CS Events

Abstract

In the field of science, a unified theory that describes every physical phenomenon and interaction in the universe has always been a hot topic: it represents the beauty of simplicity. In Computer Graphics, a unified numerical model for physics-based simulation is an equivalent, which extracts all the core parameters and eliminates the need to adjust algorithms based on different material behaviors. In this dissertation, we show our progress in developing unified models in the following aspects:

First, we introduce non-Fourier diffusion to accurately deal with the unrealistic infinite wave speed produced by the traditional diffusion solver and fundamentally explain diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann Transport Equation. It can capture some of the most characteristic visual aspects of diffusion-driven physics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake, and dendrite formation, that span from Fourier-type to non-Fourier-type diffusive phenomena. We propose a unified convection-diffusion formulation using this model that treats both the diffusive quantity and its associated flux as the primary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this formulation on staggered MAC grids and a geometric Multigrid-preconditioned Conjugate Gradients solver for fast convergence.

Second, we couple the extended Pom-Pom model with the Material Point Method (MPM) and develop a unified constitutive model for Newtonian and non-Newtonian viscous liquids, which recovers the variational Stokes solver for Newtonian viscosity and a variety of non-Newtonian models, such as Oldroyd-B and the Upper Convective Maxwell (UCM) model. In addition, we show how to two-way couple our viscoelastic liquid simulator with the non-Fourier heat diffusion solver for simulating problems with phase change, such as melting chocolate and digital fabrication with 3D printing. 

Third, we exhibit an adaptively updated Lagrangian Material Point Method (A-ULMPM), which extends the current MPM framework to alleviate non-physical artifacts, such as the cell-crossing instability and numerical fracture, that plague state-of-the-art Eulerian formulations of MPM while still allowing for large deformations that arise in fluid simulations. For better efficiency and conservation of angular momentum, we further integrate the APIC and MLS-MPM formulations in A-ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first-order derivatives. Our approach does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes.

Finally, we present a unified constitutive model for versatile physics simulation of inviscid fluids, Newtonian viscosity, hyperelasticity, viscoplasticity, elastoplasticity, and other physical effects that arise due to a mixture of these behaviors. The key ideas behind our formulation are the design of a generalized Kirchhoff stress tensor that can describe hyperelasticity, Newtonian viscosity and inviscid fluids, and the use of pre-projection and post-correction rules for simulating material behaviors that involve plasticity, including elastoplasticity and viscoplasticity. We show how our generalized Kirchhoff stress tensor can be coupled together into a unified constitutive model that allows the simulation of diverse material behaviors by only changing parameter values. More notably, our formulation allows for inverse learning of unknown material properties directly from data using differentiable physics simulations.