Abstract: We present 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. We animate such phenomena by physical simulation of fluids - in particular the incompressible viscous Navier-Stokes equations with free surfaces, treating solid and nearly-solid materials as very high viscosity fluids. The computational method is a modification of the Marker-and-Cell (MAC) algorithm in order to rapidly simulate fluids with variable and arbitrarily high viscosity. This allows the viscosity of the material to change in space and time according to variation in temperature, water content, or any other spatial variable, allowing different locations in the same continuous material to exhibit states ranging from the absolute rigidity or slight bending of hardened wax to the splashing and sloshing of water. We create detailed polygonal models of the fluid by splatting particles into a volumetric grid and we render these models using ray tracing with sub-surface scattering. We demonstrate the method with examples of several viscous materials including melting wax and sand drip castles.