“Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking” by Keeler and Bridson

  • ©Todd Keeler and Robert Bridson

  • ©Todd Keeler and Robert Bridson



Entry Number: 72


    Ocean Waves Animation using Boundary Integral Equations and Explicit Mesh Tracking



    Ocean waves are a common animation challenge. To achieve natural-looking and rich detail, physical simulation of one kind or another has generally been adopted. For non-overturning waves without significant interaction with boats or other solids, or just to provide a good ripple-scale animated displacement texture, Tessendorf’s extremely efficient FFT-based solver [2001] is typically used. However, its realism falters for stormy oceans and doesn’t account for the presence of large solids in the water.
    For full-fledged interaction with solids and for overturning waves with splashes, 3D simulation of the free-surface Navier-Stokes equations is the main alternative. However, this comes with a significant performance cost, as a large volume of water beneath the surface must be discretized and solved: though it is not directly rendered, the effect of the depth is plainly visible in terms of wave speeds and dispersion. The finite simulated domain generally has to be much smaller than the field of view in rendering as well, requiring nontrivial effort to convincingly blend the 3D region into some sort of continued surface geometry out to the edges of the view.


    1. Brochu, T., and Bridson, R. 2009. Robust topological operations for dynamic explicit surfaces. SIAM Journal on Scientific Computing 31, 4, 2472–2493.
    2. Grilli, S. T., Guyenne, P., and Dias, F. 2001. A fully non-linear model for three-dimensional overturning waves over an arbitrary bottom. International Journal for Numerical Methods in Fluids 35, 7, 829–867.
    3. Tessendorf, J., et al. 2001. Simulating ocean water. Simulating Nature: Realistic and Interactive Techniques. SIGGRAPH.
    4. Xue, M., Xu, H., Liu, Y., and Yue, D. 2001. Computations of fully nonlinear three-dimensional wave-wave and wave-body interactions. part 1. dynamics of steep three-dimensional waves. Journal of Fluid Mechanics 438, 11–39.


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