My master's thesis is "Modeling Highly Deformable Fluid," aiming to create realistic fluid animation. Modeling liquid with complex surfaces is a great challenge in computer graphics. We proposed a hybrid approach combining the volume tracking method and smoothed particle hydrodynamics (SPH) to model liquids with highly deformable surfaces. The 3-D Navier-Stokes equations are solved by the marker-and-cell (MAC) method and a density volume representing the liquid is evolved over time and space by the volume-of-fluid (VOF) method. The VOF method uses a finite-volume discretization and maintaining a value for the liquid volume in each grid cell. The advection of the volumes is calculated by using cell-face fluxes, in which the liquid volume that leaves one cell is exactly the same as the liquid volume that enters the adjacent cells. Only a scalar convective equation needs to be solved to evolve the liquid surface forward in time and space. Potentially under-resolved effects are captured by SPH particles generated in that high-deformable regions near the liquid surface. Dynamics of these particles provides a better fidelity than that of other particle methods due to their capability of approximating the equations of fluid mechanics. Particle volumes are incorporated into the interpolated volume fractions before an unified iso-surface is extracted. As a result the liquid surface is more smooth than those of previous researches which rendered the splash by coating the particles with a field functions or as hard spheres. The images are rendered by POV-Ray.
Figure: throwing a sphere into a tank of water (32x32x48 grid cells)
