High-fidelity simulations of full-flight soccer ball aerodynamics using a monolithic overset approach

Abstract This paper presents a high-fidelity model to simulate the three-dimensional full-flight aerodynamics of a spinning soccer ball during a free kick. The simulation accounts for the Magnus effect–an aerodynamic phenomenon where spin induces lateral forces–by solving Navier–Stokes equations of incompressible flows and rigid-body motion in a fully coupled fluid-object interaction setting. A monolithic overset approach, which combines a boundary-fitted moving mesh around the ball with a stationary background mesh, is developed to accurately capture near-ball flow features while allowing unrestricted ball motion in 3D space. The monolithic approach solves the flow equations on overlapping domains without using subdomain iterations. A series of simulations is performed across varying initial kick speed and spin rate to quantify their effects on the ball trajectories systematically. The results reveal that the spin rate has a significant influence on lateral deviation due to the Magnus effect, while the initial kick speed has a substantial impact on overall flight range and flight time. Comparisons between a realistic soccer ball and an idealized smooth ball highlight the aerodynamic role of surface features, with smoother balls exhibiting a more substantial Magnus effect and greater lateral deviation. Furthermore, we compare the CFD results with predictions from a conventional ordinary differential equation (ODE) model using empirical drag coefficients. These comparisons show clear limitations in the ODE-based model, particularly under high-Reynolds-number flow regimes.