Physics-Based Animation

Juntian Zheng, Zhaofeng Luo, Minchen Li

We introduce a barrier-free optimization framework for non-penetration elastodynamic simulation that matches the robustness of Incremental Potential Contact (IPC) while overcoming its two primary efficiency bottlenecks: (1) reliance on logarithmic barrier functions to enforce non-penetration constraints, which leads to ill-conditioned systems and significantly slows down the convergence of iterative linear solvers; and (2) the time-of-impact (TOI) locking issue, which restricts active-set exploration in collision-intensive scenes and requires a large number of Newton iterations. We propose a novel second-order constrained optimization framework featuring a custom augmented Lagrangian solver that avoids TOI locking by immediately incorporating all requisite contact pairs detected via CCD, enabling more efficient active-set exploration and leading to significantly fewer Newton iterations. By adaptively updating Lagrange multipliers rather than increasing penalty stiffness, our method prevents stagnation at zero TOI while maintaining a well-conditioned system. We further introduce a constraint filtering and decay mechanism to keep the active set compact and stable. A comprehensive set of experiments demonstrates the efficiency, robustness, finite-step termination, and first-order time integration accuracy of our method under a cumulative TOI-based termination criterion. With a GPU-optimized simulator design, our method achieves an up to 103x speedup over GIPC on challenging, contact-rich benchmarks – scenarios that were previously tractable only with barrier-based methods.

Robust and Efficient Penetration-Free Elastodynamics without Barriers

Alvin Shi, Florence Bertails-Descoubes, A.M. Darke, Theodore Kim

Due to its highly curved geometry, tightly coiled hair is challenging to model and edit using standard position-based tools. In this work we propose using material curvatures and twists to analyze and edit tightly coiled hair styles. Our method relies on the geometry of super-helices, primitives parametrized by piecewise constant curvatures and twists, whose helical geometry naturally resembles a coiled hair strand. Using this curvature/twist space, we introduce new editing tools that allow us to expand, shrink, “ruffle”, interpolate or guide the position of coiled hair in a natural way. We present analytical expressions for geometry and gradients that allow our method to run efficiently and without the need for any training data. We successfully apply our tools to highly coiled simulated hairs, as well as those generated procedurally.

Curvature Space Editing of Highly-Coiled Hair

Runze Zhang, Bo Ren

The intricate motion arising from fluid–boundary interactions is visually compelling, yet notoriously difficult and computationally expensive to simulate in the presence of complex boundaries. Accurately resolving boundary geometry requires body-fitted grids constructed via cut-cell methods, which often leads to poorly conditioned linear systems in the pressure projection stage and, consequently, prohibitive computational cost. We present FastVEM, an efficient boundary-conforming fluid simulation framework that enables high-fidelity flow–boundary interaction at substantially reduced cost. Computational efficiency is achieved through a coordinated, top-down design spanning numerical discretization, grid construction, and linear solvers. FastVEM adopts a Virtual Element Method (VEM) discretization to robustly
enforce incompressibility and boundary conditions on irregular body-fitted grids, and employs a VEM polynomial-space Particle-in-Cell scheme for advection. Complementing this discretization, a convexity-preserving cut-cell strategy is introduced to construct simulation-friendly body-fitted grids. To accelerate pressure projection, we develop a Galerkin geometric multigrid solver featuring a diffusion-free prolongation operator that prevents coarse-level matrix densification, along with a nested, boundary-aware grid hierarchy that ensures well-posed placement of coarse-level degrees of freedom. Compared to prior cut-cell–based fluid simulators, FastVEM speeds up the computationally dominant pressure projection stage by up to 100×, while robustly handling even more challenging boundary geometries.

Fast VEM Fluid Simulation

Ruolan Li, Yanrui Xu, Yalan Zhang, and Jiri Kosinka, Alexandru C. Telea, Jian Chang, Jian Jun Zhang, Xiaojuan Ban, Xiaokun Wang

Simulating the interactions between fluids and porous media has attracted significant attention in computer graphics. A key challenge in this domain is modeling the Poro-Elasto-Capillary (PEC) coupling effect which describes the intricate interplay of three physical phenomena in soft porous materials: pore-structure evolution, elastic deformation, and wetting driven by capillary pressure. These phenomena collectively govern dynamic behavior such as the softening and fracturing of biscuits upon water absorption or the swelling of cellulose sponges due to liquid infiltration. Most existing simulation methods model porous media either as static grids or as solid particles with augmented water content attributes, failing to capture the full spectrum of PEC-driven effects due to the lack of physical modeling for elasticity, dynamic porosity changes, and capillary interactions. We propose a multiphase particle-based framework to holistically simulate PEC coupling effects with porous media. We develop a physics-driven model that captures elasticity and dynamic pore-structure evolution under capillary action, enabling realistic simulation of softening and swelling. We derive a saturation-aware pressure Poisson equation to enforce fluid incompressibility within and around the porous medium, ensuring accurate capillary-driven flow while preserving mass and momentum. Finally, we propose a representative elementary volume-based formulation to unify the modeling of homogeneous macro-porous media and cavity-embedded structures, enhancing the representation of pore-scale PEC effects. Comparisons with prior work and real footage show the advantages of our approach in achieving visually realistic fluid-porous media interactions.

Multiphase Particle-Based Simulation of Poro-Elasto-Capillary Effects

Helge Wrede, Anton R. Wagner, Sarker Miraz Mahfuz, Wojtek Pałubicki, Dominik L. Michels, Sören Pirk

We present a novel combustion simulation framework to model fire phenomena across solids, liquids, and gases. Our approach extends traditional fluid solvers by incorporating multi-species thermodynamics and reactive transport for fuel, oxygen, nitrogen, carbon dioxide, water vapor, and residuals. Combustion reactions are governed by stoichiometry-dependent heat release, allowing an accurate simulation of premixed and diffusive flames with varying intensity and composition. We support a wide range of scenarios including jet fires, water suppression (sprays and sprinklers), fuel evaporation, and starvation conditions. Our framework enables interactive heat sources, fire detectors, and realistic rendering of flames (e.g., laminar-to-turbulent transitions and blue-to-orange color shifts). Our key contributions include the tight coupling of species dynamics with thermodynamic feedback, evaporation modeling, and a hybrid SPH-grid representation for the efficient simulation of extinguishing fires. We validate our method through numerous experiments that demonstrate its versatility in both indoor and outdoor fire scenarios.

Fire-X: Extinguishing Fire with Stoichiometric Heat Release

Timna Böttcher, Lukas Westhofen, Stefan Rhys Jeske, Jan Bender

We present a novel implicit porous flow solver using SPH, which maintains fluid incompressibility and is able to model a wide range of scenarios, driven by strongly coupled solid-fluid interaction forces. Many previous SPH porous flow methods reduce particle volumes as they transition across the solid-fluid interface, resulting in significant stability issues. This further allows us to extend SPH pressure solvers to take local porosity into account and results in strict enforcement of incompressibility. As a result, we can simulate porous flow using physically consistent pressure forces between fluid and solid. In contrast to previous SPH porous flow methods, which use explicit forces for internal fluid flow, we employ implicit non-pressure forces. These we solve as a linear system and strongly couple with fluid viscosity and solid elasticity. We capture the most common effects observed in porous flow, namely drag, buoyancy and capillary action due to adhesion. To achieve elastic behavior change based on local fluid saturation, such as bloating or softening, we propose an extension to the elasticity model. We demonstrate the efficacy of our model with various simulations that showcase the different aspects of porous flow behavior. To summarize, our system of strongly coupled non-pressure forces and enforced incompressibility across overlapping phases allows us to naturally model and stably simulate complex porous interactions.

Implicit Incompressible Porous Flow using SPH

Haoxiang Wang, Kui Wu, Hui Qiao, Mattieu Desbrun, Wei Li

Kinetic multiphase flow solvers have recently demonstrated exquisitely complex and turbulent fluid phenomena involving splashing and bubbling. However, they require full simulation of both the liquid phase and the air to capture a large spectrum of fluid behaviors. Moreover, they rely on diffuse interface tracking to properly account for the interfacial forces involved in fluid-air interactions. Consequently, simulating visually appealing fluids is extremely compute intensive given the required resolution to capture small bubbles, and foam simulation is unattainable with this family of methods. While water simulation involves density and viscosity differences between the two phases so large that one can safely ignore the dynamics of air, so-called kinetic free-surface solvers that only consider the liquid motion have been unable to reproduce the full gamut of turbulent fluid behaviors, being often unstable for even moderately complex scenarios. By revisiting kinetic solvers using sharp interfaces and incorporating recent advances in single-phase and multiphase LBM solvers, we propose a free-surface kinetic solver, which we call HOME-FREE LBM, that not only handles turbulence, glugging, and bubbling, but even foam where bubbles stick to each other through surface tension. We demonstrate that our fluid simulator allows for fast and robust bubble growth, breakup, and coalescence, at a fraction of the computational time that existing CG fluid solvers require.

Kinetic Free-Surface Flows and Foams with Sharp Interfaces

Zhiqi Li, Jinjin He, Barnabás Börcsök, Taiyuan Zhang, Duowen Chen, Tao Du, Ming C. Lin, Greg Turk, Bo Zhu

This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as the forward simulation. In the forward pass, this map transports fluid impulse variables from the initial frame to the current frame to simulate vortical dynamics. In the backward pass, the same map propagates adjoint variables from the current frame back to the initial frame to compute gradients. This shared long-range map allows the accuracy of gradient computation to benefit directly from improvements in flow map construction. Building on this insight, we introduce a novel adjoint solver that solves the adjoint equations directly on the flow map, enabling long-range and accurate differentiation of incompressible flows without differentiating intermediate numerical steps or storing intermediate variables, as required in conventional adjoint methods. To further improve efficiency, we propose a long-short time-sparse flow map representation for evolving adjoint variables. Our approach has low memory usage, requiring only 6.53GB of data at a resolution of 192^3 while preserving high accuracy in tracking vorticity, enabling new differentiable simulation tasks that require precise identification, prediction, and control of vortex dynamics.

An Adjoint Method for Differentiable Fluid Simulation on Flow Maps

Xiao Sean Zhan, Evan Thompson, Clément Jambon, Kenney Ng, Mina Konaković Luković

Generative models have recently demonstrated impressive capabilities in producing high-quality 3D shapes from a variety of user inputs (e.g., text or images). However, generated objects often lack physical integrity. We introduce PhysiOpt, a differentiable physics optimizer designed to improve the physical behavior of 3D generative outputs, enabling them to transition from virtual designs to physically plausible, real-world objects. While most generative models represent geometry as continuous implicit fields, physics-based approaches often rely on the finite element method (FEM), requiring ad hoc mesh extraction to perform shape optimization. In addition, these methods are typically slow, limiting their integration in fast, iterative generative design workflows. Instead, we bridge the representation gap and propose a fast and effective differentiable simulation pipeline that optimizes shapes directly in the latent space of generative models using an intuitive and easy-to-implement differentiable mapping. This approach enables fast optimization while preserving semantic structure, unlike traditional methods relying on local mesh-based adjustments. We demonstrate the versatility of our optimizer across a range of shape priors, from global and part-based latent models to a state-of-the-art large-scale 3D generator, and compare it to a traditional mesh-based shape optimizer. Our method preserves the native representation and capabilities of the underlying generative model while supporting user-specified materials, loads, and boundary conditions. The resulting designs exhibit improved physical behavior, remain faithful to the learned priors, and are suitable for fabrication. We demonstrate the effectiveness of our approach on both virtual and fabricated objects.

PhysiOpt: Physics-Driven Shape Optimization for 3D Generative Models

Yura Hwang, Jenny Han Lin, Jerry Hsu, Benjamin Mastripolito, James McCann, Cem Yuksel

Lightweight, mesh-level models of knit fabric behavior are useful for both interactive pattern editing and initialization of yarn-level simulations. However, existing mesh-level simulation methods abstract knitting as a homogeneous material, which prevents them from capturing more complicated mixed structures. Furthermore, these methods require different simulation parameters depending on the knit pattern, or arrangement of stitches within the knit. Thus, fitting these parameters to physical examples must be done for each new pattern, even when the same types of stitches are used. To address this, we observe that physical behavior of a stitch is determined not only by its individual structure but also by the stitch types that surround it. In our work, we extend the stitch mesh model to allow for neighbor-aware material properties at the stitch level. Using structural analysis of stitch connections, we derive a finite set of four-way kernels that combine to create general knit-purl patterns for relaxation. From this, we generate a set of reference patterns that can be measured to infer the rest-lengths of the kernels using a linear model. After knitting and measuring these reference patterns, we used the derived kernel rest lengths to run relaxation on our stitch mesh models with mixtures of knits and purls that we then validated against physical examples. Our results show that the 4 neighbors of each stitch is sufficient to account for much of the neighborhood-dependent deformation, while remaining simple enough to directly fit to measured data with a set of 11 basis swatches. This allows our relaxation method to efficiently estimate the rest shape of mixed knit-purl patterns, which enables fast fabric preview and more accurate yarn-level simulation.

Neighbor-Aware Data-Driven Relaxation of Stitch Mesh Models for Knits