A ghost-cell immersed boundary method for unified simulations of flow over finite- and zero-thickness moving bodies at large CFL numbers

Abstract

A ghost-cell immersed boundary method for unified simulations of flow over finite- and zero-thickness moving bodies at large Courant-Friedrichs-Lewy (CFL) numbers is presented. In order to handle such bodies in a unified manner, algorithms for interface construction and cell demarcation are proposed. The main challenge in treating zero-thickness bodies is to maintain sharpness and accuracy even at large CFL numbers with diminished spurious force oscillations. Thus, the effect of large CFL numbers on the solution accuracy of fluid-structure interaction (FSI) problems involving zero-thickness bodies is investigated and necessary treatments to preserve solution accuracy even at large CFL numbers are suggested. The present study suggests two treatments which are important in preserving the accuracy and stability of the solution: backward time integration for computational cells called 'swept-cells' and pressure boundary condition with mass conservation. Composite implicit time integration for the dynamic equation of a thin elastic structure is employed for a stable simulation of FSI at large CFL numbers. By using large time step sizes, the present method not only enhances computational efficiency, but also suppresses spurious force oscillations while maintaining the sharpness of an infinitesimally thin body. The efficacy and accuracy of the present method are examined through numerical examples.