Resumen de Particle-Based Simulation Methods of Fluids and Granular Media for VFX
Iván Alduán Íñiguez
Liquids are ubiquitous in our lives, from a glass of water to breaking ocean waves, they play a role. The same is true for granular media, many of the materials around us, such as soil, sand, or even beans and pop corn, can be classified as granulars. They are so common that an accurate simulation of their behavior is necessary to reproduce a variety of environments and situations in the animation and VFX industries. However, obtaining realistic simulations is a difficult task. On one hand, these materials are characterized by a continuous deformation on their entire volume, meaning computational requirements needed to simulate their rich behavior are bigger than in any other media. On the other hand, pipelines inside VFX are tight and the industry is always on demand for more accurate and efficient simulation methods to achieve better realism. Both, appropriate deformation models and efficient discretizations able to reproduce quick results are needed. In this thesis we develop novel methods that allow us to simulate a wide range of liquid and granular effects in an efficient manner. We present novel constitutive models that succeed modeling complex materials like non-Newtonian fluids or cohesive granular media. In addition, we propose several contributions in a wide range of areas, with particle-based representations as the common denominator, aiming to meet the demands inside the VFX industry. First, we focus on high-resolution granular media and present a novel system that captures fine behavior in a fraction of the time. It decouples the simulation into a low-resolution Discrete-Element Method (DEM) based model and a high-resolution up-sampling technique without sacrificing complex interactions. We then depart from discrete dynamics, and go to continuum methods based on Smoothed-Particle-Hydrodynamics (SPH). By developing a novel constitutive model for granular media simulations, and using a Predictive-Corrective solver (PCSPH), we achieve a wide range of different behaviors not seen before in particle-based methods like unilateral incompressibility, stable friction or cohesion. We demonstrate its advantages by applying it in a wide variety of scenarios, including granular piles, avalanches or cohesive sand-castle fracturing. From continuum dynamics we move to constrained dynamics. We redesign our previous solution as a framework to solve generic SPH-based constraints. Using a mixture of holonomic and non-holonomic constraints, our method is able to simulate a wide range of materials, from inviscid to non-Newtonian Bingham fluids like whipped cream. Position-Based Fluids (PBF) formulates SPH-based constraints on positions gaining additional stability, but sacrificing controllability. In this thesis, we take the advantages of PBF and propose several modifications to make a solution suitable to be used in the VFX industry, taking into account desirable properties like robustness, efficiency, controllability and versatility. The proposed framework is tested in different scenarios from a cup of wine to a waterfall. Finally, although particle-based simulations give lot of detail, sometimes it is better to use an auxiliary grid to accelerate some computations. We take the Adaptive Mesh Refinement (AMR) idea from Computational Fluid Dynamics (CFD) literature, and modify it to have value inside the graphics community. The final contribution proposes a novel hybrid method that makes use of a mix of particles, level sets, adaptive sparse-grids and adaptive multigrid solvers. This method allows the simulation of huge amounts of liquid with concentrated detail where needed, like a vast ocean with a splashy whale emerging from the deep.
