Phenomenological Simulation of Brooks

Abstract

Abstract. The goal of our work is to simulate the shape and variations of the water surface on non-turbulent brooks both efficiently and at very high resolution. In this paper, we treat only the shape and animation. We concentrate on the simulation of quasi-stationary waves and ripples in the vicinity of obstacles and banks, and more particularly, shockwaves. To achieve this, we rely on phenomenological laws such as the ones collected over the last two centuries in the field of hydrodynamics: most of the visually interesting phenomena (apart from turbulence) are known qualitatively and characterized in reasonably simplified situations. It is thus wasteful to run a full-range Navier-Stokes simulation for quiet flows when only qualitative results are needed. The complexity of the velocity field along the streambed and around the obstacles is taken into account by solving a simple Laplace equation, assuming a stationary irrotational non-compressible ideal 2D flow. We obtain a stationary solution of the surface waves, that we perturb in order to get a quasi-stationary brook simulation. This yields a real-time simulation of the fluid visible features.

Efficient simulation of large bodies of water by coupling two and three dimensional techniques

“…[Thon and Ghazanfarpour 2001] also solved the two-dimensional NavierStokes equations for the horizontal velocity in streams, but used a noise function for the vertical velocity. [Neyret and Praizelin 2001] proposed a simpler stream model using a two-dimensional Laplace equation for the bulk flow. Finally, a few authors have tackled large bodies of water with the three-dimensional NavierStokes equations, e.g.…”

Low-Memory and Interactive-Rate Animation of Water-Column Based Flows

“…To alleviate the complexity of a three-dimensional simulation of water flow on terrains, some works [22,33,34,26] focus only on what is seen in brooks and rivers, i.e., waves and ripples on the water surface near the vicinity of obstacles and banks. The water surface is assumed to be twodimensional and discretized in a regular grid to run the fluid simulation.…”

Efficient animation of water flow on irregular terrains

“…To alleviate the complexity of a three-dimensional simulation of water flow on terrains, some works [Neyret and Praizelin 2001;Thon and Ghazanfarpour 2001;Thon and Ghazanfarpour 2002;Rochet 2005] focus only on what is seen in brooks and rivers, i.e., waves and ripples on the water surface near the vicinity of obstacles and banks. The water surface is assumed to be twodimensional and discretized in a regular grid to run the fluid simulation.…”