Fractional Step Method for Simulations of Dilute Suspensions at Low Reynolds Numbers.

This study investigates a new proposed fractional step method for low Reynolds number flows. Previous attempts to simulate these flows with the typical fractional step method were constrained by a limited allowable time step size, resulting in high computational costs. Our new solution involves introducing a simple Reynolds number scaling in the fractional step method, which eliminates the restriction on time step size without sacrificing the accuracy of the results. We looked at two scenarios, first a simple channel flow case, which is fundamental to many biological applications. Secondly, we look at fluid-structure interaction cases to examine the rheology of neutrally buoyant rigid ellipsoid particles in periodic suspension which is a more complex case, and the Reynolds number approaches zero. With the typical fractional step method for Reynolds number 0.000001, the required time size (dt) was six orders smaller than the newly proposed fractional step method. This method enables us to investigate the effect of the wall on the rheology of dilute suspensions. We found that as we decrease the distance along the transverse direction, the stresslet of the suspension dramatically changes.