Physics-Based Animation

Zhiqi Li*, Ruicheng Wang*, Junlin Li*, Duowen Chen, Sinan Wang, Bo Zhu (* Co-first Authors)

We propose the Epsilon Difference Gradient Evolution (EDGE) method for accurate flow-map calculation on grids via Hermite interpolation without using velocity buffers. Our key idea is to integrate Gradient Evolution for accurate first-order derivatives and a tetrahedron-based Epsilon Difference scheme to compute higher-order derivatives with reduced memory consumption. EDGE achieves O(1) memory usage, independent of flow map length, while maintaining vorticity preservation comparable to buffer-based methods. We validate our methods across diverse vortical flow scenarios, demonstrating up to 90% backward map memory reduction and significant computational efficiency, broadening the applicability of flow-map methods to large-scale and complex fluid simulations.

EDGE: Epsilon-Difference Gradient Evolution for Buffer-Free Flow Maps

Mengdi Wang, Fan Feng, Junlin Li, Bo Zhu

We propose the adaptive hybrid particle-grid flow map method, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method in Cirrus, a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512x512x2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2x speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. The source code has been made publicly available at: https://wang-mengdi.github.io/proj/25-cirrus/.

Cirrus: Adaptive Hybrid Particle-Grid Flow Maps on GPU

Sinan Wang, Junwei Zhou, Fan Feng, Zhiqi Li, Yuchen Sun, Duowen Chen, Greg Turk, Bo Zhu

We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3-12 times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena.

Fluid Simulation on Vortex Particle Flow Maps

Leticia Mattos Da Silva, Silvia Sellán, Natalia Pacheco-Tallaj, Justin Solomon

Numerical schemes for time integration are the cornerstone of dynamical simulations for deformable solids. The most popular time integrators for isotropic distortion energies rely on nonlinear root-finding solvers, most prominently, Newton’s method. These solvers are computationally expensive and sensitive to ill-conditioned Hessians and poor initial guesses; these difficulties can particularly hamper the effectiveness of variational integrators, whose momentum conservation properties require reliable root-finding. To tackle these difficulties, this paper shows how to express variational time integration for a large class of elastic energies as an optimization problem with a “hidden” convex substructure. This hidden convexity suggests uses of optimization techniques with rigorous convergence analysis, guaranteed inversion-free elements, and conservation of physical invariants up to tolerance/numerical precision. In particular, we propose an Alternating Direction Method of Multipliers (ADMM) algorithm combined with a proximal operator step to solve our formulation. Empirically, our integrator improves the performance of elastic simulation tasks, as we demonstrate in a number of examples.

Variational Elastodynamic Simulation

Mengdi Wang, Fan Feng, Junlin Li, Bo Zhu

We propose the adaptive hybrid particle-grid flow map method, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method in Cirrus, a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512x512x2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2x speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. The source code has been made publicly available at: https://wang-mengdi.github.io/proj/25-cirrus/.

Cirrus: Adaptive Hybrid Particle-Grid Flow Maps on GPU

Zizhou Huang, Max Paik, Zachary Ferguson, Daniele Panozzo, Denis Zorin

Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding intersections, which are the cause of most robustness problems in complex deformation simulation with contact. However, existing barrier-potential methods may lead to spurious forces and imperfect satisfaction of the geometric constraints. They may have strong resolution dependence, requiring careful adaptation of the potential parameters to the object discretizations. We present a systematic derivation of a continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence on shape, and absence of forces in rest configurations. Our potential is formulated independently of surface discretization and addresses the shortcomings of existing potential-based methods while retaining their advantages. We present a discretization of our potential that is a drop-in replacement for the potential used in the incremental potential contact formulation [Li et al. 2020], and compare its behavior to other potential formulations, demonstrating that it has the expected behavior. The presented formulation connects existing barrier approaches, as all recent existing methods can be viewed as a variation of the presented potential, and lays a foundation for developing alternative (e.g., higher-order) versions.

Geometric Contact Potential

Bernhard Braun, Jan Bender, Nils Thuerey

Capturing the visually compelling features of large-scale water phenomena,such as the spray clouds of crashing waves, stormy seas, or waterfalls, involves simulating not only the water but also the motion of the air interacting with it. However, current solutions in the visual effects industry still largely rely on single-phase solvers and non-physical “white-water” heuristics. To address these limitations, we present Phase-Field-FLIP (PF-FLIP), a hybrid Eulerian/Lagrangian method for the fully physics-based simulation of very large-scale, highly turbulent multiphase flows at high Reynolds numbers and high fluid density contrasts. PF-FLIP transports mass and momentum in a consistent, non-dissipative manner and, unlike most existing multiphase approaches, does not require a surface reconstruction step. Furthermore, we employ spatial adaptivity across all critical components of the simulation algorithm, including the pressure Poisson solver. We augment PF-FLIP with a dual multiresolution scheme that couples an efficient treeless adaptive grid with adaptive particles, along with a fast adaptive Poisson solver tailored for high-density-contrast multiphase flows. Our method enables the simulation of two-phase flow scenarios with a level of physical realism and detail previously unattainable in graphics, supporting billions of particles and adaptive 3D resolutions with thousands of grid cells per dimension on a single workstation.

Adaptive Phase-Field-FLIP for Very Large Scale Two-Phase Fluid Simulation

Hossein Baktash, Nicholas Sharp, Qingnan Zhou, Keenan Crane, Alec Jacobson

This paper explores the analysis and design of the resting configurations of a rigid body, without the use of physical simulation. In particular, given a rigid body in ℝ³, we identify all possible stationary points, as well as the probability that the body will stop at these points, assuming a random initial orientation and negligible momentum. The forward version of our method can hence be used to automatically orient models, to provide feedback about object stability during the design process, and to furnish plausible distributions of shape orientation for natural scene modeling. Moreover, a differentiable inverse version of our method lets us design shapes with target resting behavior, such as dice with target, nonuniform probabilities. Here we find solutions that would be nearly impossible to find using classical techniques, such as dice with additional unstable faces that provide more natural overall geometry.

Putting Rigid Bodies to Rest

Magí Romanyà Serrasolsas, Juan J. Casafranca, Miguel A. Otaduy

We propose the formulation of forward and differentiable rigid-body dynamics using Lie-algebra rotation derivatives. In particular, we show how this approach can easily be applied to incremental-potential formulations of forward dymamics, and we introduce a novel definition of adjoints for differentiable dynamics. In contrast to other parameterizations of rotations (notably the popular rotation-vector parameterization), our approach leads to painlessly simple and compact derivatives, better conditioning, and higher runtime efficiency. We demonstrate our approach on fundamental rigid-body problems, but also on Cosserat rods as an example of multi-rigid-body dynamics.

Painless Differentiable Rotation Dynamics

David Algis, Bérenger Bramas, Emmanuelle Darles, Lilian Aveneau

The oceans cover the vast majority of the Earth. Therefore, their simulation has many scientific, industrial and military interests, including computer graphics domain. By fully exploiting the multi-threading power of GPU and CPU, current state-of-the-art tools can achieve real-time ocean simulation, even if it is sometimes needed to reduce the physical realism for large scenes. Although most of the building blocks for implementing an ocean simulator are described in the literature, a clear explanation of how they interconnect is lacking. Hence, this paper proposes to bring all these components together, detailing all their interactions, in a comprehensive and fully described real-time framework that simulates the free ocean surface and the coupling between solids and fluid. This article also presents several improvements to enhance the physical realism of our model. The two main ones are: calculating the real-time velocity of ocean fluids at any depth; computing the input of the solid to fluid coupling algorithm.

Arc Blanc: a real time ocean simulation framework