An immersed boundary method for flows with dense particle suspensions

The immersed boundary method (IBM) is a well-suited tool for the direct numerical simulation of flows with dense particle suspensions, which feature strong and complex flow-particle and particle–particle interactions. With the aim to model such flows, this paper proposes to extend the Regularised Discrete Momentum Forcing (RDMF-) IBM of Abdol Azis et al. (2018) to immersed boundaries (IBs) whose motion is coupled to the flow. A modification to the direct-forcing formulation, resulting in an offset of the imposed no-slip boundary from a moving immersed boundary, is proposed. This offset is exploited in an iterative strong flow-particle coupling scheme, where the boundary forces are applied at the location of the IB known from the previous time level, while correctly enforcing the no-slip condition at the new location of the IB. This avoids having to reconstruct the interpolation and spreading stencils for every linear iteration of the flow-particle coupling, therefore reducing the computational load of the method. A technique to ensure the stable modelling of flows involving light particles is also presented and is shown to stably cope with a wide range of particle–fluid density ratios. The framework is validated by comparing the results of the simulation of a single sedimenting sphere with published experimental results. Simulations of the fluidisation of heavy rigid particles, as well as of the ascent of closely packed light particles, are also presented. Use of the radius retraction procedure, to compensate for the diffuse representation of the smooth-interface IBM, is demonstrated to consistently yield significant improvements for moving IB cases with low to intermediate Reynolds numbers. The present framework shows good stability properties for a wide range of flow regimes with concentrated particle suspensions.