Time stepping methods for coupled fluid-rigid body simulation

Abstract

Interaction between fluids and solid objects is ubiquitous in everyday life, yet the resulting motion is too intricate for visual effects artists and animators to realistically depict by hand. Instead, artists turn to computer graphics applications that employ physics-based animation to simulate these complex phenomena. Some of these applications solve the incompressible Euler equations coupled with the rigid body equations to compute the motion of an incompressible fluid interacting with undeformable solids. Of particular interest is two-way coupling, in which the fluid and solids both affect each other’s motion. Many methods have been developed to improve the realism of fluid simulations, allowing them to simulate more compelling scenarios. There are several time stepping schemes for fluid simulation in the literature, presenting ways to evolve the motion of the fluid over time that may generate more energetic or more accurate results. In particular, we focus on the BDF2 and Advection-Reflection families of schemes due to their accuracy and their improved ability to preserve the kinetic energy of the fluid. Our goal in this thesis is to extend these time stepping schemes to two-way coupled fluid-rigid body simulation, to yield more compelling simulations of the interactions between these two types of materials. We catalogue some of the popular time stepping schemes for fluid simulation, and explain their relations to methods of solving ordinary differential equations. Then, taking as our starting point the popular method of Batty et al., we re-derive the time stepping scheme originally proposed for coupled systems, and derive new schemes for coupled systems corresponding to the previously discussed fluid schemes, along the way comparing to the coupled time stepping scheme proposed by Gibou and Min. We measure the accuracy, energy-preservation, and computational cost properties of each scheme implemented within a 2D simulation, presenting quantitative and qualitative results. We hope our work encourages further investigation into the theoretical basis as well as the qualitative properties of coupled fluid-rigid body simulation.