Two-way coupling of fluids to rigid and deformable solids and shells

Abstract

Figure 1: (Left) Many rigid balls with varying densities plunge into a pool of water. (Center) Water splashes out of an elastic cloth bag. (Right) A balloon shoots upwards, releasing a jet of smoke. AbstractWe propose a novel solid/fluid coupling method that treats the coupled system in a fully implicit manner making it stable for arbitrary time steps, large density ratios, etc. In contrast to previous work in computer graphics, we derive our method using a simple back-ofthe-envelope approach which lumps the solid and fluid momenta together, and which we show exactly conserves the momentum of the coupled system. Notably, our method uses the standard Cartesian fluid discretization and does not require (moving) conforming tetrahedral meshes or ALE frameworks. Furthermore, we use a standard Lagrangian framework for the solid, thus supporting arbitrary solid constitutive models, both implicit and explicit time integration, etc. The method is quite general, working for smoke, water, and multiphase fluids as well as both rigid and deformable solids, and both volumes and thin shells. Rigid shells and cloth are handled automatically without special treatment, and we support fully one-sided discretizations without leaking. Our equations are fully symmetric, allowing for the use of fast solvers, which is a natural result of properly conserving momentum. Finally, for simple explicit time integration of rigid bodies, we show that our equations reduce to a form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though in four spatial dimensions rather than three.

Numerically stable fluid–structure interactions between compressible flow and solid structures

“…Similar to previous fluid-structure interaction methods, we apply pressure forces to the solid and enforce a velocity boundary condition on the fluid in order to satisfy a no-slip constraint. Unlike previous methods, however, we apply these coupled interactions implicitly by adding the constraint to the pressure system and combining it with any implicit solid forces in order to obtain a strongly coupled, symmetric indefinite system (similar to [17], which only handles incompressible flow). We also show that, under a few reasonable assumptions, this system can be made symmetric positive-definite by following the methodology of [16].…”

Fluid Simulation with Articulated Bodies

“…Guendelman et al [13] use a similar object velocity/fluid pressure coupling to animate the interaction of incompressible fluids with zero volume deformable and rigid shells. [3], [15]- [17] solve simultaneosly for the fluid pressure and solid velocity to obtain a fully implicit two-way solid-fluid coupling. We chose to use the Rigid Fluid method from Carlson et al [9] to model our rigid bodies interacting with incompressible fluid.…”

“…We recognize that other coupling techniques for solid/fluid interaction such as [3] may also be appropriate for our goals. We believe that our constraint-based solver will work equally well with the other approaches listed above.…”

“…In part, use of physical simulation has provided for some very good approaches for animating fluids (see [1], [2], [3], [4] for a review). Character animation either remains in the hands of talented animators with good tools for key-framing or is performed using data-driven animation.…”

“…In these situations the object does not cause any changes to the water. Only recently have we seen animations where the motion of the object affects the fluid and vice-versa [3], [9], [12]- [17]. We use a full two-way solid-fluid coupling enabling us to demonstrate effects that were not viable before.…”