A stable tensor-based method for controlled fluid simulations

Abstract

The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This requires a customized mathematical model for describing fluid motion influenced by tensor. In this work, we propose a formulation for fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accommodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.