A direct-forcing fictitious domain method for particulate flows

A direct-forcing fictitious domain (DF/FD) method for the simulation of particulate flows is reported. The new method is a non-Lagrange-multiplier version of our previous DLM/FD code and is obtained by employing a discrete δ-function in the form of bi(tri-) function to transfer explicitly quantities between the Eulerian and Lagrangian nodes, as in the immersed boundary method. Due to the use of the collocation-point approach for the rigidity constraint and the integration over the particle domain, the Lagrangian nodes are retracted a little from the particle boundary. Our method in case of a prescribed velocity on the boundary is verified via the comparison to the benchmark results on the flow over a fixed cylinder in a wide channel and to our spectral-element results for a channel with the width of four cylinder diameters. We then verify our new method for the case of the particulate flows through various typical flow situations, including the sedimentation of a circular particle in a vertical channel, the sedimentation of a sphere in a vertical pipe, the inertial migration of a sphere in a circular Poiseuille flow, the behavior of a neutrally-buoyant sphere in Couette flow, and the rotation of a prolate spheroid in Couette flow. The accuracy and robustness of the new method are fully demonstrated, in particular for the case of relatively low Reynolds numbers and the neutrally-buoyant case.