Height-field fluids for computer graphics

The author presents a novel method for animating water based on a simple, rapid, and stable solution of a set of partial differential equations resulting from an approximation to the shallow water equations. The approximation gives rise to a version of the wave equation on a height field where the wave velocity is proportional to the square root of the depth of the water. The resulting wave equation is then solved with an alternating-direction implicit method on a uniform finite-difference grid. The computational work required for an iteration consists mainly of solving a simple tridiagonal linear system for each row and column of the height field. A single iteration per frame suffices in most cases for convincing animation. Unlike previous models, the proposed method handles wave reflections, net transport of water, and boundary conditions with changing topology