Lightning Stokes solver
Numerical Analysis
2021-07-06 v1 Numerical Analysis
Abstract
Gopal and Trefethen recently introduced "lightning solvers" for the 2D Laplace and Helmholtz equations, based on rational functions with poles exponentially clustered near singular corners. Making use of the Goursat representation in terms of analytic functions, we extend these methods to the biharmonic equation, specifically to 2D Stokes flow. Solutions to model problems are computed to 10-digit accuracy in less than a second of laptop time. As an illustration of the high accuracy, we resolve two or more counter-rotating Moffatt eddies near a singular corner.
Cite
@article{arxiv.2107.01572,
title = {Lightning Stokes solver},
author = {Pablo D. Brubeck and Lloyd N. Trefethen},
journal= {arXiv preprint arXiv:2107.01572},
year = {2021}
}