polynomial that results from an equation with one condition and one unknown. Numerical experiments demonstrate that the new regularization retains the same order of convergence as the regularization developed by Tlupova and Beale but shows a decreased magnitude of the error. |
Keywords
Stokes flow, boundary integral equations, regularization
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Mathematical Subject Classification
Primary: 65B99
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Milestones
Received: 30 August 2021
Revised: 16 November 2021
Accepted: 18 November 2021
Published: 2 December 2022
Communicated by Michael Dorff
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Authors |
| J. Thomas Beale | |
| Department of Mathematics Duke University Durham, NC United States |
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| Christina Jones | |
| Department of Mathematics Farmingdale State College Farmingdale, NY United States |
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| Jillian Reale | |
| Department of Mathematics Farmingdale State College Farmingdale, NY United States |
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| Svetlana Tlupova | |
| Department of Mathematics Farmingdale State College Farmingdale, NY United States |
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