Chaotic Behaviour of Multiple Immersed Ellipsoids

Building on previous work (Essmann et al, 2020) exploring the complex dynamics of a single immersed ellipsoid, we investigate the dynamics of multiple immersed ellipsoids under both inviscid and viscous environments. Earlier, using our in-house fully-coupled 6DoF solid-fluid DNS solver, GISS (https://github.com/eessmann/GISS, Essmann et al 2020), we showed that a single body can present chaotic motions even under viscous environments under certain conditions due to vortex shedding. Here, we extend Kirchoff’s equations to multiple bodies under inviscid conditions, using Lamb (1932) as a starting point. Analytical solutions for added mass and inertia are no longer available for multiple bodies, and so we solve for the potential flow using boundary integral equations (BIE), and resolve for the forces on the bodies by evaluating the flow using a regularisation of the hypersingular BIE (Toh et al, 1994). Calculations are carried out in Rust and are parallelised with a high degree of efficiency. Rotational motion is represented using quaternions. Using recurrence quantification and cross-correlation analyses (Marwan et al, 2007), we will present how we can characterise chaos and how the number of solids affects chaos.