Realistic Animation of Liquids

We present a comprehensive methodology for realistically animating liquid phenomena Physically accurate D mo tion is achieved by performing a two stage calculation over an arbitrary environment of static obstacles surrounded by uid A nite di erence approximation to the Navier Stokes equations is rst applied to a low resolution vox elized representation of the scene The resulting velocity and pressure elds describe the gross transport of liquid including e ects such as splashing vorticity and overturn ing Local uid velocity is then used to drive a height eld equation or to convect massless marker particles The po sition of any free surface can thus be determined to a sig ni cantly higher resolution than that of the Navier Stokes calculation In addition the pressure eld together with the Lagrange equations of motion is used to simulate dy namic buoyant objects Typical disadvantages to volumet ric methods such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the nite di erence discretization and by appending driving functions to the Navier Stokes equa tions The output from our system is suitable for many of the water rendering algorithms presented by researchers in recent years