Realistic animation of liquids

We present a comprehensive methodology for realistically animating liquid phenomena. Physically accurate 3D motion is achieved by performing a two-stage calculation over an arbitrary environment of static obstacles surrounded by fluid. A finite difference approximation to the Navier-Stokes equations is first applied to a low resolution, voxelized representation of the scene. The resulting velocity and pressure fields describe the gross transport of liquid, including effects such as splashing, vorticity and overturning. Local fluid velocity is then used to drive a height field equation or to convect massless marker particles. The position of any free surface can thus be determined to a significantly higher resolution than that of the Navier-Stokes calculation. In addition, the pressure field, together with the Lagrange equations of motion, is used to simulate dynamic buoyant objects. Typical disadvantages to volumetric methods such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending driving functions to the Navier-Stokes equations. The output from our system is suitable for many of the water rendering algorithms presented by researchers in recent years.