Multiscale techniques for increasing the efficiency and controllability of water simulations

Abstract

An important goal in computer graphics is to produce visually rich scene with many small-scale details. However, due to the artificial dissipations occur during the numerical simulation, this generally requires high resolution. But it inevitably requires high-computational cost. Thus, this dissertation seeks to provide algorithms that are more efficient at producing detail with a given resolution domain. In this dissertation, algorithms for the simulation of fluid with enhanced subgrid-scale details are presented. The focus is on reproducing missing details by selectively increasing the fidelity of a simulation. In contrast to the previous numerical dissipation suppressing methods which concern the high order of accuracy, and exploit low order methods to selectively increase the fidelity of simulations, often with the use of multi-level techniques.

First, an Eulerian grid system based on multi-level approach that support refinement of the vorticity in multiple scales is presented. Physically based fluid simulation can provide realism but simulating water turbulence remains challenging. This dissertation presents a novel technique for simulating water turbulence. Results show that sub-grid turbulence can be created by employing a flow scale separation technique. Adopted the multi-scale flow separation method was successfully exploited to derive a special small-scale equation. Small scale velocities are then generated and manipulated by the equation. To simulate the turbulence effect, this work employed the vorticity confinement method. By extending the original method to multi-level, we effectively simulate energy cascading effects.

Second, turning to Lagrangian fluid, this dissertation presents a hybrid framework for enhancing vortical motion in the Lagrangian method, which can be extended to multiple-level. A single particle system combined with multiple Eulerian grids into one hybrid framework that allows enhancing the particle vorticity at the hi...