The immersed boundary method for confined flows: Numerical diffusion and simulation accuracy of a boundary retraction scheme

Abstract

Diffuse-interface immersed boundary methods (IBM) have been successfully applied to numerous complex fluid–structure interaction problems because of their simple and efficient implementation. Despite their ability to suppress numerical oscillations significantly compared to sharp-interface methods, the diffuse interface is likely to reduce simulation accuracy of the flow field around the solid boundary. The present work investigates the diffusive effects of IBM and the mitigation method for surface-confined particulate flows by comparing results to sharp-interface methods. It is found that increasingly-confined geometries accentuate interface diffusion effects and decrease simulation accuracy. To minimise the diffusive effects of IBM, a boundary retraction scheme is used and its effectiveness is examined, in particular for particles in close contact where the diffuse interfaces overlap. It is shown that this simple implementation is capable of alleviating interface diffusion errors, thus increasing accuracy while limiting computational costs. With an optimal boundary retraction scheme, IBM can successfully capture fluid–structure interactions at different degrees of confinement, comparable to sharp-interface methods.