A two‐grid fictitious domain method for direct simulation of flows involving non‐interacting particles of a very small size

Abstract

AbstractThe full resolution of flows involving particles whose scale is hundreds or thousands of times smaller than the size of the flow domain is a challenging problem. A naive approach would require a tremendous number of degrees of freedom in order to bridge the gap between the two spatial scales involved. The approach used in the present study employs two grids whose grid size fits the two different scales involved, one of them (the micro‐scale grid) being embedded into the other (the macro‐scale grid). Then resolving first the larger scale on the macro‐scale grid, we transfer the so obtained data to the boundary of the micro‐scale grid and solve the smaller size problem. Since the particle is moving throughout the macro‐scale domain, the micro‐scale grid is fixed at the centroid of the moving particle and therefore moves with it. In this study we combine such an approach with a fictitious domain formulation of the problem resulting in a very efficient algorithm that is also easy to implement in an existing CFD code. We validate the method against existing experimental data for a sedimenting sphere, as well as analytical results for motion of an inertia‐less ellipsoid in a shear flow. Finally, we apply the method to the flow of a high aspect ratio ellipsoid in a model of a human lung airway bifurcation. Copyright © 2009 John Wiley & Sons, Ltd.