Simulation of fluid dynamics is a well known, widely studied, but still open problem in engineering, computational physics and computer science. Understanding dynamics of a fluid is crucial for many applications, spanning from entertainment and computer graphics, to simulation and validation of safety critical systems such as planes and ships. Despite the need of efficient and reliable software for fluid simulation, this task is still hard to accomplish. Furthermore, moving out from Euclidean domains makes things even worse, since there also is a lack of study and understanding of fluid dynamics on curved surfaces.
The purpose of this project is twofold. At first, we want to provide an efficient GPU algorithm for fluid simulation on curved domains, allowing both a further understanding of fluid dynamics from a different point of view and a simplification of simulation tasks in higher dimensions domains. Then, we want to apply this technique to the field of computer graphics for the task of simulating realistic erosion phenomena, so to simplify the work of 3D artists.
At the current state of the art the study of Navier-Stokes equations on non-Euclidean domains is far to be sterile. Even if much is known from a theoretical point of view, there is still more that can be done on an experimental and practical setting. Some first steps have been done in this direction, but they are restricted to radial manifolds, which are definitely very far from the wide range of surfaces used in practical 3D applications. Also, these methods does not take advantage of the full capabilities of modern machines, which allow a new, unprecedented degree of parallelism.
By having such a powerful instrument, the classical problem of simulating erosion on terrains could be easily extended to generic triangular meshes. Furthermore, simulating hydraulic erosion using the dynamics of a fluid allows a more precise and physics based approach to the problem, rather than relying on methods built upon intuitive modelling and ad-hoc adjustments.
In both the goals presented in this project, the crucial point is the massive parallelization, through which it is possible to achieve an almost real time simulation.