Lightning Stokes solver

TL;DR

This paper extends lightning solvers, originally for Laplace and Helmholtz equations, to efficiently solve the 2D Stokes flow with high accuracy, demonstrating rapid computation and detailed flow features near singular corners.

Contribution

It introduces a novel extension of lightning solvers to the biharmonic equation for 2D Stokes flow, achieving high accuracy and fast computation.

Findings

Solutions computed to 10-digit accuracy in less than a second

Successfully resolved complex flow features near singular corners

Extended lightning solvers to biharmonic equations for fluid dynamics

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.