Physics-Based Animation

Sergio Sancho, Jingwei Tang, Christopher Batty, Vinicius Azevedo

An ongoing challenge in fluid animation is the faithful preservation of vortical details, which impacts the visual depiction of flows. We propose the Impulse Particle-In-Cell (IPIC) method, a novel extension of the popular Affine Particle-In-Cell (APIC) method that makes use of the impulse gauge formulation of the fluid equations. Our approach performs a coupled advection-stretching during particle-based advection to better preserve circulation and vortical details. The associated algorithmic changes are simple and straightforward to implement, and our results demonstrate that the proposed method is able to achieve more energetic and visually appealing smoke and liquid flows than APIC.

The Impulse Particle-In-Cell Method

Ryan S. Zesch, Vismay Modi, Shinjiro Sueda, David I.W. Levin

We present neural collision fields as an alternative to contact point sampling in physics simulations. Our approach is built on top of a novel smoothed integral formulation for the contact surface patches between two triangle meshes. By reformulating collisions as an integral, we avoid issues of sampling common to many collision-handling algorithms. Because the resulting integral is difficult to evaluate numerically, we store its solution in an integrated neural collision field — a 6D neural field in the space of triangle pair vertex coordinates. Our network generalizes well to new triangle meshes without retraining. We demonstrate the effectiveness of our method by implementing it as a constraint in a position-based dynamics framework and show that our neural formulation successfully handles collisions in practical simulations involving both volumetric and thin-shell geometries.

Neural Collision Fields for Triangle Primitives

Mitsuki Hamamichi, Kentaro Nagasawa, Masato Okada, Ryohei Seto, Yonghao Yue

We estimate the three Herschel–Bulkley parameters (yield stress, power-law index, and consistency parameter) for shear-dependent fluid-like materials possibly with large-scale inclusions, for which rheometers may fail to provide a useful measurement. We perform experiments using the unknown material for dam-break (or column collapse) setups and capture video footage. We then use simulations to optimize for the material parameters. For better match up with the simple shear flow encountered in a rheometer, we modify the flow rule for the elasto-viscoplastic Herschel-Bulkley model. Analyzing the loss landscape for optimization, we realize a similarity relation; material parameters far away within this relation would result in matched simulations, making it hard to distinguish the parameters. We found that by exploiting the setup dependency of the similarity relation, we can improve on the estimation using multiple setups, which we propose by analyzing the Hessian of the similarity relation. We validate the efficacy of our method by comparing the estimations to the measurements from a rheometer (for materials without large-scale inclusions) and show applications to materials with large-scale inclusions, including various salad or pasta sauces, and congee.

Non-Newtonian ViRheometry via Similarity Analysis

Otman Benchekroun, Ty Trusty, Eitan Grinspun, Danny M. Kaufman, David I.W. Levin

Real-time elastodynamic solvers are well-suited for the rapid simulation of homogeneous elastic materials, with high-rates generally enabled by aggressive early termination of timestep solves. Unfortunately, the introduction of strong domain heterogeneities can make these solvers slow to converge. Stopping the solve short creates visible damping artifacts and rotational errors. To address these challenges we develop a reduced mixed finite element solver that pre serves rich rotational motion, even at low-iteration regimes. Specifically, this solver augments time-step solve optimizations with auxiliary stretch degrees of freedom at mesh elements, and maintains consistency with the primary positional degrees of freedoms at mesh nodes via explicit constraints. We make use of a Skinning Eigenmode subspace for our positional degrees of freedom. We accelerate integration of non-linear elastic energies with a cubature approximation, placing stretch degrees of freedom at cubature points. Across a wide range of examples we demonstrate that this subspace is particularly well suited for heterogeneous material simulation. Our resulting method is a subspace mixed finite element method completely decoupled from the resolution of the mesh that is well-suited for real-time simulation of heterogeneous domains.

Subspace Mixed Finite Elements for Real-Time Heterogeneous Elastodynamics

Doug L. James, David I.W. Levin

Motion control of large-scale, multibody physics animations with contact is difficult. Existing approaches, such as those based on optimization, are computationally daunting, and, as the number of interacting objects increases, can fail to find satisfactory solutions. We present a new, complementary method for the visual control of multibody animations that exploits object motion and visibility, and has overall cost comparable to a single simulation. Our method is highly practical, and is demonstrated on numerous large-scale, contact-rich examples involving both rigid and deformable bodies.

ViCMA: Visual Control of Multibody Animations

Kinfung Chu, Jiawei Huang, Hidemasa Takan, Yoshifumi Kitamura

We present a framework that captures sparse Lagrangian flow information from a volume of real liquid and reconstructs its detailed kinematic information in real time. Our framework can perform flow reconstruction even when the liquid is disturbed by an object of unknown movement and shape. Through a large dataset of liquid moving under external disturbance, an agent is trained using reinforcement learning to reproduce the target flow kinematics with only the captured sparse information as inputs while remaining oblivious to the movement and the shape of the disturbance sources. To ensure that the underlying simulation model faithfully obeys physical reality, we also optimize the viscosity parameters in Smoothed Particle Hydrodynamics (SPH) using classical fluid dynamics knowledge and gradient-based optimization. By quantitatively comparing the reconstruction results against real-world and simulated ground truth, we verified that our reconstruction method is resilient to different agitation patterns.

Real-Time Reconstruction of Fluid Flow under Unknown Disturbance

Jiayi Eris Zhang, Jérémie Dumas, Yun (Raymond) Fei, Alec Jacobson, Doug L. James, Danny M. Kaufman

Thin shell structures exhibit complex behaviors critical for modeling and design across wide-ranging applications. Capturing their mechanical response requires finely detailed, high-resolution meshes. Corresponding simulations for predicting equilibria with these meshes are expensive, whereas coarse-mesh simulations can be fast but generate unacceptable artifacts and inaccuracies. The recently proposed progressive simulation framework [Zhang et al. 2022] offers a promising avenue to address these limitations with consistent and progressively improving simulation over a hierarchy of increasingly higher-resolution models. Unfortunately, it is currently severely limited in application to meshes and shapes generated via Loop subdivision. We propose Progressive Shells Quasistatics to extend progressive simulation to the high-fidelity modeling and design of all input shell (and plate) geometries with unstructured (as well as structured) triangle meshes. To do so, we construct a fine-to-coarse hierarchy with a novel nonlinear prolongation operator custom-suited for curved-surface simulation that is rest-shape preserving, supports complex curved boundaries, and enables the reconstruction of detailed geometries from coarse-level meshes. Then, to enable convergent, high-quality solutions with robust contact handling, we propose a new, safe, and efficient shape-preserving upsampling method that ensures non-intersection and strain limits during refinement. With these core contributions, Progressive Shell Quasistatics enables, for the first time, wide generality for progressive simulation, including support for arbitrary curved-shell geometries, progressive collision objects, curved boundaries, and unstructured triangle meshes – all while ensuring that preview and final solutions remain free of intersections. We demonstrate these features across a wide range of stress tests where progressive simulation captures the wrinkling, folding, twisting, and buckling behaviors of frictionally contacting thin shells with orders-of-magnitude speed-up in examples over direct fine-resolution simulation.

Progressive Shell Quasistatics for Unstructured Meshes

Payam Khanteimouri, Marcel Campen

We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space).

3D Bézier Guarding: Boundary-Conforming Curved Tetrahedral Meshing

Stefan Rhys Jeske, Lukas Westhofen, Fabian Löschner, José Antonio Fernández-Fernández, Jan Bender

The numerical simulation of surface tension is an active area of research in many different fields of application and has been attempted using a wide range of methods. Our contribution is the derivation and implementation of an implicit cohesion force based approach for the simulation of surface tension effects using the Smoothed Particle Hydrodynamics (SPH) method. We define a continuous formulation inspired by the properties of surface tension at the molecular scale which is spatially discretized using SPH. An adapted variant of the linearized backward Euler method is used for time discretization, which we also strongly couple with an implicit viscosity model. Finally, we extend our formulation with adhesion forces for interfaces with rigid objects. Existing SPH approaches for surface tension in computer graphics are mostly based on explicit time integration, thereby lacking in stability for challenging settings. We compare our implicit surface tension method to these approaches and further evaluate our model on a wider variety of complex scenarios, showcasing its efficacy and versatility. Among others, these include but are not limited to simulations of a water crown, a dripping faucet and a droplet-toy.

Implicit Surface Tension for SPH Fluid Simulation