ASYMPTOTIC STOKES FLOWS USING AXIAL GREEN FUNCTION METHOD WITH REFINEMENT

초록

The axial Green function methods (AGMs) have been developed for efficient numerical computations of the solutions of partial differential equations that come from physical phenomena, for instance, the electric potential, the heat, the convection-diffusion, and the flows. Recent progress in AGM enables us to calculate problems caused by the geometric singularity and/or multi-scale of a domain. The axial lines should be refined enough to resolve the solution near the geometric singular/extreme region of interest, and elsewhere the axial lines are coarsely distributed. This often gives rise to the non-matching axial lines along the interface between the extreme and the other regions. At the non-matching nodes on the interface, we develop how to glue the solutions together across the interface numerically. On the other hand, the stress/drag blow-up in Stokes flow is one of extreme phenomena of interest. Here, the stress blow-ups take place between two adjacent circular bodies that are asymptotically close. Since it is fundamental to understand singular behavior of the solution in this case, we accurately calculate the blow-up stress between close bodies to predict how serious it is. To do this efficiently, the AGM with refinement has to be employed. According to our calculation, the stress blow-up becomes the reciprocal of square distance between bodies, which is quite interesting result particularly in collision model.

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