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.

In this paper, we introduce a novel method for intelligently resizing a wide range of volumetric data including fluids. Fluid carving, the technique we build upon, only supported particle-based liquid data, and because it was based on image-based techniques, it was constrained to rectangular boundaries. We address these limitations to allow a much more versatile method for volumetric post-processing. By enclosing a region of interest in our lattice structure, users can retarget regions of a volume with non-rectangular boundaries and non-axis-aligned motion. Our approach generalizes to images, videos, liquids, meshes, and even previously unexplored domains such as fire and smoke. We also present a seam computation method that is significantly faster than the previous approach while maintaining the same level of quality, thus making our method more viable for production settings where post-processing workflows are vital.

We present a method for intelligently resizing fluid simulation data using seam carving methods. While advances in post-processing techniques have allowed artists greater control over content late in the production process, this technology has largely remained confined to image processing. Our fluid carving system allows fluid simulation post-processing by performing content-aware non-uniform scaling on baked-out fluid simulation data. Specifically, we extend video seam carving techniques to 4-dimensional animated fluid volume data with a graph cut energy function based on mean curvature and kinetic energy. To reduce the complexity of performing graph cuts on 4D data, we provide a new graph construction formulation that greatly reduces the run-time and memory consumption, which are otherwise prohibitively expensive. We demonstrate that our system is useful for post-production fluid simulation changes and editable fluid FX libraries.

An Eulerian approach to fluid flow provides an efficient, stable paradigm for realistic fluid simulation. However, its traditional reliance on a fixed-resolution grid is not ideal for simulations that simultaneously exhibit both large and small-scale fluid phenomena. Octree-based fluid simulation approaches have provided the needed adaptivity, but the inherent weakness of a pointer-based tree structure has limited their effectiveness. We present a linear octree structure that provides a significant runtime speedup using these octree-based simulation algorithms. As memory prices continue to decline, we leverage additional memory when compared to traditional octree structures to provide this improvement. In addition to reducing the level of indirection in the data, because our linear octree is stored contiguously in memory as a simple Carray rather than a recursive set of pointers, we provide a more cache-friendly data layout than a traditional octree. In our testing, our approach yielded run-times that were 1.5 to nearly 5 times faster than the same simulations running on a traditional octree implementation.