Real-Time Water Wave Simulation with Surface Advection based on Mass Conservancy

  • Published : 2008.06.30


In this paper, we present a real-time physical simulation model of water surfaces with a novel method to represent the water mass flow in full three dimensions. In a physical simulation model, the state of the water surfaces is represented by a set of physical values, including height, velocity, and the gradient. The evolution of the velocity field in previous works is handled by a velocity solver based on the Navier-Stokes equations, which occurs as a result of the unevenness of the velocity propagation. In this paper, we integrate the principle of the mass conservation in a fluid of equilateral density to upgrade the height field from the unevenness, which in mathematical terms can be represented by the divergence operator. Thus the model generates waves induced by horizontal velocity, offering a simulation that puts forces added in all direction into account when calculating the values for height and velocity for the next frame. Other effects such as reflection off the boundaries, and interactions with floating objects are involved in our method. The implementation of our method demonstrates to run with fast speed scalable to real-time rates even for large simulation domains. Therefore, our model is appropriate for a real-time and large scale water surface simulation into which the animator wishes to visualize the global fluid flow as a main emphasis.


Water Surfaces;Navier-Stokes;Real-Time Simulation


  1. B. Adams, M. Pauly, R. Keiser, and L. J. Guibas, "Adaptively sampled particle fluids," ACM Transaction on Graphhics(Proceedings of ACM SIGGRAPH ’07). Vol. 26, No.3, 2007, pp. 48-54.
  2. J. X. Chen and N. V. Lobo, "Toward Interactive-Rate Simulation of Fluids with Moving Obstacles Using Navier-Stokes Equations," Graphical Models and Image Processing, Vol.57, No.2, March, 1995, pp. 107-116.
  3. D. Enright, S. Marschner and R. Fedkiw, "Animation and Rendering of Complex Water Surfaces," Proceedings of ACM SIGGRAPH '02, 2002, pp. 736–744.
  4. N. Foster and R. Fedkiw, "Practical Animation of Liquids," Proceedings of ACM SIGGRAPH ‘01, 2001, pp. 23–30.
  5. W. R. Fox and A. T. McDonald, Introduction to Fuild Mechanics, 4th Edition, Wiley, New York, 1992.
  6. A. Iglesias, "Computer Graphics for Water Modeling and Rendering: a Survey," Future Generation Computer Systems, Vol.20, 2004, pp. 1355-1374.
  7. A. T. Layton and Michiel van de Panne, "A numerically efficient and stable algorithm for animating water waves, " The Visual Computer, Vol. 18, No. 1, pp. 41-53, 2002.
  8. J. J. Monaghan, "Simulating free surface flows with SPH," Journal of Computational Physics, Vol.110, No.2, 1994, pp. 399-406.
  9. J. Stam, "Stable Fluids." Proceedings of ACM SIGGRAPH ‘99, 1999, pp. 121–128.
  10. J. Stam, "Real-Time Fluid Dynamics for Games." Proceedings of Game Development Conference '03, 2003.
  11. C. Yuksel, D. House and J. Keyser, "Wave Particles," Proceedings of ACM SIGGRAPH '07, Vol.26, No.3, 2007, pp. 1-8.
  12. OGRE, Object-Oriented Graphics Rendering Engine,