A single oblate spheroid settling in unbounded ambient fluid: A benchmark for simulations in steady and unsteady wake regimes

Abstract

We have performed spectral/spectral-element simulations of a single oblate spheroid with small geometrical aspect ratio settling in an unbounded ambient fluid, for a range of Galileo numbers covering the various regimes of motion (steady vertical, steady oblique, vertical periodic and chaotic). The high-fidelity data provided includes particle quantities (statistics in the chaotic case), as well as flow profiles and pressure maps. The reference data can be used as an additional benchmark for other numerical approaches, where a careful grid convergence study for a specific target parameter point is often useful. We further describe an extension of a specific immersed boundary method (Uhlmann, J. Comput. Phys, 209(2):448–476, 2005) to enable the tracking of non-spherical particles. Finally, the reference cases are computed with this immersed boundary method at various spatial and temporal resolutions, and grid convergence is discussed over the various regimes of spheroidal particle motion. The cross-validation results can serve as a guideline for the design of simulations with the aid of similar non-conforming methods, involving spheroidal particles with Galileo numbers of O(100).