Experience with DNS of particulate flow using a variant of the immersed boundary method

We perform a grid convergence study for a recently proposed immersed boundary method for DNS of particulate flows with interface resolution [Uhlmann, J. Comput. Phys., 209(2):448-476, 2005]. Two cases of vertical plane Poiseuille flow with suspended heavy particles (with terminal particle Reynolds number >100) are considered, in the laminar and in the turbulent flow regimes. The solutions obtained for different spatial refinements while keeping the CFL number constant are analyzed. A convergence rate of approximately second order in the mesh width is determined for the prediction of the particle motion in the laminar shear flow. A quantitative evaluation of the grid-related discrepancies is presented for the time-dependent individual particle velocity, the Lagrangian particle statistics and the Eulerian fluid statistics in the turbulent case.