The accuracy of the Immersed Boundary Method (IBM) of Uhlmann (2005) for particulate flows has been drastically improved, while the efficiency of the method is retained. The main modifications are: (1) the implementation of the multi-direct forcing scheme of Luo et al. (2007), (2) a slight retraction of the Lagrangian grid points from the surface towards the interior of a particle with a fraction of the grid spacing and (3) direct account of the acceleration of the fluid contained within the space occupied by the particles (Kempe et al., 2009). The effects of multi-direct forcing and retraction of the Lagrangian grid points are studied for slow flow through a regular array of fixed spheres. Increasing the number of iterations in multi-direct forcing improves the approximation of the desired no-slip / no-penetration conditions at the particle's surface. Two iterations are considered as optimal for increasing the accuracy with little loss in efficiency. Retraction appears to influence the order-of-convergence of the IBM: at a retraction of 0.3 times the grid spacing the IBM becomes second-order against the near first-order accuracy of the original method without retraction.
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