Nearly singular integrals in 3D stokes flow

A straightforward method is presented for computing three-dimensional Stokes flow, due to forces on a surface, with high accuracy at points near the surface. The flowquantities arewritten as boundary integrals using the free-spaceGreen's function. To evaluate the integrals near the boundary, the singular kernels are regularized and a simple quadrature is applied in coordinate charts. High order accuracy is obtained by adding special corrections for the regularization and discretization errors, derived here using local asymptotic analysis. Numerical tests demonstrate the uniform convergence rates of the method. © 2013 Global-Science Press.

Duke Scholars

Author J. Thomas Beale Mathematics