This work addresses the challenges of distributing large physics-based simulations often encountered in the visual effects industry. These simulations, based on partial differential equations, model complex phenomena such as free surface liquids, flames, and explosions, and are characterized by domains whose shapes and topologies evolve rapidly. In this context, we propose a novel partitioning algorithm employing optimal transport —which produces a power diagram—and designed to handle a vast variety of simulation domain shapes undergoing rapid changes over time. Our Power partitioner ensures an even distribution of computational tasks, reduces inter-node data exchange, and maintains temporal consistency, all while being intuitive and artist-friendly. To quantify partitioning quality we introduce two metrics, the surface index and the temporal consistency index, which we leverage in a range of comparisons on real-world film production data, showing that our method outperforms the state of the art in a majority of cases.

Abstract 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.

We introduce Loki, a new framework for robust simulation of fluid, rigid, and deformable objects with non-compromising fidelity on any single element, and capabilities for coupling and representation transitions across multiple elements. Loki adapts multiple best-in-class solvers into a unified framework driven by a declarative state machine where users declare 'what' is simulated but not 'when,' so an automatic scheduling system takes care of mixing any combination of objects. This leads to intuitive setups for coupled simulations such as hair in the wind or objects transitioning from one representation to another, for example bulk water FLIP particles to SPH spray particles to volumetric mist. We also provide a consistent treatment for components used in several domains, such as unified collision and attachment constraints across 1D, 2D, 3D deforming and rigid objects. Distribution over MPI, custom linear equation solvers, and aggressive application of sparse techniques keep performance within production requirements. We demonstrate a variety of solvers within the framework and their interactions, including FLIPstyle liquids, spatially adaptive volumetric fluids, SPH, MPM, and mesh-based solids, including but not limited to discrete elastic rods, elastons, and FEM with state-of-the-art constitutive models. Our framework has proven powerful and intuitive enough for voluntary artist adoption and has delivered creature and FX simulations for multiple major movie productions in the preceding four years.

We present a method for enhancing fluid simulations with realistic bubble and foam detail. We treat bubbles as discrete air particles, two-way coupled with a sparse volumetric Euler flow, as first suggested in [Stomakhin et al. 2020]. We elaborate further on their scheme and introduce a bubble inertia correction term for improved convergence. We also show how one can add bubbles to an already existing fluid simulation using our novel guiding technique, which performs local re-simulation of fluid to achieve more interesting bubble dynamics through coupling. As bubbles reach the surface, they are converted into foam and simulated separately. Our foam is discretized with smoothed particle hydrodynamics (SPH), and we replace forces normal to the fluid surface with a fluid surface manifold advection constraint to achieve more robust and stable results. The SPH forces are derived through proper constitutive modeling of an incompressible viscous liquid, and we explain why this choice is appropriate for "wet" types of foam. This allows us to produce believable dynamics from close-up scenarios to large oceans, with just a few parameters that work intuitively across a variety of scales. Additionally, we present relevant research on air entrainment metrics and bubble distributions that have been used in this work.

We present a novel approach to guiding physically based particle simulations using boundary conditions. Unlike commonly used ad hoc particle techniques for adding and removing the material from a simulation, our approach is principled by utilizing the concept of volumetric flux. Artists are provided with a simple yet powerful primitive called a fluxed animated boundary (FAB) , allowing them to specify a control shape and a material flow field. The system takes care of enforcing the corresponding boundary conditions and necessary particle reseeding. We show how FABs can be used artistically or physically. Finally, we demonstrate production examples that show the efficacy of our method.

Hybrid Lagrangian/Eulerian simulation is commonplace in computer graphics for fluids and other materials undergoing large deformation. In these methods, particles are used to resolve transport and topological change, while a background Eulerian grid is used for computing mechanical forces and collision responses. Particle-in-Cell (PIC) techniques, particularly the Fluid Implicit Particle (FLIP) variants have become the norm in computer graphics calculations. While these approaches have proven very powerful, they do suffer from some well known limitations. The original PIC is stable, but highly dissipative, while FLIP, designed to remove this dissipation, is more noisy and at times, unstable. We present a novel technique designed to retain the stability of the original PIC, without suffering from the noise and instability of FLIP. Our primary observation is that the dissipation in the original PIC results from a loss of information when transferring between grid and particle representations. We prevent this loss of information by augmenting each particle with a locally affine, rather than locally constant, description of the velocity. We show that this not only stably removes the dissipation of PIC, but that it also allows for exact conservation of angular momentum across the transfers between particles and grid.

Practical time steps in today's state-of-the-art simulators typically rely on Newton's method to solve large systems of nonlinear equations. In practice, this works well for small time steps but is unreliable at large time steps at or near the frame rate, particularly for difficult or stiff simulations. We show that recasting backward Euler as a minimization problem allows Newton's method to be stabilized by standard optimization techniques with some novel improvements of our own. The resulting solver is capable of solving even the toughest simulations at the [Formula: see text] frame rate and beyond. We show how simple collisions can be incorporated directly into the solver through constrained minimization without sacrificing efficiency. We also present novel penalty collision formulations for self collisions and collisions against scripted bodies designed for the unique demands of this solver. Finally, we show that these techniques improve the behavior of Material Point Method (MPM) simulations by recasting it as an optimization problem.

In this paper, we introduce a novel material point method for heat transport, melting and solidifying materials. This brings a wider range of material behaviors into reach of the already versatile material point method. This is in contrast to best-of-breed fluid, solid or rigid body solvers that are difficult to adapt to a wide range of materials. Extending the material point method requires several contributions. We introduce a dilational/deviatoric splitting of the constitutive model and show that an implicit treatment of the Eulerian evolution of the dilational part can be used to simulate arbitrarily incompressible materials. Furthermore, we show that this treatment reduces to a parabolic equation for moderate compressibility and an elliptic, Chorin-style projection at the incompressible limit. Since projections are naturally done on marker and cell (MAC) grids, we devise a staggered grid MPM method. Lastly, to generate varying material parameters, we adapt a heat-equation solver to a material point framework.

Snow is a challenging natural phenomenon to visually simulate. While the graphics community has previously considered accumulation and rendering of snow, animation of snow dynamics has not been fully addressed. Additionally, existing techniques for solids and fluids have difficulty producing convincing snow results. Specifically, wet or dense snow that has both solid- and fluid-like properties is difficult to handle. Consequently, this paper presents a novel snow simulation method utilizing a user-controllable elasto-plastic constitutive model integrated with a hybrid Eulerian/Lagrangian Material Point Method. The method is continuum based and its hybrid nature allows us to use a regular Cartesian grid to automate treatment of self-collision and fracture. It also naturally allows us to derive a grid-based semi-implicit integration scheme that has conditioning independent of the number of Lagrangian particles. We demonstrate the power of our method with a variety of snow phenomena including complex character interactions.