Direct numerical simulations of the swirling von Kármán flow using a semi-implicit moving immersed boundary method

We present a novel moving immersed boundary method (IBM) and employ it in direct numerical simulations (DNS) of the closed-vessel swirling von Karman flow laminar turbulent regimes. The IBM extends direct-forcing approaches by leveraging time integration scheme, that embeds forcing step within semi-implicit iterative Crank-Nicolson scheme. overall is robust, stable, yields excellent results canonical cases with static boundaries. allows us to reproduce geometry parameters experiments (F. Ravelet, A. Chiffaudel, F. Daviaud, JFM 601, 339 (2008)) on Cartesian grid. In these DNS, driven two-counter rotating impellers fitted curved inertial stirrers. analyze transition from increasing rotation rate counter-rotating attain four Reynolds numbers 90, 360, 2000, 4000. regime at number 90 we observe features similar those reported particular, appearance symmetry-breaking instability 360. transitional turbulence 2000. Fully developed achieved Non-dimensional torque computed matches correlations experimental data. low symmetries, lost number, are recovered mean fully regime, where two tori symmetrical about mid-height plane. note fluctuations central region device remain anisotropic even highest 4000, suggesting isotropization requires significantly higher numbers.