Rigid, melting, and flowing fluid

This work focuses on the simulation of fluids as they transition between a solid and a liquid state, and as they interact with rigid bodies in a realistic fashion. The equations of motion that are generally considered appropriate only for liquids or gas can also be used to model solids. Without adding extra constraints, one can model a solid simply as a fluid with a high viscosity. This Melting and Flowing solver is a fast and stable system for animating materials that melt, flow, and solidify. Examples of real-world materials that exhibit these phenomena include melting candles, lava flow, the hardening of cement, icicle formation, and limestone deposition. Key to this fluid solver is the idea that we can plausibly simulate such phenomena by simply varying the viscosity inside a standard fluid solver, treating solid and nearly-solid materials as very high viscosity fluids. Another way to represent solids with the fluid equations is to add extra constraints to the equations. I use this representation in the parts of this work that focus on the two-way coupling of liquids with rigid bodies. The coupling affects both how the liquid moves the rigid bodies, and how the rigid bodies in turn affect the motion of the fluid. Distributed Lagrange multipliers are used to ensure two-way coupling that generates realistic motion for both the solid objects and the fluid as they interact with one another. The rigid fluid method is so named because the simulator treats the rigid objects as if they were made of fluid. The rigidity of such an object is maintained by identifying the region of the velocity field that is inside the object and constraining those velocities to be rigid body motion. The rigid fluid method is straightforward to implement, incurs very little computational overhead, and can be added as a bridge between current fluid simulators and rigid body solvers. Many solid objects of different densities (e.g., wood or lead) can be combined in the same animation.