Deformation of 2D flow fields using stream functions

Recently, visual simulation of fluids has become an important element in many applications, such as movies and computer games. These fluid animations are usually created by physically-based fluid simulation. However, the simulation often requires very expensive computational cost for creating realistic fluid animations. Therefore, when the user tries to create various fluid animations, he or she must execute fluid simulation repeatedly, which requires a prohibitive computational time. To address this problem, this paper proposes a method for deforming velocity fields of fluids while preserving the divergence-free condition. In this paper, we focus on grid-based 2D fluid simulations. Our system allows the user to interactively create various fluid animations from a single set of velocity fields generated by the fluid simulation. In a preprocess, our method converts the input velocity fields into scalar fields representing the stream functions. At run-time, the user deforms the grid representing the scalar stream functions and the deformed velocity fields are then obtained by applying a curl operator to the deformed scalar stream functions. The velocity fields obtained by this process naturally perseveres the divergence-free condition. For the deformation of the grid, we use a method based on Moving Least Squares. The usefulness of our method is demonstrated by several examples.