A versatile implicit iterative approach for fully resolved simulation of self-propulsion

摘要

We present a computational approach for fully resolved simulation of self-propulsion of organisms through a fluid. A new implicit iterative algorithm is developed that solves for the swimming velocities of the organism with prescribed deformation kinematics. A solution for the surrounding flow field is also obtained. This approach uses a constraint-based formulation of the problem of self-propulsion developed by Shirgaonkar et al. [1]. The approach in this paper is unlike the previous work [1] where a fractional time stepping scheme was used. Fractional time stepping schemes, while efficient for moderate to high Reynolds number problems, are not suitable for zero or low Reynolds number problems where the inertia term in the governing equation is absent or negligible. In such cases the implicit iterative algorithm presented here is more appropriate. We validate the method by simulating self-propulsion of bacterial flagellum, jellyfish (Aurelia aurita), and larval zebrafish (Danio rerio). Comparison of the computational results with theoretical and experimental results for the test cases is found to be very good.