An immersed boundary method for high-fidelity simulations of moving objects on a Cartesian mesh

Abstract

Despite breakthroughs in the field of computational fluid dynamics, performing simulations of moving objects with complex geometries on supercomputers remains a considerable challenge. Body-conforming methods are costly (due to re-meshing) and suffer from mesh-related issues. Hence, non-body-conforming Immersed Boundary Methods (IBMs), which eliminate re-meshing have emerged. Here, a simple and scalable Alternating Direction Reconstruction IBM (ADR-IBM) is proposed for high-fidelity simulations with multiple moving geometries in laminar and turbulent flows. The method imposes the boundary conditions at the walls via 1D cubic spline interpolations and is combined with high-order finite-difference schemes. The accuracy and convergence of the method are assessed for the flow around a cylinder at Re = 40. A comparison of second- and sixth-order schemes with the ADR-IBM is presented for 2D and 3D flows. The scalability of the method is demonstrated for up to 65,536 cores for the flow over a moving sphere at Re = 3700. Further, a Smooth Interface IBM is proposed for turbulent simulations of multiple moving geometries on supercomputers. It suppresses spurious force oscillations (SFOs) by smoothing the boundary interface. However, the ADR-IBM remains superior by providing lower error levels at lower cost with no treatment for the SFOs. Additionally, a harmonically forced laminar bluff body wake by two rear pitching flaps is studied. The forced flow over a 2D rectangle at Re = 100 is considered with in-phase and out-of-phase forcing. A fundamental (subharmonic) resonance is observed for the in-phase (out-of-phase) forcing. Both strategies produce significant drag reductions through a wake symmetrisation and propulsion mechanisms. It is postulated that the ejection of two vortex dipoles leads to the symmetrisation of the wake. Further, a single scaling parameter is proposed to predict the mean drag reduction of the forced flow. To identify the strategy with the highest net energy saving potential, the efficiency is assessed.