Physics-Based Animation

Joel Wretborn, Alexey Stomakhin, Christopher Batty

We introduce a novel unified mixture-based method for simulating underwater bubbles across a range of bubble scales. Our approach represents bubbles as a set of Lagrangian particles that are coupled with the surrounding Eulerian water volume. When bubble particles are sparsely distributed, each particle, typically smaller than the liquid grid voxel size, corresponds to an individual spherical bubble. As the sub-grid particles increase in local density our model smoothly aggregates them, ultimately forming connected, fully aerated volumetric regions that are properly resolved by the Eulerian grid. We complement our scheme with a continuous surface tension model, defined via the gradient of the bubbles’ local volume fractions, which works seamlessly across this scale transition. Our unified representation allows us to capture a wide range of effects across different scales—from tiny dispersed sub-grid air pockets to fully Eulerian two-phase interfacial flows.

A unified multi-scale method for simulating immersed bubbles

Yuchen Sun, Linglai Chen, Weiyuan Zeng, Tao Du, Shiying Xiong, Bo Zhu

This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings.

An Impulse Ghost Fluid Method for Simulating Two-Phase Flows

• A Unified Multi-scale Method for Simulating Immersed Bubbles
• A Semi-Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence
• A Hybrid Lagrangian-Eulerian Formulation of Thin-shell Fracture
• Rest Shape Optimization for Sag-Free Discrete Elastic Rods
• BlendSim: Simulation on Parametric Blendshapes using Spacetime Projective Dynamics
• A Unified Discrete Collision Framework for Triangle Primitives
• Cloth Animation with Time-dependent Persistent Wrinkles
• Corotational Hinge-based Thin Plates/Shells
• Eigenvalue Blending for Projected Newton

Tetsuya Takahashi, Christopher Batty

We propose a new rest shape optimization framework to achieve sag-free simulations of discrete elastic rods. To optimize rest shape parameters, we formulate a minimization problem based on the kinetic energy with a regularizer while imposing box constraints on these parameters to ensure the system’s stability. Our method solves the resulting constrained minimization problem via the Gauss-Newton algorithm augmented with penalty methods. We demonstrate that the optimized rest shape parameters enable discrete elastic rods to achieve static equilibrium for a wide range of strand geometries and material parameters.

Rest Shape Optimization for Sag-Free Discrete Elastic Rods

L. Fan, Floyd M. Chitalu, Taku Komura

The hybrid Lagrangian/Eulerian formulation of continuum shells is highly effective for producing challenging simulations of thin materials like cloth with bending resistance and frictional contact. However, existing formulations are restricted to materials that do not undergo tearing nor fracture due to the difficulties associated with incorporating strong discontinuities of field quantities like velocity via basis enrichment while maintaining C^1 continuity or H^2 regularity. We propose an extension of this formulation to simulate dynamic tearing and fracturing of thin-shells using Kirchhoff-Love continuum theory. Damage, which manifests as cracks or tears, is propagated by tracking the evolution of a time-dependent phase-field in the co-dimensional manifold, where a moving least-squares (MLS) approximation then captures the strong discontinuities of interpolated field quantities near the crack. Our approach is capable of simulating challenging scenarios of this tearing and fracture, all-the-while harnessing the existing benefits of the hybrid Lagrangian/Eulerian formulation to expand the domain of possible effects. The method is also amenable to user-guided control, which serves to influence the propagation of cracks or tears such that they follow prescribed paths during simulation.

A Hybrid Lagrangian–Eulerian Formulation of Thin-Shell Fracture

Meng Zhang, Jun Li

Achieving efficient, high-fidelity, high-resolution garment simulation is challenging due to its computational demands. Conversely, low-resolution garment simulation is more accessible and ideal for low-budget devices like smartphones. In this paper, we introduce a lightweight, learning-based method for garment dynamic super-resolution, designed to efficiently enhance high-resolution, high-frequency details in low-resolution garment simulations. Starting with low-resolution garment simulation and underlying body motion, we utilize a mesh-graph-net to compute super-resolution features based on coarse garment dynamics and garment-body interactions. These features are then used by a hyper-net to construct an implicit function of detailed wrinkle residuals for each coarse mesh triangle. Considering the influence of coarse garment shapes on detailed wrinkle performance, we correct the coarse garment shape and predict detailed wrinkle residuals using these implicit functions. Finally, we generate detailed high-resolution garment geometry by applying the detailed wrinkle residuals to the corrected coarse garment. Our method enables roll-out prediction by iteratively using its predictions as input for subsequent frames, producing fine-grained wrinkle details to enhance the low-resolution simulation. Despite training on a small dataset, our network robustly generalizes to different body shapes, motions, and garment types not present in the training data. We demonstrate significant improvements over state-of-the-art alternatives, particularly in enhancing the quality of high-frequency, fine-grained wrinkle details.

Neural Garment Dynamic Super-Resolution

Huancheng Lin, Floyd M. Chitalu, Taku Komura

Anisotropic hyperelastic distortion energies are used to solve many problems in fields like computer graphics and engineering with applications in shape analysis, deformation, design, mesh parameterization, biomechanics and more. However, formulating a robust anisotropic energy that is low-order and yet sufficiently non-linear remains a challenging problem for achieving the convergence promised by Newton-type methods in numerical optimization. In this paper, we propose a novel analytic formulation of an anisotropic energy that is smooth everywhere, low-order, rotationally-invariant and at-least twice differentiable. At its core, our approach utilizes implicit rotation factorizations with invariants of the Cauchy-Green tensor that arises from the deformation gradient. The versatility and generality of our analysis is demonstrated through a variety of examples, where we also show that the constitutive law suggested by the anisotropic version of the well-known As-Rigid-As-Possible energy is the foundational parametric description of both passive and active elastic materials. The generality of our approach means that we can systematically derive the force and force-Jacobian expressions for use in implicit and quasistatic numerical optimization schemes, and we can also use our analysis to rewrite, simplify and speedup several existing anisotropic and isotropic distortion energies with guaranteed inversion-safety.

Analytic rotation-invariant modelling of anisotropic finite elements

Yuanyuan Tao, Ivan Puhachov, Derek Nowrouzezahrai, Paul Kry

High-fidelity simulation of fluid dynamics is challenging because of the high dimensional state data needed to capture fine details and the large computational cost associated with advancing the system in time. We present neural implicit reduced fluid simulation (NIRFS), a reduced fluid simulation technique that combines an implicit neural representation of fluid shapes and a neural ordinary differential equation to model the dynamics of fluid in the reduced latent space. The latent trajectories are computed at very little cost in comparison to simulations for training, while preserving fine physical details. We show that this approach can work well, capturing the shapes and dynamics involved in a variety of scenarios with constrained initial conditions, e.g., droplet-droplet collisions, crown splashes, and fluid slosh in a container. In each scenario, we learn the latent implicit representation of fluid shapes with a deep-network signed distance function, as well as the energy function and parameters of a damped Hamiltonian system, which helps guarantee desirable properties of the latent dynamics. To ensure that latent shape representations form smooth and physically meaningful trajectories, we simultaneously learn the latent representation and dynamics. We evaluate novel simulations for conservation of volume and momentum conservation, discuss design decisions, and demonstrate an application of our method to fluid control.

Neural Implicit Reduced Fluid Simulation

Liangwang Ruan , Bin Wang, Tiantian Liu, Baoquan Chen

We propose MiNNIE, a simple yet comprehensive framework for real-time simulation of nonlinear near-incompressible elastics. To avoid the common volumetric locking issues at high Poisson’s ratios of linear finite element methods (FEM), we build MiNNIE upon a mixed FEM framework and further incorporate a pressure stabilization term to ensure excellent convergence of multigrid solvers. Our pressure stabilization strategy injects bounded influence on nodal displacement which can be eliminated using a quasi-Newton method. MiNNIE has a specially tailored GPU multigrid solver including a modified skinning-space interpolation scheme, a novel vertex Vanka smoother, and an efficient dense solver using Schur complement. MiNNIE supports various elastic material models and simulates them in real-time, supporting a full range of Poisson’s ratios up to 0.5 while handling large deformations, element inversions, and self-collisions at the same time.

MiNNIE: a Mixed Multigrid Method for Real-time Simulation of Nonlinear Near-Incompressible Elastics

Ryoichi Ando

This paper presents a new cubic barrier with elasticity-inclusive dynamic stiffness for penetration-free contact resolution and strain limiting. We show that our method enlarges tight strain-limiting gaps where logarithmic barriers struggle and enables highly scalable contact-rich simulation.

A Cubic Barrier with Elasticity-Inclusive Dynamic Stiffness