A numerically efficient and stable algorithm for animating water waves

Water motion can be realistically captured by physically based fluid models. We begin by presenting a survey on fluid simulation models that are based on fluid dynamics equations, from the most comprehensive Navier–Stokes equations to the simple wave equation. We then present a model that is based on the two-dimensional shallow water equations. The equations are integrated by a novel numerical method – the implicit semi-Lagrangian integration scheme – which allows large timesteps while maintaining stability, and which is described in detail in this paper. Gentle wave motions, the superposition of waves, drifting objects, and obstacles and boundaries of various shapes can be efficiently simulated with this model.

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