Chaotic Orbits of Multiple Immersed Bodies

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 (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. Now, 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 not 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 interpolating over the body and integrating. Calculations are carried out in Rust and are parallelised with a high degree of efficiency. Using recurrence quantification and cross-correlation analyses (Marwan et al, 2007), we present ways to characterise chaos. We show that chaos is a strong function of interparticulate distance, number of solids and density ratio. Results are compared to DNS simulations run on Xcompact3D (https://www.incompact3d.com/).