A space-time adaptive approach to orientation dynamics in particle laden flows

Abstract 1949 Toms discovered that a minute amount of polymer fibers suspended into a Newtonian solvent can increase the flow-rate of the fluid and thus reduce the turbulent drag. Today, the mechanism behind this effect is still not completely understood. We aim at studying this phenomenon numerically by directly solving the governing FokkerPlanck equation (FoP) for particle orientation statistics. From a numerical analysis point of view, this is a convectiondominated convection-diffusion equation in orientation space where the convection term depends on the fluid flow. Since the orientation space is naturally given by the surface of the unit sphere, we tackle the problem by combining a geodesic grid discretization with the Finite Volume Method (FVM). Due to an isolated moving peak in the solution of the FoP, we employ a space-time adaptive approach and discuss the performance of the adaptive algorithm with respect to different refinement strategies for an analytical test problem (simple shear flow) and for input data from the direct numerical simulation of a turbulent channel flow. Furthermore, the results are compared to previous approaches based on uniform grids. It turns out that the space-time adaptive algorithm is indeed advantageous for certain flow fields but so far not as robust as approaches with fixed grids.

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