We propose a unified, few-step generative modeling framework based on cumulative flow maps for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a cumulative-flow abstraction that connects local, instantaneous updates with finite-time transport, enabling generative models to reason about global state transitions. This perspective yields a unified few-step framework built on cumulative transport and cumulative parameterization that applies broadly to existing diffusion- and flow-based models without being tied to a specific prediction instantiation. Our formulation supports few-step and even one-step generation while preserving synthesis quality, requiring only minimal changes to time embeddings and training objectives, and no increase in model capacity. We demonstrate its effectiveness across diverse tasks, including image generation, geometric distribution modeling, joint prediction, and SDF generation, with reduced inference cost.

We present Orbit-Space Geometric Probability Paths (OGPP) , a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries , so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; (ii) particles live in physical space, so the flow's terminal velocity has physical meaning and can encode geometric attributes (e.g., surface normals). OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state-of-the-art with 5× fewer steps and reaches airplane EMD comparable to DiT-3D with 26× fewer parameters and 5× fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

We introduce a novel approach to simulate the interaction between fluids and thin elastic solids without any penetration. Our approach is centered around an optimization system augmented with barriers, which aims to find a configuration that ensures the absence of penetration while enforcing incompressibility for the fluids and minimizing elastic potentials for the solids. Unlike previous methods that primarily focus on velocity coherence at the fluid-solid interfaces, we demonstrate the effectiveness and flexibility of explicitly resolving positional constraints, including both explicit representation of solid positions and the implicit representation of fluid level-set interface. To preserve the volume of the fluid, we propose a simple yet efficient approach that adjusts the associated level-set values. Additionally, we develop a distance metric capable of measuring the separation between an implicitly represented surface and a Lagrangian object of arbitrary codimension. By integrating the inertia, solid elastic potential, damping, barrier potential, and fluid incompressibility within a unified system, we are able to robustly simulate a wide range of processes involving fluid interactions with lower-dimensional objects such as shells and rods. These processes include topology changes, bouncing, splashing, sliding, rolling, floating, and more.

Compliant mechanisms enable the creation of compact and easy-to-fabricate devices for tangible interaction. This work explores interconnected compliant mechanisms consisting of multiple joints and rigid bodies to transmit and process displacements as signals that result from physical interactions. As these devices are difficult to design due to their vast and complex design space, we developed a graph-based design algorithm and computational tool to help users program and customize such computational functions and procedurally model physical designs. When combined with active materials with actuation and sensing capabilities, these devices can also render and detect haptic interaction. Our design examples demonstrate the tool's capability to respond to relevant HCI concepts, including building modular physical interface toolkits, encrypting tangible interactions, and customizing user augmentation for accessibility. We believe the tool will facilitate the generation of new interfaces with enriched affordance.

We study reconstructing and predicting 3D fluid appearance and velocity from a single video. Current methods require multi-view videos for fluid reconstruction. We present FluidNexus, a novel framework that bridges video generation and physics simulation to tackle this task. Our key insight is to synthesize multiple novel-view videos as references for reconstruction. FluidNexus consists of two key components: (1) a novel-view video synthesizer that combines frame-wise view synthesis with video diffusion refinement for generating realistic videos, and (2) a physics-integrated particle representation coupling differentiable simulation and rendering to simultaneously facilitate 3D fluid reconstruction and prediction. To evaluate our approach, we collect two new real-world fluid datasets featuring textured backgrounds and object interactions. Our method enables dynamic novel view synthesis, future prediction, and interaction simulation from a single fluid video. Project website: https://yuegao.me/FluidNexus.

Numerous recent works have utilized 3D Gaussian Splatting to represent high-fidelity digital avatars. However, none have enabled interactive multilayer Gaussian garments for virtual try-ons without relying on expensive hardware, such as a camera array and/or multiple GPUs. To enable affordable mix-and-match dressing—dressing 3D avatars with realistic and complex combinations of garments—it is crucial to handle the interactions between multiple layers of garments using consumer-level capturing hardware. To address this, we present a novel screenspace layer resolution method combined with physical simulation and Gaussian garments to enable realistic multilayer mix-and-match avatar dressing at interactive rates using low-cost hardware. As an offline process, we capture multiple static garments individually using only a single mobile camera on a static mannequin and then perform a dual reconstruction of Gaussians and simulation mesh. During runtime, these Gaussians are driven by a fast but simple physics simulator, whose output may contain inter-penetrations across garment layers. Our method fixes these in screenspace by rasterizing the simulation mesh from various camera views and culling the Gaussians that are skinned to unseen mesh triangles. We show the effectiveness of our approach by demonstrating mix-and-match dressing results at interactive rates using short-sleeves, long-sleeves, a fur vest, and a singlet. Additionally, we showcase a webcam-based interactive try-on application to further illustrate the capabilities of our system.

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 1923 while preserving high accuracy in tracking vorticity, enabling new differentiable simulation tasks that require precise identification, prediction, and control of vortex dynamics.

This paper presents a unified compressible flow map framework designed to accommodate diverse compressible flow systems, including high-Mach-number flows (e.g., shock waves and supersonic aircraft), weakly compressible systems (e.g., smoke plumes and ink diffusion), and incompressible systems evolving through compressible acoustic quantities (e.g., free-surface shallow water). At the core of our approach is a theoretical foundation for compressible flow maps based on Lagrangian path integrals, a novel advection scheme for the conservative transport of density and energy, and a unified numerical framework for solving compressible flows with varying pressure treatments. We validate our method across three representative compressible flow systems, characterized by varying fluid morphologies, governing equations, and compressibility levels, demonstrating its ability to preserve and evolve spatiotemporal features such as vortical structures and wave interactions governed by different flow physics. Our results highlight a wide range of novel phenomena, from ink torus breakup to delta wing tail vortices and vortex shedding on free surfaces, significantly expanding the range of fluid systems that flow-map methods can handle.

We propose a neural particle level set (Neural PLS) method to accommodate tracking and evolving dynamic neural representations. At the heart of our approach is a set of oriented particles serving dual roles of interface trackers and sampling seeders. These dynamic particles are used to evolve the interface and construct neural representations on a multi-resolution grid-hash structure to hybridize coarse sparse distance fields and multi-scale feature encoding. Based on these parallel implementations and neural-network-friendly architectures, our neural particle level set method combines the computational merits on both ends of the traditional particle level sets and the modern implicit neural representations, in terms of feature representation and dynamic tracking. We demonstrate the efficacy of our approach by showcasing its performance surpassing traditional level-set methods in both benchmark tests and physical simulations.

We propose a novel gauge fluid solver that evolves Clebsch wave functions on particle flow maps (PFMs). The key insight underlying our work is that particle flow maps exhibit superior performance in transporting point elements—such as Clebsch components—compared to line and surface elements, which were the focus of previous methods relying on impulse and vortex gauge variables for flow maps. Our Clebsch PFM method incorporates three main contributions: a novel gauge transformation enabling accurate transport of wave functions on particle flow maps, an enhanced velocity reconstruction method for coarse grids, and a PFM-based simulation framework designed to better preserve fine-scale flow structures. We validate the Clebsch PFM method through a wide range of benchmark tests and simulation examples, ranging from leapfrogging vortex rings and vortex reconnections to Kelvin-Helmholtz instabilities, demonstrating that our method outperforms its impulse- or vortex-based counterparts on particle flow maps, particularly in preserving and evolving small-scale features.

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.

We propose Leapfrog Flow Maps (LFM) to simulate incompressible fluids with rich vortical flows in real time. Our key idea is to use a hybrid velocityimpulse scheme enhanced with leapfrog method to reduce the computational workload of impulse-based flow map methods, while possessing strong ability to preserve vortical structures and fluid details. In order to accelerate the impulse-to-velocity projection, we develop a fast matrix-free Algebraic Multigrid Preconditioned Conjugate Gradient (AMGPCG) solver with customized GPU optimization, which makes projection comparable with impulse evolution in terms of time cost. We demonstrate the performance of our method and its efficacy in a wide range of examples and experiments, such as real-time simulated burning fire ball and delta wingtip vortices.

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 propose the V ortex P article F low M ap (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.

We present a novel particle-grid scheme for simulating bubble and foam flow. At the core of our approach lies a particle representation that combines the computational nature of moving least-squares particles and particle level-set methods. Specifically, we assign a dedicated particle system to each individual bubble, enabling accurate tracking of its interface evolution and topological changes in a foaming fluid system. The particles within each bubble's particle system serve dual purposes. First, they function as a surface discretization, allowing for the solution of surfactant flow physics on the bubble's membrane. Additionally, these particles act as interface trackers, facilitating the evolution of the bubble's shape and topology within the multiphase fluid domain. The combination of particle systems from all bubbles contributes to the generation of an unsigned level-set field, further enhancing the simulation of coupled multiphase flow dynamics. By seamlessly integrating our particle representation into a multiphase, volumetric flow solver, our method enables the simulation of a broad range of intricate bubble and foam phenomena. These phenomena exhibit highly dynamic and complex structural evolution, as well as interfacial flow details.

We present NeuralFluid, a novel framework to explore neural control and design of complex fluidic systems with dynamic solid boundaries. Our system features a fast differentiable Navier-Stokes solver with solid-fluid interface handling, a low-dimensional differentiable parametric geometry representation, a control-shape co-design algorithm, and gym-like simulation environments to facilitate various fluidic control design applications. Additionally, we present a benchmark of design, control, and learning tasks on high-fidelity, high-resolution dynamic fluid environments that pose challenges for existing differentiable fluid simulators. These tasks include designing the control of artificial hearts, identifying robotic end-effector shapes, and controlling a fluid gate. By seamlessly incorporating our differentiable fluid simulator into a learning framework, we demonstrate successful design, control, and learning results that surpass gradient-free solutions in these benchmark tasks.

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The solid-fluid coupling is enabled by implementing two novel mechanisms: first, we developed an impulse-to-velocity transfer mechanism to unify the exchanged physical quantities; second, we devised a particle path integral mechanism to accumulate coupling forces along each flow-map trajectory. Our framework integrates these two mechanisms into an Eulerian-Lagrangian impulse fluid simulator to accommodate traditional coupling models, exemplified by the Material Point Method (MPM) and Immersed Boundary Method (IBM), within a particle flow map framework. We demonstrate our method's efficacy by simulating solid-fluid interactions exhibiting strong vortical dynamics, including various vortex shedding and interaction examples across swimming, falling, breezing, and combustion.

We introduce a differentiable moving particle representation based on the multi-level partition of unity (MPU) to represent dynamic implicit geometries. At the core of our representation are two groups of particles, named feature particles and sample particles, which can move in space and produce dynamic surfaces according to external velocity fields or optimization gradients. These two particle groups iteratively guide and correct each other by alternating their roles as inputs and outputs. Each feature particle carries a set of coefficients for a local quadratic patch. These particle patches are assembled with partition-of-unity weights to derive a continuous implicit global shape. Each sampling particle carries its position and orientation, serving as dense surface samples for optimization tasks. Based on these moving particles, we develop a fully differentiable framework to infer and evolve highly detailed implicit geometries, enhanced by a multi-level background grid for particle adaptivity, across different inverse tasks. We demonstrated the efficacy of our representation through various benchmark comparisons with state-of-the-art neural representations, achieving lower memory consumption, fewer training iterations, and orders of magnitude higher accuracy in handling topologically complex objects and dynamic tracking tasks.

We develop a computational pipeline to facilitate the biomimetic design of winged seeds. Our approach leverages 3D scans of natural winged seeds to construct a bio-inspired design space by interpolating them with geodesic coordinates in the 3D diffeomorphism group. We formulate aerodynamic design tasks with probabilistic performance objectives and adapt a gradient-free optimizer to explore the design space and minimize the expectation of performance objectives efficiently and effectively. Our pipeline discovers novel winged seed designs that outperform natural counterparts in aerodynamic tasks, including long-distance dispersal and guided flight. We validate the physical fidelity of our pipeline by showcasing paper models of selected winged seeds in the design space and reporting their similar aerodynamic behaviors in simulation and reality.

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures.

This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings.

This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film's tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.

We present an Eulerian vortex method based on the theory of flow maps to simulate the complex vortical motions of incompressible fluids. Central to our method is the novel incorporation of the flow-map transport equations for line elements , which, in combination with a bi-directional marching scheme for flow maps, enables the high-fidelity Eulerian advection of vorticity variables. The fundamental motivation is that, compared to impulse m , which has been recently bridged with flow maps to encouraging results, vorticity ω promises to be preferable for its numerical stability and physical interpretability. To realize the full potential of this novel formulation, we develop a new Poisson solving scheme for vorticity-to-velocity reconstruction that is both efficient and able to accurately handle the coupling near solid boundaries. We demonstrate the efficacy of our approach with a range of vortex simulation examples, including leapfrog vortices, vortex collisions, cavity flow, and the formation of complex vortical structures due to solid-fluid interactions.

We propose a novel Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like leapfrog, vortex tube, and turbulent flow.

We study recovering fluid density and velocity from sparse multiview videos. Existing neural dynamic reconstruction methods predominantly rely on optical flows; therefore, they cannot accurately estimate the density and uncover the underlying velocity due to the inherent visual ambiguities of fluid velocity, as fluids are often shapeless and lack stable visual features. The challenge is further pronounced by the turbulent nature of fluid flows, which calls for properly designed fluid velocity representations. To address these challenges, we propose hybrid neural fluid fields (HyFluid), a neural approach to jointly infer fluid density and velocity fields. Specifically, to deal with visual ambiguities of fluid velocity, we introduce a set of physics-based losses that enforce inferring a physically plausible velocity field, which is divergence-free and drives the transport of density. To deal with the turbulent nature of fluid velocity, we design a hybrid neural velocity representation that includes a base neural velocity field that captures most irrotational energy and a vortex particle-based velocity that models residual turbulent velocity. We show that our method enables recovering vortical flow details. Our approach opens up possibilities for various learning and reconstruction applications centered around 3D incompressible flow, including fluid re-simulation and editing, future prediction, and neural dynamic scene composition. Project website: https://kovenyu.com/HyFluid/

We present a computational framework for simulating deformable surfaces from planar rest shape with second-order triangular finite elements. Our method develops numerical schemes for discretizing stretching, shearing, and bending energies of deformable surfaces in a second-order finite-element setting. In particular, we introduce a novel discretization scheme for approximating mean curvatures on a curved triangle mesh. Our framework also integrates a virtual-node finite-element scheme that supports two-way coupling between cut-cell rods without expensive remeshing. We compare our approach with traditional simulation methods using linear and higher-order finite elements and demonstrate its advantages in several challenging settings, such as low-resolution meshes, anisotropic triangulation, and stiff materials. Finally, we showcase several applications of our framework, including cloth simulation, mixed Origami and Kirigami, and biologically-inspired soft wing simulation.

We introduce Neural Flow Maps, a novel simulation method bridging the emerging paradigm of implicit neural representations with fluid simulation based on the theory of flow maps, to achieve state-of-the-art simulation of in-viscid fluid phenomena. We devise a novel hybrid neural field representation, Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a pyramid of overlapping, multi-resolution, and spatially sparse grids, to compactly represent long-term spatiotemporal velocity fields at high accuracy. With this neural velocity buffer in hand, we compute long-term, bidirectional flow maps and their Jacobians in a mechanistically symmetric manner, to facilitate drastic accuracy improvement over existing solutions. These long-range, bidirectional flow maps enable high advection accuracy with low dissipation, which in turn facilitates high-fidelity incompressible flow simulations that manifest intricate vortical structures. We demonstrate the efficacy of our neural fluid simulation in a variety of challenging simulation scenarios, including leapfrogging vortices, colliding vortices, vortex reconnections, as well as vortex generation from moving obstacles and density differences. Our examples show increased performance over existing methods in terms of energy conservation, visual complexity, adherence to experimental observations, and preservation of detailed vortical structures.

research-article Share on GARM-LS: A Gradient-Augmented Reference-Map Method for Level-Set Fluid Simulation Authors: Xingqiao Li School of IST & National Key Lab. of AGI, Peking University, China School of IST & National Key Lab. of AGI, Peking University, China 0000-0002-8131-6140View Profile , Xingyu Ni School of CS & National Key Lab. of AGI, Peking University, China School of CS & National Key Lab. of AGI, Peking University, China 0000-0003-1127-2848View Profile , Bo Zhu Georgia Institute of Technology, United States of America and Dartmouth College, United States of America Georgia Institute of Technology, United States of America and Dartmouth College, United States of America 0000-0002-1392-0928View Profile , Bin Wang Beijing Institute for General Artificial Intelligence, China Beijing Institute for General Artificial Intelligence, China 0000-0001-9496-772XView Profile , Baoquan Chen School of IST & National Key Lab. of AGI, Peking University, China School of IST & National Key Lab. of AGI, Peking University, China 0000-0003-4702-036XView Profile Authors Info & Claims ACM Transactions on GraphicsVolume 42Issue 6Article No.: 192pp 1–20https://doi.org/10.1145/3618377Published:05 December 2023Publication History 1citation71DownloadsMetricsTotal Citations1Total Downloads71Last 12 Months71Last 6 weeks23 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We propose a new incompressible Navier-Stokes solver based on the impulse gauge transformation. The mathematical model of our approach draws from the impulse-velocity formulation of Navier-Stokes equations, which evolves the fluid impulse as an auxiliary variable of the system that can be projected to obtain the incompressible flow velocities at the end of each time step. We solve the impulse-form equations numerically on a Cartesian grid. At the heart of our simulation algorithm is a novel model to treat the impulse stretching and a harmonic boundary treatment to incorporate the surface tension effects accurately. We also build an impulse PIC/FLIP solver to support free-surface fluid simulation. Our impulse solver can naturally produce rich vortical flow details without artificial enhancements. We showcase this feature by using our solver to facilitate a wide range of fluid simulation tasks including smoke, liquid, and surface-tension flow. In addition, we discuss a convenient mechanism in our framework to control the scale and strength of the turbulent effects of fluid.

We propose a novel system for low-cost multi-color Fused Filament Fabrication (FFF) 3D printing, allowing for the creation of customizable colored filament using a pre-processing approach. We developed an open-source device to automatically ink filament using permanent markers. Our device can be built using 3D printed parts and off-the-shelf electronics. An accompanying web-based interface allows users to view GCODE toolpaths for a multi-color print and quickly generate filament color profiles. Taking a pre-processing approach makes this system compatible with the majority of desktop 3D printers on the market, as the processed filament behaves no differently from conventional filaments. Furthermore, inked filaments can be produced economically, reducing the need for excessive purchasing of material to expand color options. We demonstrate the efficacy of our system by fabricating monochromatic objects, objects with gradient colors, objects with bi-directional properties, as well as multi-color objects with up to four colors in a single print.

Magnetoelastic thin shells exhibit great potential in realizing versatile functionalities through a broad range of combination of material stiffness, remnant magnetization intensity, and external magnetic stimuli. In this paper, we propose a novel computational method for forward simulation and inverse design of magnetoelastic thin shells. Our system consists of two key components of forward simulation and backward optimization. On the simulation side, we have developed a new continuum mechanics model based on the Kirchhoff-Love thin-shell model to characterize the behaviors of a megnetolelastic thin shell under external magnetic stimuli. Based on this model, we proposed an implicit numerical simulator facilitated by the magnetic energy Hessian to treat the elastic and magnetic stresses within a unified framework, which is versatile to incorporation with other thin shell models. On the optimization side, we have devised a new differentiable simulation framework equipped with an efficient adjoint formula to accommodate various PDE-constraint, inverse design problems of magnetoelastic thin-shell structures, in both static and dynamic settings. It also encompasses applications of magnetoelastic soft robots, functional Origami, artworks, and meta-material designs. We demonstrate the efficacy of our framework by designing and simulating a broad array of magnetoelastic thin-shell objects that manifest complicated interactions between magnetic fields, materials, and control policies.

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.

Fluidic devices are crucial components in many industrial applications involving fluid mechanics. Computational design of a high-performance fluidic system faces multifaceted challenges regarding its geometric representation and physical accuracy. We present a novel topology optimization method to design fluidic devices in a Stokes flow context. Our approach is featured by its capability in accommodating a broad spectrum of boundary conditions at the solid-fluid interface. Our key contribution is an anisotropic and differentiable constitutive model that unifies the representation of different phases and boundary conditions in a Stokes model, enabling a topology optimization method that can synthesize novel structures with accurate boundary conditions from a background grid discretization. We demonstrate the efficacy of our approach by conducting several fluidic system design tasks with over four million design parameters.

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.

This paper presents a novel approach to simulating surface tension flow within a position-based dynamics (PBD) framework. We enhance the conventional PBD fluid method in terms of its surface representation and constraint enforcement to furnish support for the simulation of interfacial phenomena driven by strong surface tension and contact dynamics. The key component of our framework is an on-the-fly local meshing algorithm to build the local geometry around each surface particle. Based on this local mesh structure, we devise novel surface constraints that can be integrated seamlessly into a PBD framework to model strong surface tension effects. We demonstrate the efficacy of our approach by simulating a multitude of surface tension flow examples exhibiting intricate interfacial dynamics of films and drops, which were all infeasible for a traditional PBD method.

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 novel three-way coupling method to model the contact interaction between solid and fluid driven by strong surface tension. At the heart of our physical model is a thin liquid membrane that simultaneously couples to both the liquid volume and the rigid objects, facilitating accurate momentum transfer, collision processing, and surface tension calculation. This model is implemented numerically under a hybrid Eulerian-Lagrangian framework where the membrane is modelled as a simplicial mesh and the liquid volume is simulated on a background Cartesian grid. We devise a monolithic solver to solve the interactions among the three systems of liquid, solid, and membrane. We demonstrate the efficacy of our method through an array of rigid-fluid contact simulations dominated by strong surface tension, which enables the faithful modeling of a host of new surface-tension-dominant phenomena including: objects with higher density than water that remains afloat; 'Cheerios effect' where floating objects attract one another; and surface tension weakening effect caused by surface-active constituents.

We propose a novel numerical scheme to simulate interactions between a magnetic field and nonlinearly magnetized objects immersed in it. Under our nonlinear magnetization framework, the strength of magnetic forces is effectively saturated to produce stable simulations without requiring any parameter tuning. The mathematical model of our approach is based upon Langevin's nonlinear theory of paramagnetism, which bridges microscopic structures and macroscopic equations after a statistical derivation. We devise a hybrid Eulerian-Lagrangian numerical approach to simulating this strongly nonlinear process by leveraging the discrete material points to transfer both material properties and the number density of magnetic micro-particles in the simulation domain. The magnetic equations can then be built and solved efficiently on a background Cartesian grid, followed by a finite difference method to incorporate magnetic forces. The multi-scale coupling can be processed naturally by employing the established particle-grid interpolation schemes in a conventional MLS-MPM framework. We demonstrate the efficacy of our approach with a host of simulation examples governed by magnetic-mechanical coupling effects, ranging from magnetic deformable bodies to magnetic viscous fluids with nonlinear elastic constitutive laws.

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.

We propose a novel Lagrangian geometric representation using segment clouds to simulate incompressible fluid exhibiting strong anisotropic vortical features. The central component of our approach is a cloud of discrete segments enhanced by a set of local segment reseeding operations to facilitate both the geometrical evolution and the topological updates of vortical flow. We build a vortex dynamics solver with the support for dynamic solid boundaries based on discrete segment primitives. We demonstrate the efficacy of our approach by simulating a broad range of challenging flow phenomena, such as reconnection of non-closed vortex tubes and vortex shedding behind a rotating object.

We propose a novel gauge fluid solver based on Clebsch wave functions to solve incompressible fluid equations. Our method combines the expressive power of Clebsch wave functions to represent coherent vortical structures and the generality of gauge methods to accommodate a broad array of fluid phenomena. By evolving a transformed wave function as the system's gauge variable enhanced by an additional projection step to enforce pressure jumps on the free boundaries, our method can significantly improve the vorticity generation and preservation ability for a broad range of gaseous and liquid phenomena. Our approach can be easily implemented by modifying a standard grid-based fluid simulator. It can be used to solve various fluid dynamics, including complex vortex filament dynamics, fluids with different obstacles, and surface-tension flow.

This paper presents a method of computing free motions of a planar assembly of rigid bodies connected by loose joints. Joints are modeled using local distance constraints, which are then linearized with respect to configuration space velocities, yielding a linear programming formulation that allows analysis of systems with thousands of rigid bodies. Potential applications include analysis of collections of modular robots, structural stability perturbation analysis, tolerance analysis for mechanical systems, and formation control of mobile robots.

We introduce Sparse Symplectically Integrated Neural Networks (SSINNs), a novel model for learning Hamiltonian dynamical systems from data. SSINNs combine fourth-order symplectic integration with a learned parameterization of the Hamiltonian obtained using sparse regression through a mathematically elegant function space. This allows for interpretable models that incorporate symplectic inductive biases and have low memory requirements. We evaluate SSINNs on four classical Hamiltonian dynamical problems: the Hénon-Heiles system, nonlinearly coupled oscillators, a multi-particle mass-spring system, and a pendulum system. Our results demonstrate promise in both system prediction and conservation of energy, often outperforming the current state-of-the-art black-box prediction techniques by an order of magnitude. Further, SSINNs successfully converge to true governing equations from highly limited and noisy data, demonstrating potential applicability in the discovery of new physical governing equations.

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an embedded recursive architecture that interactively enforces learned underpinning constraints and predicts the various governed behaviors of different physical systems. Our neural projection operator is motivated by the position-based dynamics model that has been used widely in game and visual effects industries to unify the various fast physics simulators. Our method can automatically and effectively uncover a broad range of constraints from observation point data, such as length, angle, bending, collision, boundary effects, and their arbitrary combinations, without any connectivity priors. We provide a multi-group point representation in conjunction with a configurable network connection mechanism to incorporate prior inputs for processing complex physical systems. We demonstrated the efficacy of our approach by learning a set of challenging physical systems all in a unified and simple fashion including: rigid bodies with complex geometries, ropes with varying length and bending, articulated soft and rigid bodies, and multi-object collisions with complex boundaries.

Black-box topology optimization (BBTO) uses evolutionary algorithms and other soft computing techniques to generate near-optimal topologies of mechanical structures. Although evolutionary algorithms are widely used to compensate the limited applicability of conventional gradient optimization techniques, methods based on BBTO have been criticized due to numerous drawbacks. In this article, we discuss topology optimization as a black-box optimization problem. We review the main BBTO methods, discuss their challenges and present approaches to relax them. Dealing with those challenges effectively can lead to wider applicability of topology optimization, as well as the ability to tackle industrial, highly constrained, nonlinear, many-objective, and multimodal problems. Consequently, future research in this area may open the door for innovating new applications in science and engineering that may go beyond solving classical optimization problems of mechanical structures. Furthermore, algorithms designed for BBTO can be added to existing software toolboxes and packages of topology optimization.

We present a method for performance-driven optimization of fluidic devices. In our approach, engineers provide a high-level specification of a device using parametric surfaces for the fluid-solid boundaries. They also specify desired flow properties for inlets and outlets of the device. Our computational approach optimizes the boundary of the fluidic device such that its steady-state flow matches desired flow at outlets. In order to deal with computational challenges of this task, we propose an efficient, differentiable Stokes flow solver. Our solver provides explicit access to gradients of performance metrics with respect to the parametric boundary representation. This key feature allows us to couple the solver with efficient gradient-based optimization methods. We demonstrate the efficacy of this approach on designs of five complex 3D fluidic systems. Our approach makes an important step towards practical computational design tools for high-performance fluidic devices.

We present a versatile numerical approach to simulating various magnetic phenomena using a level-set method. At the heart of our method lies a novel two-way coupling mechanism between a magnetic field and a magnetizable mechanical system, which is based on the interfacial Helmholtz force drawn from the Minkowski form of the Maxwell stress tensor. We show that a magnetic-mechanical coupling system can be solved as an interfacial problem, both theoretically and computationally. In particular, we employ a Poisson equation with a jump condition across the interface to model the mechanical-to-magnetic interaction and a Helmholtz force on the free surface to model the magnetic-to-mechanical effects. Our computational framework can be easily integrated into a standard Euler fluid solver, enabling both simulation and visualization of a complex magnetic field and its interaction with immersed magnetizable objects in a large domain. We demonstrate the efficacy of our method through an array of magnetic substance simulations that exhibit rich geometric and dynamic characteristics, encompassing ferrofluid, rigid magnetic body, deformable magnetic body, and multi-phase couplings.

We propose a new Eulerian-Lagrangian approach to simulate the various surface tension phenomena characterized by volume, thin sheets, thin filaments, and points using Moving-Least-Squares (MLS) particles. At the center of our approach is a meshless Lagrangian description of the different types of codimensional geometries and their transitions using an MLS approximation. In particular, we differentiate the codimension-1 and codimension-2 geometries on Lagrangian MLS particles to precisely describe the evolution of thin sheets and filaments, and we discretize the codimension-0 operators on a background Cartesian grid for efficient volumetric processing. Physical forces including surface tension and pressure across different codimensions are coupled in a monolithic manner by solving one single linear system to evolve the surface-tension driven Navier-Stokes system in a complex non-manifold space. The codimensional transitions are handled explicitly by tracking a codimension number stored on each particle, which replaces the tedious meshing operators in a conventional mesh-based approach. Using the proposed framework, we simulate a broad array of visually appealing surface tension phenomena, including the fluid chain, bell, polygon, catenoid, and dripping, to demonstrate the efficacy of our approach in capturing the complex fluid characteristics with mixed codimensions, in a robust, versatile, and connectivity-free manner.

Enabling adaptivity on a uniform Cartesian grid is challenging due to its highly structured grid cells and axis-aligned grid lines. In this paper, we propose a new grid structure - the adaptive staggered-tilted (AST) grid - to conduct adaptive fluid simulations on a regular discretization. The key mechanics underpinning our new grid structure is to allow the emergence of a new set of tilted grid cells from the nodal positions on a background uniform grid. The original axis-aligned cells, in conjunction with the populated axis-tilted cells, jointly function as the geometric primitives to enable adaptivity on a regular spatial discretization. By controlling the states of the tilted cells both temporally and spatially, we can dynamically evolve the adaptive discretizations on an Eulerian domain. Our grid structure preserves almost all the computational merits of a uniform Cartesian grid, including the cache-coherent data layout, the easiness for parallelization, and the existence of high-performance numerical solvers. Further, our grid structure can be integrated into other adaptive grid structures, such as an Octree or a sparsely populated grid, to accommodate the T-junction-free hierarchy. We demonstrate the efficacy of our AST grid by showing examples of large-scale incompressible flow simulation in domains with irregular boundaries.

Hybrid unmanned aerial vehicles (UAV) combine advantages of multicopters and fixed-wing planes: vertical take-off, landing, and low energy use. However, hybrid UAVs are rarely used because controller design is challenging due to its complex, mixed dynamics. In this paper, we propose a method to automate this design process by training a mode-free, model-agnostic neural network controller for hybrid UAVs. We present a neural network controller design with a novel error convolution input trained by reinforcement learning. Our controller exhibits two key features: First, it does not distinguish among flying modes, and the same controller structure can be used for copters with various dynamics. Second, our controller works for real models without any additional parameter tuning process, closing the gap between virtual simulation and real fabrication. We demonstrate the efficacy of the proposed controller both in simulation and in our custom-built hybrid UAVs (Figure 1, 8). The experiments show that the controller is robust to exploit the complex dynamics when both rotors and wings are active in flight tests.

A variety of structures in nature exhibit sparse, thin, and intricate features. It is challenging to investigate these structural characteristics using conventional numerical approaches since such features require highly refined spatial resolution to capture and therefore they incur a prohibitively high computational cost. We present a novel computational framework for high-resolution topology optimization that delivers leaps in simulation capabilities, by two orders of magnitude, from the state-of-the-art approaches. Our technique accommodates computational domains with over one billion grid voxels on a single shared-memory multiprocessor platform, allowing automated emergence of structures with both rich geometric features and exceptional mechanical performance. To achieve this, we track the evolution of thin structures and simulate its elastic deformation in a dynamic narrow-band region around high-density sites to avoid wasted computational effort on large void regions. We have also designed a mixed-precision multigrid-preconditioned iterative solver that keeps the memory footprint of the simulation to a compact size while maintaining double-precision accuracy. We have demonstrated the efficacy of the algorithm through optimizing a variety of complex structures from both natural and engineering systems.

Computer Aided Design (CAD) is a multi-billion dollar industry used by almost every mechanical engineer in the world to create practically every existing manufactured shape. CAD models are not only widely available but also extremely useful in the growing field of fabrication-oriented design because they are parametric by construction and capture the engineer's design intent, including manufacturability. Harnessing this data, however, is challenging, because generating the geometry for a given parameter value requires time-consuming computations. Furthermore, the resulting meshes have different combinatorics, making the mesh data inherently discontinuous with respect to parameter adjustments. In our work, we address these challenges and develop tools that allow interactive exploration and optimization of parametric CAD data. To achieve interactive rates, we use precomputation on an adaptively sampled grid and propose a novel scheme for interpolating in this domain where each sample is a mesh with different combinatorics. Specifically, we extract partial correspondences from CAD representations for local mesh morphing and propose a novel interpolation method for adaptive grids that is both continuous/smooth and local (i.e., the influence of each sample is constrained to the local regions where mesh morphing can be computed). We show examples of how our method can be used to interactively visualize and optimize objects with a variety of physical properties.

In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut -- the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.

In this article, we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut—the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set field. Next, we propose an efficient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially varying material properties onto the microstructures with the corresponding properties to generate a high-resolution printable structure. We demonstrate the efficacy of our framework by designing, optimizing, and fabricating objects in different material property spaces on the level of a trillion voxels, that is, several orders of magnitude higher than what can be achieved with current systems.

We present an interactive system for computational design, optimization, and fabrication of multicopters. Our computational approach allows non-experts to design, explore, and evaluate a wide range of different multicopters. We provide users with an intuitive interface for assembling a multicopter from a collection of components (e.g., propellers, motors, and carbon fiber rods). Our algorithm interactively optimizes shape and controller parameters of the current design to ensure its proper operation. In addition, we allow incorporating a variety of other metrics (such as payload, battery usage, size, and cost) into the design process and exploring tradeoffs between them. We show the efficacy of our method and system by designing, optimizing, fabricating, and operating multicopters with complex geometries and propeller configurations. We also demonstrate the ability of our optimization algorithm to improve the multicopter performance under different metrics.

We present a novel method to simulate codimensional non-Newtonian fluids on simplicial complexes. Our method extends previous work for codimensional incompressible flow to various types of non-Newtonian fluids including both shear thinning and thickening, Bingham plastics, and elastoplastics. We propose a novel time integration scheme for semi-implicitly treating elasticity, which when combined with a semi-implicit method for variable viscosity alleviates the need for small time steps. Furthermore, we propose an improved treatment of viscosity on the rims of thin fluid sheets that allows us to capture their elusive, visually appealing twisting motion. In order to simulate complex phenomena such as the mixing of colored paint, we adopt a multiple level set framework and propose a discretization on simplicial complexes that facilitates the tracking of material interfaces across codimensions. We demonstrate the efficacy of our approach by simulating a wide variety of non-Newtonian fluid phenomena exhibiting various codimensional features.

Many visually interesting natural phenomena are characterized by thin liquid sheets, long filaments, and droplets. We present a new Lagrangian-based numerical method to simulate these codimensional surface tension driven phenomena using non-manifold simplicial complexes. Tetrahedra, triangles, segments, and points are used to model the fluid volume, thin films, filaments, and droplets, respectively. We present a new method for enforcing fluid incompressibility on simplicial complexes along with a physically-guided meshing algorithm to provide temporally consistent information for interparticle forces. Our method naturally allows for transitions between codimensions, either from tetrahedra to triangles to segments to points or vice versa, regardless of the simulation resolution. We demonstrate the efficacy of this method by simulating various natural phenomena that are characterized by thin fluid sheets, filaments, and surface tension effects.

We present an efficient grid structure that extends a uniform grid to create a significantly larger far-field grid by dynamically extending the cells surrounding a fine uniform grid while still maintaining fine resolution about the regions of interest. The far-field grid preserves almost every computational advantage of uniform grids including cache coherency, regular subdivisions for parallelization, simple data layout, the existence of efficient numerical discretizations and algorithms for solving partial differential equations, etc. This allows fluid simulations to cover large domains that are often infeasible to enclose with sufficient resolution using a uniform grid, while still effectively capturing fine scale details in regions of interest using dynamic adaptivity.

This paper presents a lightweight sketching system that enables interactive illustration of complex fluid systems. Users can sketch on a 2.5-dimensional (2.5D) canvas to design the shapes and connections of a fluid circuit. These input sketches are automatically analyzed and abstracted into a hydraulic graph, and a new hybrid fluid model is used in the background to enhance the illustrations. The system provides rich simple operations for users to edit the fluid system incrementally, and the new internal flow patterns can be simulated in real time. Our system is used to illustrate various fluid systems in medicine, biology, and engineering. We asked professional medical doctors to try our system and obtained positive feedback from them.

Abstract We present a new method to create and preserve the turbulent details generated around moving objects in SPH fluid. In our approach, a high‐resolution overlapping grid is bounded to each object and translates with the object. The turbulence formation is modeled by resolving the local flow around objects using a hybrid SPH‐FLIP method. Then these vortical details are carried on SPH particles flowing through the local region and preserved in the global field in a synthetic way. Our method provides a physically plausible way to model the turbulent details around both rigid and deformable objects in SPH fluid, and can efficiently produce animations of complex gaseous phenomena with rich visual details.