Fast and scalable methods for the simulation of incompressible flow [electronic resource]

This dissertation presents efficient and scalable algorithms for the simulation of incompressible fluids. Physical simulation of fluids is one of the most interesting and challenging problems because of the amount of small scale details that realistic fluids exhibit. Although a large number of high fidelity simulations can be obtained with existing techniques, the resolution that these techniques can obtain is limited by the amount of computational power available. The simulation of incompressible flow has two main aspects: advection and projection. This thesis addresses performance and scalability issues related to both aspects and demonstrates a number of algorithms that work to massively reduce the computational cost of simulations. In the first chapters we concentrate on improving the performance and scalability of fluid simulations by investigating new conservative advection methods based off the established semi-Lagrangian method. Applying a conservative limiter to the typical semi-Lagrangian interpolation step can guarantee that the amount of the quantity being advected (e.g. mass, momentum, volume, etc.) does not increase. In addition, a new second step can be utilized that forward advects any of the quantity that was not accounted for in the typical semi-Lagrangian advection. Using this new conservative semi-Lagrangian method, mass and momentum can be conservatively advected in order to improve visual fidelity of smoke simulations at large time steps. In addition to conserving momentum during advection, the commonly used vorticity confinement turbulence model can be modified to exactly conserve momentum as well. It is shown that this new method is amenable to efficient smoke simulation with one time step per frame, whereas the traditional non-conservative semi-Lagrangian method experiences serious artifacts when run with these large time steps, especially when object interaction is considered. This method is then extended for water simulation when taking large time steps where, in contrast to smoke, an extrapolated velocity field is required. Inaccuracies with the extrapolated velocity field are alleviated by not using it when it is incorrect, which is determined via conservative advection of a color function that adds forwardly advected semi-Lagrangian rays to maintain conservation when mass is lost. This method is then coupled to the more visually appealing particle levelset method to obtain both a visually appealing and accurate method for simulating water at large time steps. In the final chapters we discuss improving the performance and scalability of the projection step through the use of faster methods for the pressure solve. This technique coarsens the Eulerian fluid grid during the pressure solve, allowing for a fast implicit update but still maintaining the resolution obtained with a large grid. This allows simulations to run at a fraction of the cost of existing techniques (~60x faster) while still providing the fine scale structure and details obtained with a full projection. This algorithm scales well to very large grids and large numbers of processors, allowing for high fidelity simulations that would otherwise be intractable.

Advisor: Fedkiw Ronald P.
Khatib Oussama
Teran Joseph M. advisor. Thesis advisor