Lukas Bystricky: Resolving Stokes Flow Around Geometries With Sharp Corners
Time: Thu 2019-03-28 14.15 - 15.00
Lecturer: Lukas Bystricky, KTH
Location: KTH Mathematics, Lindstedtsvägen 25, floor 4, room 3418
Boundary integral methods can be used to efficiently solve creeping flow problems. In many physical applications it can be of interest to model flow around a geometry that contains one or more corners. In such cases the layer density function becomes singular at the corners. Standard Nyström discretization requires a highly refined grid around the corners to achieve acceptable accuracy. This leads to a significant increase in the computational cost and can become numerically unstable. By using a technique known as recursively compressed inverse preconditioning, we can solve the boundary integral equation without increasing the resolution beyond what is necessary to resolve the geometry. This technique does not require any knowledge about the behaviour of the layer density or the kernel near the corner, and allows the solution to the Stokes equations to be found to high digit accuracy even very close to corners. This allows the solution of interesting problems, including the investigation of drop movement near sharp corners.