The knit structure consists of interlocked yarns, with each yarn comprising multiple plies comprising tens to hundreds of twisted fibers. This intricate geometry and the large number of geometric primitives present substantial challenges for achieving high-fidelity simulation and rendering in real-time applications. In this work, we introduce the first real-time framework that takes an animated stitch mesh as input and enhances it with yarn-level simulation and fiber-level rendering. Our approach relies on a knot-based representation to model interlocked yarn contacts. The knot positions are interpolated from the underlying mesh, and associated yarn control points are optimized using a physically inspired energy formulation, which is solved through a GPU-based Gauss-Newton scheme for real-time performance. The optimized control points are sent to the GPU rasterization pipeline and rendered as yarns with fiber-level details. In real-time rendering, we introduce several decomposition strategies to enable realistic lighting effects on complex knit structures, even under environmental lighting, while maintaining computational and memory efficiency. Our simulation faithfully reproduces yarn-level structures under deformations, e.g., stretching and shearing, capturing interlocked yarn behaviors. The rendering pipeline achieves near-ground-truth visual quality while being 120,000× faster than path tracing reference with fiber-level geometries. The whole system provides real-time performance and has been evaluated through various application scenarios, including knit simulation for small patches and full garments and yarn-level relaxation in the design pipeline.

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 512 × 512 × 2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2× 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/.

We present the Moving Eulerian-Lagrangian Particles (MELP), a novel mesh-free method for simulating incompressible fluid on thin films and foams. Employing a bi-layer particle structure, MELP jointly simulates detailed, vigorous flow and large surface deformation at high stability and efficiency. In addition, we design multi-MELP: a mechanism that facilitates the physically-based interaction between multiple MELP systems, to simulate bubble clusters and foams with non-manifold topological evolution. We showcase the efficacy of our method with a broad range of challenging thin film phenomena, including the Rayleigh-Taylor instability across double-bubbles, foam fragmentation with rim surface tension, recovery of the Plateau borders, Newton black films, as well as cyclones on bubble clusters.

We propose a novel solid-fluid coupling method to capture the subtle hydrophobic and hydrophilic interactions between liquid, solid, and air at their multi-phase junctions. The key component of our approach is a Lagrangian model that tackles the coupling, evolution, and equilibrium of dynamic contact lines evolving on the interface between surface-tension fluid and deformable objects. This contact-line model captures an ensemble of small-scale geometric and physical processes, including dynamic waterfront tracking, local momentum transfer and force balance, and interfacial tension calculation. On top of this contact-line model, we further developed a mesh-based level set method to evolve the three-phase T-junction on a deformable solid surface. Our dynamic contact-line model, in conjunction with its monolithic coupling system, unifies the simulation of various hydrophobic and hydrophilic solid-fluid-interaction phenomena and enables a broad range of challenging small-scale elastocapillary phenomena that were previously difficult or impractical to solve, such as the elastocapillary origami and self-assembly, dynamic contact angles of drops, capillary adhesion, as well as wetting and splashing on vibrating surfaces.

We propose a novel Clebsch method to simulate the free-surface vortical flow. At the center of our approach lies a level-set method enhanced by a wave-function correction scheme and a wave-function extrapolation algorithm to tackle the Clebsch method's numerical instabilities near a dynamic interface. By combining the Clebsch wave function's expressiveness in representing vortical structures and the level-set function's ability on tracking interfacial dynamics, we can model complex vortex-interface interaction problems that exhibit rich free-surface flow details on a Cartesian grid. We showcase the efficacy of our approach by simulating a wide range of new free-surface flow phenomena that were impractical for previous methods, including horseshoe vortex, sink vortex, bubble rings, and free-surface wake vortices.

We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.