Stochastic modeling of immersed rigid-body dynamics

The simulation of immersed rigid-body dynamics involves the coupling between objects and turbulent flows, which is a complicated task in computer animation. In this paper, we propose a stochastic model of the dynamics of rigid bodies immersed in viscous flows to solve this problem. We first modulate the dynamic equations of rigid bodies using generalized Kirchhoff equations (GKE). Then, a stochastic differential equation called the Langevin equation is proposed to represent the velocity increments due to the turbulences. After the precomputation of the Kirchhoff tensor and the kinetic energy of a synthetic turbulence induced by the object moving, we utilize a fractional-step method to solve the GKE with vortical loads of drag and lift dynamics in runtime. The resulting animations include both inertial and viscous effects from the surrounding flows for arbitrary geometric objects. Our model is coherent and effective to simulate immersed rigid-body dynamics in real-time.