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Regularized single and double layer integrals in 3D Stokes flow

Publication ,  Journal Article
Tlupova, S; Beale, JT
Published in: Journal of Computational Physics
June 1, 2019

We present a numerical method for computing the single layer (Stokeslet) and double layer (stresslet) integrals in Stokes flow. The method applies to smooth, closed surfaces in three dimensions, and achieves high accuracy both on and near the surface. The singular Stokeslet and stresslet kernels are regularized and, for the nearly singular case, corrections are added to reduce the regularization error. These corrections are derived analytically for both the Stokeslet and the stresslet using local asymptotic analysis. For the case of evaluating the integrals on the surface, as needed when solving integral equations, we design high order regularizations for both kernels that do not require corrections. This approach is direct in that it does not require grid refinement or special quadrature near the singularity, and therefore does not increase the computational complexity of the overall algorithm. Numerical tests demonstrate the uniform convergence rates for several surfaces in both the singular and near singular cases, as well as the importance of corrections when two surfaces are close to each other.

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Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

June 1, 2019

Volume

386

Start / End Page

568 / 584

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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Tlupova, S., & Beale, J. T. (2019). Regularized single and double layer integrals in 3D Stokes flow. Journal of Computational Physics, 386, 568–584. https://doi.org/10.1016/j.jcp.2019.02.031
Tlupova, S., and J. T. Beale. “Regularized single and double layer integrals in 3D Stokes flow.” Journal of Computational Physics 386 (June 1, 2019): 568–84. https://doi.org/10.1016/j.jcp.2019.02.031.
Tlupova S, Beale JT. Regularized single and double layer integrals in 3D Stokes flow. Journal of Computational Physics. 2019 Jun 1;386:568–84.
Tlupova, S., and J. T. Beale. “Regularized single and double layer integrals in 3D Stokes flow.” Journal of Computational Physics, vol. 386, June 2019, pp. 568–84. Scopus, doi:10.1016/j.jcp.2019.02.031.
Tlupova S, Beale JT. Regularized single and double layer integrals in 3D Stokes flow. Journal of Computational Physics. 2019 Jun 1;386:568–584.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

June 1, 2019

Volume

386

Start / End Page

568 / 584

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences