Physics-Based Animation

Lei Lan, Minchen Li, Chenfanfu Jiang, Huamin Wang, Yin Yang

In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton’s method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries.

Second-order Stencil Descent for Interior-point Hyperelasticity

Jingwei Tang, Byungsoo Kim, Vinicius Azevedo, Barbara Solenthaler

Controlling fluid simulations is notoriously difficult due to its high computational cost and the fact that user control inputs can cause unphysical motion. We present an interactive method for deformation-based fluid control. Our method aims at balancing the direct deformations of fluid fields and the preservation of physical characteristics. We train convolutional neural networks with physics-inspired loss functions together with a differentiable fluid simulator, and provide an efficient workflow for flow manipulations at test time. We demonstrate diverse test cases to analyze our carefully designed objectives and show them leading that they lead to physical and eventually visually appealing modifications on edited fluid data.

Physics-Informed Neural Corrector for Deformation-based Fluid Control

Timo Probst, Matthias Teschner,

We propose a novel monolithic pure SPH formulation to simulate fluids strongly coupled with rigid bodies. This includes fluid incompressibility, fluid-rigid interface handling and rigid-rigid contact handling with a viable implicit particle-based dry friction formulation. The resulting global system is solved using a new accelerated solver implementation that outperforms existing fluid and coupled rigid-fluid simulation approaches. We compare results of our simulation method to analytical solutions, show performance evaluations of our solver and present a variety of new and challenging simulation scenarios.

Monolithic Friction and Contact Handling for Rigid Bodies and Fluids using SPH

He Chen, Elie Diaz, Cem Yuksel

We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.

Shortest Path to Boundary for Self-Intersecting Meshes

Gilles Daviet

We devise a local–global solver dedicated to the simulation of Discrete Elastic Rods (DER) with Coulomb friction that can fully leverage the massively parallel compute capabilities of moderns GPUs. We verify that our simulator can reproduce analytical results on recently published cantilever, bend–twist, and stick–slip experiments, while drastically decreasing iteration times for high-resolution hair simulations. Being able to handle contacting assemblies of several thousand elastic rods in real-time, our fast solver paves the ways for new workflows such as interactive physics-based editing of digital grooms.

Interactive Hair Simulation on the GPU using ADMM

Hang Yin, Mohammad Sina Nabizadeh, Baichun Wu, Stephanie Wang, Albert Chern

The vorticity-streamfunction formulation for incompressible inviscid fluids is the basis for many fluid simulation methods in computer graphics, including vortex methods, streamfunction solvers, spectral methods, and Monte Carlo methods. We point out that current setups in the vorticity-streamfunction formulation are insufficient at simulating fluids on general non-simply-connected domains. This issue is critical in practice, as obstacles, periodic boundaries, and nonzero genus can all make the fluid domain multiply connected. These scenarios introduce nontrivial cohomology components to the flow in the form of harmonic fields. The dynamics of these harmonic fields have been previously overlooked. In this paper, we derive the missing equations of motion for the fluid cohomology components. We elucidate the physical laws associated with the new equations, and show their importance in reproducing physically correct behaviors of fluid flows on domains with general topology.

Fluid Cohomology

Tianye Xie, Minchen Li, Yin Yang, Chenfanfu Jiang

We present a robust and efficient method for simulating Lagrangian solid-fluid coupling based on a new operator splitting strategy. We use variational formulations to approximate fluid properties and solid-fluid interactions, and introduce a unified two-way coupling formulation for SPH fluids and FEM solids using interior point barrier-based frictional contact. We split the resulting optimization problem into a fluid phase and a solid-coupling phase using a novel time-splitting approach with augmented contact proxies, and propose efficient custom linear solvers. Our technique accounts for fluids interaction with nonlinear hyperelastic objects of different geometries and codimensions, while maintaining an algorithmically guaranteed non-penetrating criterion. Comprehensive benchmarks and experiments demonstrate the efficacy of our method.

A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling

• A Contact Proxy Splitting Method for Lagrangian Solid-Fluid Coupling
• Second-order Stencil Descent for Interior-point Hyperelasticity
• A Sparse Distributed Gigascale Resolution Material Point Method
• PolyStokes: A Polynomial Model Reduction Method for Viscous Fluid Simulation
• Data-Free Learning of Reduced-Order Kinematics
• Generalizing Shallow Water Simulations with Dispersive Surface Waves
• Fluid Cohomology
• Complex Wrinkle Field Evolution
• Sag-free Initialization for Strand-based Hybrid Hair Simulation
• Interactive Hair Simulation on the GPU Using ADMM
• Beyond Chainmail: Computational Modeling of Discrete Interlocking Materials
• Fast Complementary Dynamics via Skinning Eigenmodes
• Motion From Shape Change
• Nonlinear Compliant Modes for Large-deformation Analysis of Flexible Structures
• Improved Water Sound Synthesis Using Coupled Bubbles
• Building a Virtual Weakly-compressible Wind Tunnel Testing Facility
• Fluid-solid Coupling in Kinetic Two-phase Flow Simulation
• In-Timestep Remeshing for Contacting Elastodynamics
• Fast GPU-based Two-way Continuous Collision Handling
• Shortest Path to Boundary for Self-Intersecting Meshes
• Sum-of-squares Collision Detection for Curved Shapes and Paths
• High-order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes
• Multi-Layer Thick Shells
• Constraint-Based Simulation of Passive Suction Cups
• Nonlinear Compliant Modes for Large-Deformation Analysis of Flexible Structures
• Anatomically Detailed Simulation of Human Torso

Fan Feng, Jinyuan Liu, Shiying Xiong, Shuqi Yang, Yaorui Zhang, Bo Zhu

We propose a new incompressible Navier–Stokes solver based on the impulse gauge transformation. The mathematical model of our approach draws from the impulse–velocity formulation of Navier–Stokes equations, which evolves the fluid impulse as an auxiliary variable of the system that can be projected to obtain the incompressible flow velocities at the end of each time step. We solve the impulse-form equations numerically on a Cartesian grid. At the heart of our simulation algorithm is a novel model to treat the impulse stretching and a harmonic boundary treatment to incorporate the surface tension effects accurately. We also build an impulse PIC/FLIP solver to support free-surface fluid simulation. Our impulse solver can naturally produce rich vortical flow details without artificial enhancements. We showcase this feature by using our solver to facilitate a wide range of fluid simulation tasks including smoke, liquid, and surface-tension flow. In addition, we discuss a convenient mechanism in our framework to control the scale and strength of the turbulent effects of fluid.

Impulse Fluid Simulation

Tianyu Wang, Jiong Chen, Dongping Li, Xiaowei Liu, Huamin Wang, Kun Zhou

Step-and-project is a popular way to simulate non-penetrated deformable bodies in physically-based animation. First integrating the system in time regardless of contacts and post resolving potential intersections practically strike a good balance between plausibility and efficiency. However, existing methods could be defective and unsafe when the time step is large, taking risks of failures or demands of repetitive collision testing and resolving that severely degrade performance. In this paper, we propose a novel two-way method for fast and reliable continuous collision handling. Our method launches the optimization at both ends of the intermediate time-integrated state and the previous intersection-free state, progressively generating a piecewise-linear path and finally reaching a feasible solution for the next time step. Technically, our method interleaves between a forward step and a backward step at a low cost, until the result is conditionally converged. Due to a set of unified volume-based contact constraints, our method can flexibly and reliably handle a variety of codimensional deformable bodies, including volumetric bodies, cloth, hair and sand. The experiments show that our method is safe, robust, physically faithful and numerically efficient, especially suitable for large deformations or large time steps.

Fast GPU-Based Two-Way Continuous Collision Handling