An Efficient Solver for Two-way Coupling Rigid Bodies with Incompressible Flow

We present an efficient solver for monolithic two-way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low-dimensional nature of the solid equations. We observe that a single Multigrid V-cycle for the fluid equations serves as a very effective preconditioner for solving the Schur-complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly-free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two-way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation.