A wall treatment for confined Stokes flow
(English)Article in journal (Other academic) Submitted
The study of bodies immersed in Stokes flow is crucial in various microfluidic applications. Recasting the governing equations in a boundary integral formulation reduces the three-dimensional problem to two-dimensional integral equations to be discretized over the surface of the submerged objects. The present work focuses on the development and validation of a wall treatment where the wall is discretized in the same fashion as the immersed bodies. For this purpose, a set of high-order quadrature rules for the numerical integration of integrals containing the singular Green’s function-the so-called Stokeslet - has been developed. By coupling the wall discretization to the discretization of immersed objects, we exploit the structure of the block matrix corresponding to the wall discretization in order to substantially reduce the memory usage. For validation, the classical problem of a sedimenting sphere in the vicinity of solid walls is studied.
IdentifiersURN: urn:nbn:se:kth:diva-29762OAI: oai:DiVA.org:kth-29762DiVA: diva2:397505
QS 201203282011-02-152011-02-152012-11-22Bibliographically approved