Two-phase flows are ubiquitous in nature, exhibiting complex fluid-fluid interactions that challenges numerical simulators. To accurately and efficiently solve two-phase flows, grid-based methods have been widely adopted. Navier-Stokes (NS) solvers consume a small memory footprint, but simultaneously achieving both high performance and low numerical dissipation remains a significant challenge. In contrast, lattice Boltzmann solvers are efficient and have low numerical dissipation, yet they remain memoryintensive, even with state-of-the-art moment-encoding schemes. To date, the simultaneous attainment of high accuracy, exceptional efficiency, and a low memory footprint remains a major challenge in the field. In this paper, we propose a novel two-phase flow solver that achieves this objective. Our work is motivated by extending gas-kinetic scheme (GKS), which is adapted to handle nearly incompressible flows. To allow stable and accurate two-phase flow simulations, we systematically derive a coupled formulation of the GKS method and the phase-field model, incorporating novel mathematical constructs. Combined with robust boundary treatments and specialized techniques for handling turbulent flows, this results a unified framework capable of efficiently simulating two-phase flows, even those with large density contrasts and high Reynolds numbers. Since our formulation is explicit, it achieves exceptional performance when optimized on GPU, making it the fastest kinetic two-phase flow solver to date. Additionally, as it is derived from GKS, it obviates the need to store distribution functions. Thus, it has a small memory footprint, competitive with, or even lower than, that of many NS solvers. As a result, our solver can efficiently simulate complex two-phase flow dynamics at high resolutions using a single commodity GPU. We validate the accuracy of our solver via several benchmark tests, compare its performance with recent methods in various aspects, and demonstrate its capability to replicate a broad range of two-phase flow phenomena, encompassing both typical and large-scale scenarios.

The simultaneous pursuit of high fidelity, large computational throughput, and a minimal memory footprint has long constituted the central challenge in fluid simulation research. Yet state-of-the-art methods struggle to reconcile all these objectives, and often entail navigating trade-offs among them. We present Kinetic Predicted-Moment Flux Reconstruction (KPM-FR), a high-order kinetic-based scheme for low-Mach-number weakly compressible flows that advances all three fronts within a single framework. KPM-FR is a flux-form fluid flow solver rooted in the principles of the gas-kinetic scheme (GKS), deriving numerical fluxes from the locally evolved Boltzmann-BGK equation to recover Navier-Stokes (NS) solutions. Departing from the GKS and its variants, it carries out kinetic evolution entirely in moment space within the high-order flux reconstruction (FR) framework through a concise predictor-corrector scheme. This translates to two fused GPU kernels per time step, streamlining computation and confining intermediate data to on-chip memory. This design confers several practical advantages. First, compared to conventional high-fidelity lattice Boltzmann methods (LBM), the moment-based formulation reduces the per-point memory footprint by more than fivefold. Second, at matched resolutions, its high-order spatial formulation exhibits markedly lower numerical dissipation, preserving fine-scale vortical structures with greater fidelity. Combining these advantages with a near-saturated throughput exceeding 8 billion solution-point updates per second on a single consumer GPU, KPM-FR delivers large-scale fluid simulation on commodity hardware. Quantitative benchmarks confirm highorder spatial convergence and spectral-like dissipation characteristics, while validation against reference data for flow past solid bodies verifies its practical accuracy. Ultimately, we demonstrate the versatility of KPM-FR across complex geometries and large-scale turbulent flows, capturing multiscale structures with 1.8 billion solution points on a single desktop workstation.

Multiphase and multi-component fluid flows are highly intricate, exhibiting dynamic behaviors that challenge conventional simulation methods, especially across a wide range of operating conditions. Adding fluid-solid interactions further escalates this complexity, requiring simulations that are both physically accurate and computationally more tractable. Existing methods often fall short in aspects of either accuracy, efficiency, or stability, and sometimes may also consume excessive memory, rendering them unsuitable for many practical applications. In this paper, we introduce a novel, more practical solution combining a collision-enhanced lattice Boltzmann method with a finite-volume approach. This hybrid solver is designed to effectively simulate multiphase, multi-component flows via the phase-field modeling with a novel wetting boundary treatment in the finite-volume framework, while significantly reducing memory consumption. It enables simulations of multiple fluid phases under varied conditions, capturing rich interfacial behaviors. Additionally, it incorporates an immersed-boundary method to efficiently handle complex fluid-solid interactions. Validation tests confirm that our method produces physically consistent results and demonstrates accuracy across multiple evaluations. We provide comprehensive simulation results, along with comparisons of memory consumption and efficiency, highlighting the practical utility and superiority of our solver over conventional methods.

Robotic fish face considerable challenges in natural environment due to the absence of a comprehensive and precise model that can depict the intricate fluid-structure interactions, particularly in the presence of background flow fields. To this end, we present a novel data-driven dynamic modeling framework capable of characterizing the swimming motions of the robotic fish under various background flow conditions without the necessity for explicit flow information. The model is synthesized by an internal model with an adaptive residual acceleration model to effectively isolate and address external flow effects. Notably, the residual model employs the innovative Domain Adversarially Invariant Meta-Learning (DAIML) approach, allowing the framework to adapt to fluctuating and previously unseen background flow scenarios, enhancing its robustness and scalability. Validation through high-fidelity Computational Fluid Dynamics (CFD) simulations demonstrates the framework’s effectiveness in improving the performance of robotic fish across diverse real-world aquatic environments.

Accurate aerodynamic interaction modeling in multi-drone tasks is crucial for enhancing system stability and efficiency, especially when facing major disturbances from downwash wake effects. Conventional data-driven and empirical models mainly address simplified cases where one drone hovers or all vehicles have low absolute and relative velocities (≤ 0.5 m/s), and rely merely on relative states. In this study, we use high-fidelity Computational Fluid Dynamics (CFD) simulations to explore quadrotor interactions at higher speeds (0.5-4.0 m/s). We find that as the absolute velocities of the UAVs rise, downwash effects change significantly. To account for these discrepancies, we present a data-driven model considering both the absolute and relative properties of the downwash problem. We propose a geometric deep neural network predictor and compare its performance with existing data-driven and empirical models. Validations on two quadrotor settings show that our model gives more reliable predictions in tough scenarios and performs better in training without rigorous fine-tuning. Finally, we combine our predictor with a nonlinear feedback controller to enhance flight control under downwash disturbances. However, we encounter limitations for our speed ranges during trajectory tracking such as delays and velocity loss. Despite these challenges, our encoding and prediction method shows to be a promising step to address the downwash effects at higher speeds.We release our dataset, method, and re-implementations at: https://github.com/pavelkharitenko/flare-dw.

ABSTRACT The Harris Hawks Optimization (HHO) algorithm is a nature‐inspired metaheuristic that mimics the cooperative hunting behavior of hawks. Despite its success in various optimization tasks, it suffers from several limitations, including low computational accuracy, a tendency to become trapped in local optima, and difficulty in balancing exploration and exploitation. To address these challenges, this paper proposes an enhanced version of HHO, named FL‐HHO, which integrates four key improvements: the Halton sequence for enhanced population diversity, a modified Escaping Energy Factor E, an improved Frog‐leaping mechanism, and a convergence trend analysis module. FL‐HHO is evaluated on seven classical benchmark functions and 30 functions from the CEC2014 benchmark suite. The experimental results demonstrate that FL‐HHO exhibits a significant advantage on classical benchmarks, achieving top performance in search precision across nearly all functions and reaching the theoretical optimum on three of them. In terms of computational efficiency, FL‐HHO ranks third among all compared algorithms. On the CEC2014 benchmarks, it secures first place on over 50% of the functions, with slightly lower performance observed on certain multimodal functions. Ablation experiments further verify the effectiveness of each proposed component, particularly highlighting the contribution of the modified Frog‐leaping mechanism to global exploitation and the Halton sequence to initialization robustness. In practical scenarios, FL‐HHO is applied to industrial robot path planning, where it achieves the shortest travel distance among all evaluated methods, confirming its effectiveness in real‐world tasks. The implementation code is publicly available at: https://github.com/zhu‐cheng/FL‐HHO/tree/main .

Turbulent boundary layer represents one of the most complex but interesting phenomena in fluid flows. While the generation and alteration of sheared vortices in various interacting scales near the boundary are visually appealing, it is difficult to correctly replicate such phenomena by simulation, especially at high Reynolds numbers. Practical methodologies typically incorporate empirical wall modeling to substantially curtail the computational expenses while retaining physical consistency. Nevertheless, these are predominantly applicable to steady-state flow solvers. While complex scenarios involving dynamic fluid-solid interaction and its application to create time-dependent flow phenomena invariably necessitate unsteady flow solvers, the underlying wall modeling techniques are imprecise, leading to a different formation of near-wall vortices, especially for the highly efficient lattice Boltzmann solver operating on Cartesian grids. In this paper, we propose a novel hybrid near-wall model for the lattice Boltzmann solver, which can handle turbulent boundary layer flows in a simple and efficient manner, inspired by measuring the degree of boundary layer separation. Our model comprises both macroscopic and mesoscopic algebraic models, which collaborate to let the low dissipation lattice Boltzmann solver naturally form the turbulent boundary layer appropriately. By leveraging the multi-resolution technique, accurate simulation outcomes can be obtained. Our model is parameterized to approximate different physical attributes of the solid surface that can potentially influence the boundary layer distribution, and comparable boundary layer flow behaviors can be simulated at various grid resolutions. Rigorous benchmark tests are carried out to validate our model at different grid resolutions by comparing with experimental data and visualizations. We showcase the applications of our new model in both facilitating computational design and generating visual animations, accompanied by specific examples and comparisons with actual experimental setups and photographic images. All demonstrations affirm the physical consistency of our solver even when simulated with a relatively coarse grid resolution.

In the realm of digital twin systems, establishing simulation environments for creating and testing virtual agents has garnered substantial attention across various applications. The obtained control policies endow virtual agents with more realistic behaviors and interactive capabilities, finding applications in both computer animation and robotic control. While rigid-body simulators are widely used for virtual agents, achieving similar feats in fluid environments presents formidable challenges due to high complexity and exorbitant costs. One major reason is that most fluid simulators feature a fixed domain, which struggles to enable agents to freely navigate in an unbounded, obstacle-filled space, especially when computational resources are limited, thus restricting their wide utility for creating virtual agents. In this paper, we introduce a novel fluid-solid interaction simulator grounded in an efficient lattice Boltzmann solver. A key feature of this simulator is a dynamically moving local domain that encircles the agent, offering greater flexibility for obtaining control policy while maintaining efficiency in simulation. Previous methods, which anchored a square moving local domain along with the agent, suffered from severe spurious flows when the agent underwent rapid acceleration especially when the domain had to rotate, such as during a U-turn. This led to inaccurate results and instability. Conversely, we propose a novel domain-tracking method that harnesses optimal control techniques to address this issue. Our approach not only bolsters local-domain simulation stability, but also improves efficiency by employing a slender domain, which broadens the application scope of direct fluid-solid interactions for virtual agents. We validate our method by comparing simulations to physical phenomena and obtaining control policies for various virtual agents to accomplish challenging tasks. This effort culminates in a series of animations that vividly demonstrate the efficacy of the entire framework potentially used in both computer animation and robotics.

Unmanned aerial vehicles (UAVs) have demonstrated remarkable efficacy across diverse fields. Nevertheless, developing flight controllers tailored to a specific UAV design, particularly in environments with strong fluid-interactive dynamics, remains challenging. Conventional controller design experiences often fall short in such cases, rendering it infeasible to apply time-tested practices. Consequently, a simulation test bed becomes indispensable for controller design and evaluation prior to its actual implementation on the physical UAV. This platform should allow for meticulous adjustment of controllers and should be able to transfer to real-world systems without significant performance degradation. Existing simulators predominantly hinge on empirical models due to high efficiency, often overlooking the dynamic interplay between the UAV and the surrounding airflow. This makes it difficult to mimic more complex flight maneuvers, such as an abrupt midair halt inside narrow channels, in which the UAV may experience strong fluid-structure interactions. On the other hand, simulators considering the complex surrounding airflow are extremely slow and inadequate to support the design and evaluation of flight controllers. In this paper, we present a novel remedy for highly-efficient UAV flight simulations, which entails a hybrid modeling that deftly combines our novel far-field adaptive block-based fluid simulator with parametric empirical models situated near the boundary of the UAV, with the model parameters automatically calibrated. With this newly devised simulator, a broader spectrum of flight scenarios can be explored for controller design and assessment, encompassing those influenced by potent close-proximity effects, or situations where multiple UAVs operate in close quarters. The practical worth of our simulator has been authenticated through comparisons with actual UAV flight data. We further showcase its utility in designing flight controllers for fixed-wing, multi-rotor, and hybrid UAVs, and even exemplify its application when multiple UAVs are involved, underlining the unique value of our system for flight controllers.

Simulating the coupled dynamics between rigid bodies and two-phase fluids, especially those with a large density ratio and a high Reynolds number, is computationally demanding but visually compelling with a broad range of applications. Traditional approaches that directly solve the Navier-Stokes equations often struggle to reproduce these flow phenomena due to stronger numerical diffusion, resulting in lower accuracy. While recent advancements in kinetic lattice Boltzmann methods for two-phase flows have notably enhanced efficiency and accuracy, challenges remain in correctly managing fluid-rigid boundaries, resulting in physically inconsistent results. In this article, we propose a novel kinetic framework for fluid-rigid interaction involving two fluid phases. Our approach leverages the idea of an overset grid, and proposes a novel formulation in the two-phase flow context with multiple improvements to handle complex scenarios and support moving multi-resolution domains with boundary layer control. These new contributions successfully resolve many issues inherent in previous methods and enable physically more consistent simulations of two-phase flow phenomena. We have conducted both quantitative and qualitative evaluations, compared our method to previous techniques, and validated its physical consistency through real-world experiments. Additionally, we demonstrate the versatility of our method across various scenarios.

Training model-free intelligent agents in complex real-world scenarios using reinforcement learning (RL) often necessitates simulation-based environments due to high physical expenses. However, when simulation takes a long time, e.g., in an unsteady 3D fluid simulation with interactions to the controllable solids, existing RL algorithms meet difficulty to accomplish training within a reasonable timeframes. In this paper, we propose a novel multi-level framework for RL to accelerate convergence as the first attempt to address this difficulty. Motivated by the idea of multi-grid solver, the control policy on a virtual agent over time can be decomposed into different frequency levels, which can be progressively learned via a set of simulations in a coarse-to-fine manner. It is expected that most RL trials are performed in coarser simulations to learn lower control frequency levels with more efficient convergence, while higher frequency levels require much less RL trials, thus significantly accelerating the learning process. To implement our idea, we designed a novel multi-level residual network with a filter module attached, where each level of the network is learned by performing RL for a given simulation resolution. The proposed framework is evaluated by conducting policy learning experiments on a virtual aerial (2D) and an underwater (3D) robot, both requiring time-consuming physical simulations. Our results demonstrate a decrease in almost half in learning time compared to a direct RL approach, while achieving similar control performance.

The study of motion control for the fish-like robots in complex fluid fields is of great importance in improving the performance of underwater vehicles, due to its strong maneuverability, propulsion efficiency, and deceptive visual appearance. In this article, a novel learning-based control framework is first proposed to autonomously explore efficient control policies that are capable of performing motion control tasks in non-quiescent and unknown background flows. First, we utilize a high-fidelity simulation system, named FishGym, to generate various uniform flows. Next, a DRL-based algorithm is incorporated with the FishGym to train the fish-like robot to control its motion to optimally complete a delicately designed task (Approaching Target and Stay) in both quiescent and uniform flow. Then, the obtained control policy together with an online estimator is directly applied to a Path-Following Task. The proposed framework well balances the simulation accuracy and the computational efficiency, which is of crucial importance for effective coupling with the learning algorithm. The simulation results indicate that, via the proposed learning framework, the robot successfully acquired a swimming strategy that can be used to adapt to different background flows and tasks. Furthermore, we also observe some adaptation behavior of the robot, such as rheotaxis, that is similar to the fish in nature, which gains us more insight into the mechanism underlying the adaptation behavior of fish in a complex environment.

Boundary layer flow plays a very important role in shaping the entire flow feature near and behind obstacles inside fluids. Thus, boundary treatment methods are crucial for a physically consistent fluid simulation, especially when turbulence occurs at a high Reynolds number, in which accurately handling thin boundary layer becomes quite challenging. Traditional Navier-Stokes solvers usually construct multi-resolution body-fitted meshes to achieve high accuracy, often together with near-wall and sub-grid turbulence modeling. However, this could be time-consuming and computationally intensive even with GPU accelerations. An alternative and much faster approach is to switch to a kinetic solver, such as the lattice Boltzmann model, but boundary treatment has to be done in a cut-cell manner, sacrificing accuracy unless grid resolution is much increased. In this paper, we focus on simulating the boundary-dominated turbulent flow phenomena with an efficient kinetic solver. In order to significantly improve the cut-cell-based boundary treatment for higher accuracy without excessively increasing the simulation resolution, we propose a novel parametric boundary treatment model, including a semi-Lagrangian scheme at the wall for non-equilibrium distribution functions, together with a purely link-based near-wall analytical mesoscopic model by analogy with the macroscopic wall modeling approach, which is yet simple to compute. Such a new method is further extended to handle moving boundaries, showing increased accuracy. Comprehensive analyses are conducted, with a variety of simulation results that are both qualitatively and quantitatively validated with experiments and real life scenarios, and compared to existing methods, to indicate superiority of our method. We highlight that our method not only provides a more accurate way for boundary treatment, but also a valuable tool to control boundary layer behaviors. This has not been achieved and demonstrated before in computer graphics, which we believe will be very useful in practical engineering.

Virtual wind tunnel testing is a key ingredient in the engineering design process for the automotive and aeronautical industries as well as for urban planning: through visualization and analysis of the simulation data, it helps optimize lift and drag coefficients, increase peak speed, detect high pressure zones, and reduce wind noise at low cost prior to manufacturing. In this paper, we develop an efficient and accurate virtual wind tunnel system based on recent contributions from both computer graphics and computational fluid dynamics in high-performance kinetic solvers. Running on one or multiple GPUs, our massively-parallel lattice Boltzmann model meets industry standards for accuracy and consistency while exceeding current mainstream industrial solutions in terms of efficiency --- especially for unsteady turbulent flow simulation at very high Reynolds number (on the order of 10 7 ) --- due to key contributions in improved collision modeling and boundary treatment, automatic construction of multiresolution grids for complex models, as well as performance optimization. We demonstrate the efficacy and reliability of our virtual wind tunnel testing facility through comparisons of our results to multiple benchmark tests, showing an increase in both accuracy and efficiency compared to state-of-the-art industrial solutions. We also illustrate the fine turbulence structures that our system can capture, indicating the relevance of our solver for both VFX and industrial product design.

Bionic underwater robots have demonstrated their superiority in many applications. Yet, training their intelligence for a variety of tasks that mimic the behavior of underwater creatures poses a number of challenges in practice, mainly due to lack of a large amount of available training data as well as the high cost in real physical environment. Alternatively, simulation has been considered as a viable and important tool for acquiring datasets in different environments, but it mostly targeted rigid and soft body systems. There is currently dearth of work for more complex fluid systems interacting with immersed solids that can be efficiently and accurately simulated for robot training purposes. In this paper, we propose a new platform called “FishGym”, which can be used to train fish-like underwater robots. The framework consists of a robotic fish modeling module using articulated body with skinning, a GPU-based high-performance localized two-way coupled fluid-structure interaction simulation module that handles both finite and infinitely large domains, as well as a reinforcement learning module. We leveraged existing training methods with adaptations to underwater fish-like robots and obtained learned control policies for multiple benchmark tasks. The training results are demonstrated with reasonable motion trajectories, with comparisons and analyses to empirical models as well as known real fish swimming behaviors to highlight the advantages of the proposed platform.

Real-life multiphase flows exhibit a number of complex and visually appealing behaviors, involving bubbling, wetting, splashing, and glugging. However, most state-of-the-art simulation techniques in graphics can only demonstrate a limited range of multiphase flow phenomena, due to their inability to handle the real water-air density ratio and to the large amount of numerical viscosity introduced in the flow simulation and its coupling with the interface. Recently, kinetic-based methods have achieved success in simulating large density ratios and high Reynolds numbers efficiently; but their memory overhead, limited stability, and numerically-intensive treatment of coupling with immersed solids remain enduring obstacles to their adoption in movie productions. In this paper, we propose a new kinetic solver to couple the incompressible Navier-Stokes equations with a conservative phase-field equation which remedies these major practical hurdles. The resulting two-phase immiscible fluid solver is shown to be efficient due to its massively-parallel nature and GPU implementation, as well as very versatile and reliable because of its enhanced stability to large density ratios, high Reynolds numbers, and complex solid boundaries. We highlight the advantages of our solver through various challenging simulation results that capture intricate and turbulent air-water interaction, including comparisons to previous work and real footage.

Fluid simulations are often performed using the incompressible Navier-Stokes equations (INSE), leading to sparse linear systems which are difficult to solve efficiently in parallel. Recently, kinetic methods based on the adaptive-central-moment multiple-relaxation-time (ACM-MRT) model [1], [2] have demonstrated impressive capabilities to simulate both laminar and turbulent flows, with quality matching or surpassing that of state-of-the-art INSE solvers. Furthermore, due to its local formulation, this method presents the opportunity for highly scalable implementations on parallel systems such as GPUs. However, an efficient ACM-MRT-based kinetic solver needs to overcome a number of computational challenges, especially when dealing with complex solids inside the fluid domain. In this article, we present multiple novel GPU optimization techniques to efficiently implement high-quality ACM-MRT-based kinetic fluid simulations in domains containing complex solids. Our techniques include a new communication-efficient data layout, a load-balanced immersed-boundary method, a multi-kernel launch method using a simplified formulation of ACM-MRT calculations to enable greater parallelism, and the integration of these techniques into a parametric cost model to enable automated prameter search to achieve optimal execution performance. We also extended our method to multi-GPU systems to enable large-scale simulations. To demonstrate the state-of-the-art performance and high visual quality of our solver, we present extensive experimental results and comparisons to other solvers.

Simulating turbulent smoke flows with fine details is computationally intensive. For iterative editing or simply faster generation, efficiently upsampling a low-resolution numerical simulation is an attractive alternative. We propose a novel learning approach to the dynamic upsampling of smoke flows based on a training set of flows at coarse and fine resolutions. Our multiscale neural network turns an input coarse animation into a sparse linear combination of small velocity patches present in a precomputed over-complete dictionary. These sparse coefficients are then used to generate a high-resolution smoke animation sequence by blending the fine counterparts of the coarse patches. Our network is initially trained from a sequence of example simulations to both construct the dictionary of corresponding coarse and fine patches and allow for the fast evaluation of a sparse patch encoding of any coarse input. The resulting network provides an accurate upsampling when the coarse input simulation is well approximated by patches present in the training set (e.g., for re-simulation), or simply visually plausible upsampling when input and training sets differ significantly. We show a variety of examples to ascertain the strengths and limitations of our approach and offer comparisons to existing approaches to demonstrate its quality and effectiveness.

Predicting the fine and intricate details of a turbulent flow field in both space and time from a coarse input remains a major challenge despite the availability of modern machine learning tools. In this paper, we present a simple and effective dictionary-based approach to spatio-temporal upsampling of fluid simulation. We demonstrate that our neural network approach can reproduce the visual complexity of turbulent flows from spatially and temporally coarse velocity fields even when using a generic training set. Moreover, since our method generates finer spatial and/or temporal details through embarrassingly-parallel upsampling of small local patches, it can efficiently predict high-resolution turbulence details across a variety of grid resolutions. As a consequence, our method offers a whole range of applications varying from fluid flow upsampling to fluid data compression. We demonstrate the efficiency and generalizability of our method for synthesizing turbulent flows on a series of complex examples, highlighting dramatically better results in spatio-temporal upsampling and flow data compression than existing methods as assessed by both qualitative and quantitative comparisons.

The intricate motions and complex vortical structures generated by the interaction between fluids and solids are visually fascinating. However, reproducing such a two-way coupling between thin objects and turbulent fluids numerically is notoriously challenging and computationally costly: existing approaches such as cut-cell or immersed-boundary methods have difficulty achieving physical accuracy, or even visual plausibility, of simulations involving fast-evolving flows with immersed objects of arbitrary shapes. In this paper, we propose an efficient and versatile approach for simulating two-way fluid-solid coupling within the kinetic (lattice-Boltzmann) fluid simulation framework, valid for both laminar and highly turbulent flows, and for both thick and thin objects. We introduce a novel hybrid approach to fluid-solid coupling which systematically involves a mesoscopic double-sided bounce-back scheme followed by a cut-cell velocity correction for a more robust and plausible treatment of turbulent flows near moving (thin) solids, preventing flow penetration and reducing boundary artifacts significantly. Coupled with an efficient approximation to simplify geometric computations, the whole boundary treatment method preserves the inherent massively parallel computational nature of the kinetic method. Moreover, we propose simple GPU optimizations of the core LBM algorithm which achieve an even higher computational efficiency than the state-of-the-art kinetic fluid solvers in graphics. We demonstrate the accuracy and efficacy of our two-way coupling through various challenging simulations involving a variety of rigid body solids and fluids at both high and low Reynolds numbers. Finally, comparisons to existing methods on benchmark data and real experiments further highlight the superiority of our method.

Multiphase flows exhibit a large realm of complex behaviors such as bubbling, glugging, wetting, and splashing which emerge from air-water and water-solid interactions. Current fluid solvers in graphics have demonstrated remarkable success in reproducing each of these visual effects, but none have offered a model general enough to capture all of them concurrently. In contrast, computational fluid dynamics have developed very general approaches to multiphase flows, typically based on kinetic models. Yet, in both communities, there is dearth of methods that can simulate density ratios and Reynolds numbers required for the type of challenging real-life simulations that movie productions strive to digitally create, such as air-water flows. In this article, we propose a kinetic model of the coupling of the Navier-Stokes equations with a conservative phase-field equation, and provide a series of numerical improvements over existing kinetic-based approaches to offer a general multiphase flow solver. The resulting algorithm is embarrassingly parallel, conservative, far more stable than current solvers even for real-life conditions, and general enough to capture the typical multiphase flow behaviors. Various simulation results are presented, including comparisons to both previous work and real footage, to highlight the advantages of our new method.

Vectorizing vortex-core lines is crucial for high-quality visualization and analysis of turbulence. While several techniques exist in the literature, they can only be applied to classical fluids. As quantum fluids with turbulence are gaining attention in physics, extracting and visualizing vortex-core lines for quantum fluids is increasingly desirable. In this article, we develop an efficient vortex-core line vectorization method for quantum fluids enabling real-time visualization of high-resolution quantum turbulence structure. From a dataset obtained through simulation, our technique first identifies vortex nodes based on the circulation field. To vectorize the vortex-core lines interpolating these vortex nodes, we propose a novel graph-based data structure, with iterative graph reduction and density-guided local optimization, to locate sub-grid-scale vortex-core line samples more precisely, which are then vectorized by continuous curves. This vortex-core representation naturally captures complex topology, such as branching during reconnection. Our vectorization approach reduces memory consumption by orders of magnitude, enabling real-time visualization performance. Different types of interactive visualizations are demonstrated to show the effectiveness of our technique, which could help further research on quantum turbulence.

Despite their cinematic appeal, turbulent flows involving fluid-solid coupling remain a computational challenge in animation. At the root of this current limitation is the numerical dispersion from which most accurate Navier-Stokes solvers suffer: proper coupling between fluid and solid often generates artificial dispersion in the form of local, parasitic trains of velocity oscillations, eventually leading to numerical instability. While successive improvements over the years have led to conservative and detail-preserving fluid integrators, the dispersive nature of these solvers is rarely discussed despite its dramatic impact on fluid-structure interaction. In this paper, we introduce a novel low-dissipation and low-dispersion fluid solver that can simulate two-way coupling in an efficient and scalable manner, even for turbulent flows. In sharp contrast with most current CG approaches, we construct our solver from a kinetic formulation of the flow derived from statistical mechanics. Unlike existing lattice Boltzmann solvers, our approach leverages high-order moment relaxations as a key to controlling both dissipation and dispersion of the resulting scheme. Moreover, we combine our new fluid solver with the immersed boundary method to easily handle fluid-solid coupling through time adaptive simulations. Our kinetic solver is highly parallelizable by nature, making it ideally suited for implementation on single- or multi-GPU computing platforms. Extensive comparisons with existing solvers on synthetic tests and real-life experiments are used to highlight the multiple advantages of our work over traditional and more recent approaches, in terms of accuracy, scalability, and efficiency.

Abstract Turbulent flows are multi‐scale with vortices spanning a wide range of scales continuously. Due to such complexities, turbulence scales are particularly difficult to analyse and visualize. In this work, we present a novel and efficient optimization‐based method for continuous‐scale turbulence structure visualization with scale decomposition directly in the Kolmogorov energy spectrum. To achieve this, we first derive a new analytical objective function based on integration approximation. Using this new formulation, we can significantly improve the efficiency of the underlying optimization process and obtain the desired filter in the Kolmogorov energy spectrum for scale decomposition. More importantly, such a decomposition allows a ‘continuous‐scale visualization’ that enables us to efficiently explore the decomposed turbulence scales and further analyse the turbulence structures in a continuous manner. With our approach, we can present scale visualizations of direct numerical simulation data sets continuously over the scale domain for both isotropic and boundary layer turbulent flows. Compared with previous works on multi‐scale turbulence analysis and visualization, our method is highly flexible and efficient in generating scale decomposition and visualization results. The application of the proposed technique to both isotropic and boundary layer turbulence data sets verifies the capability of our technique to produce desirable scale visualization results.

Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches have not been widely adopted in graphics mainly due to the underlying inaccuracy, instability and inflexibility. In this paper, we try to tackle these problems in order to make kinetic approaches practical for graphical applications. To achieve more accurate and stable simulations, we propose to employ the non-orthogonal central-moment-relaxation model, where we develop a novel adaptive relaxation method to retain both stability and accuracy in turbulent flows. To achieve flexibility, we propose a novel continuous-scale formulation that enables samples at arbitrary resolutions to easily communicate with each other in a more continuous sense and with loose geometrical constraints, which allows efficient and adaptive sample construction to better match the physical scale. Such a capability directly leads to an automatic sample construction which generates static and dynamic scales at initialization and during simulation, respectively. This effectively makes our method suitable for simulating turbulent flows with arbitrary geometrical boundaries. Our simulation results with applications to smoke animations show the benefits of our method, with comparisons for justification and verification.

The exploration and analysis of data mining methodologies is an important task for effective knowledge discovery, especially in today's heterogeneous information networks. Previously presented approaches for mining optimization aim primarily at the improvements of time complexity, space complexity, accuracy, and robustness. We extend the state-of-the-art method by concentrating on user-availability and algorithm understandability. Specifically, we use Rankclus, a classic clustering algorithm as an example. After uncovering the unseen computing processes to be displayed in a visual form, the whole clustering processes are transparent to the users, which may help them more clearly and quickly understand how the algorithms are computed, how does each object influence one another. In addition, we use a density approach to intuitively simplify the discovery of data patterns, and through the visualized results, users can adjust algorithm parameters with or without professional training. Finally, we use another two visual techniques to improve the visualization quality: a heatmap matrix designed for checking the similarities of objects which are in the same cluster, and a DOItree implemented to further analyze the accuracy of the algorithms.

Superfluidity is a special state of matter exhibiting macroscopic quantum phenomena and acting like a fluid with zero viscosity. In such a state, superfluid vortices exist as phase singularities of the model equation with unique distributions. This paper presents novel techniques to aid the visual understanding of superfluid vortices based on the state-of-the-art non-linear Klein-Gordon equation, which evolves a complex scalar field, giving rise to special vortex lattice/ring structures with dynamic vortex formation, reconnection, and Kelvin waves, etc. By formulating a numerical model with theoretical physicists in superfluid research, we obtain high-quality superfluid flow data sets without noise-like waves, suitable for vortex visualization. By further exploring superfluid vortex properties, we develop a new vortex identification and visualization method: a novel mechanism with velocity circulation to overcome phase singularity and an orthogonal-plane strategy to avoid ambiguity. Hence, our visualizations can help reveal various superfluid vortex structures and enable domain experts for related visual analysis, such as the steady vortex lattice/ring structures, dynamic vortex string interactions with reconnections and energy radiations, where the famous Kelvin waves and decaying vortex tangle were clearly observed. These visualizations have assisted physicists to verify the superfluid model, and further explore its dynamic behavior more intuitively.

Traditional methods in graphics to simulate liquid-air dynamics under different scenarios usually employ separate approaches with sophisticated interface tracking/reconstruction techniques. In this paper, we propose a novel unified approach which is easy and effective to produce a variety of liquid-air interface phenomena. These phenomena, such as complex surface splashes, bubble interactions, as well as surface tension effects, can co-exist in one single simulation, and are created within the same computational framework. Such a framework is unique in that it is free from any complicated interface tracking/reconstruction procedures. Our approach is developed from the two-phase lattice Boltzmann method with the mean field model, which provides a unified framework for interface dynamics but is numerically unstable under turbulent conditions. Considering the drawbacks of the existing approaches, we propose techniques to suppress oscillations for significant stability enhancement, as well as derive a new subgrid-scale model to further improve stability, faithfully preserving liquid-air interface details without excessive diffusion by taking into account the density variation. The whole framework is highly parallel, enabling very efficient implementation. Comparisons with the related approaches show superiority on stable simulations with detail preservation and multiphase phenomena simultaneously involved. A set of animation results demonstrate the effectiveness of our method.

This paper addresses a challenging single-view modeling and animation problem with cartoon images. Our goal is to model the hairs in a given cartoon image with consistent layering and occlusion, so that we can produce various visual effects from just a single image. We propose a novel 2.5D modeling approach to deal with this problem. Given an input image, we first segment the hairs of the cartoon character into regions of hair strands. Then, we apply our novel layering metric, which is derived from the Gestalt psychology, to automatically optimize the depth ordering among the hair strands. After that, we employ our hair completion method to fill the occluded part of each hair strand, and create a 2.5D model of the cartoon hair. By using this model, we can produce various visual effects, e.g., we develop a simplified fluid simulation model to produce wind blowing animations with the 2.5D hairs. To further demonstrate the applicability and versatility of our method, we compare our results with real cartoon hair animations, and also apply our model to produce a wide variety of hair manipulation effects, including hair editing and hair braiding.

This paper presents a novel approach to simulating turbulent flows by developing an adaptive multirelaxation scheme in the framework of lattice Boltzmann equation (LBE). Existing LBE methods in graphics simulations are usually insufficient for turbulent flows since the collision term disturbs the underlying stability and accuracy. We adopt LBE with the multiple relaxation time (MRT) collision model (MRT-LBE), and address this issue by enhancing the collision-term modeling. First, we employ renormalization group analysis and formulate a new turbulence model with an adaptive correction method to compute more appropriate eddy viscosities on a uniform lattice structure. Efficient algebraic calculations are retained with small-scale turbulence details while maintaining the system stability. Second, we note that for MRT-LBE, predicting single eddy viscosity per lattice node may still result in instability. Hence, we simultaneously predict multiple eddy viscosities for stress-tensor-related elements, thereby asynchronously computing multiple relaxation parameters to further enhance the MRT-LBE stability. With these two new strategies, turbulent flows can be simulated with finer visual details even on coarse grid configurations. We demonstrate our results by simulating and visualizing various turbulent flows, particularly with smoke animations, where stable turbulent flows with high Reynolds numbers can be faithfully produced.

Commercial 3D scene acquisition systems such as the Microsoft Kinect sensor can reduce the cost barrier of realizing mid-air interaction. However, since it can only sense hand position but not hand orientation robustly, current mid-air interaction methods for 3D virtual object manipulation often require contextual and mode switching to perform translation, rotation, and scaling, thus preventing natural continuous gestural interactions. A novel handle bar metaphor is proposed as an effective visual control metaphor between the user's hand gestures and the corresponding virtual object manipulation operations. It mimics a familiar situation of handling objects that are skewered with a bimanual handle bar. The use of relative 3D motion of the two hands to design the mid-air interaction allows us to provide precise controllability despite the Kinect sensor's low image resolution. A comprehensive repertoire of 3D manipulation operations is proposed to manipulate single objects, perform fast constrained rotation, and pack/align multiple objects along a line. Three user studies were devised to demonstrate the efficacy and intuitiveness of the proposed interaction techniques on different virtual manipulation scenarios.

Estimating illumination and deformation fields on textures is essential for both analysis and application purposes. Traditional methods for such estimation usually require complicated and sometimes labor-intensive processing. In this paper, we propose a new perspective for this problem and suggest a novel statistical approach which is much simpler and more efficient. Our experiments show that many textures in daily life are statistically invariant in terms of colors and gradients. Variations of such statistics can be assumed to be influenced by illumination and deformation. This implies that we can inversely estimate the spatially varying illumination and deformation according to the variation of the texture statistics. This enables us to decompose a texture photo into an illumination field, a deformation field, and an implicit texture which are illumination- and deformation-free, within a short period of time, and with minimal user input. By processing and recombining these components, a variety of synthesis effects, such as exemplar preparation, texture replacement, surface relighting, as well as geometry modification, can be well achieved. Finally, convincing results are shown to demonstrate the effectiveness of the proposed method.

We propose a novel reaction diffusion (RD) simulator to evolve image-resembling mazes. The evolved mazes faithfully preserve the salient interior structures in the source images. Since it is difficult to control the generation of desired patterns with traditional reaction diffusion, we develop our RD simulator on a different computational platform, cellular neural networks. Based on the proposed simulator, we can generate the mazes that exhibit both regular and organic appearance, with uniform and/or spatially varying passage spacing. Our simulator also provides high controllability of maze appearance. Users can directly and intuitively "paint" to modify the appearance of mazes in a spatially varying manner via a set of brushes. In addition, the evolutionary nature of our method naturally generates maze without any obvious seam even though the input image is a composite of multiple sources. The final maze is obtained by determining a solution path that follows the user-specified guiding curve. We validate our method by evolving several interesting mazes from different source images.

In this paper, we present an example-based colorization technique robust to illumination differences between grayscale target and color reference images. To achieve this goal, our method performs color transfer in an illumination-independent domain that is relatively free of shadows and highlights. It first recovers an illumination-independent intrinsic reflectance image of the target scene from multiple color references obtained by web search. The reference images from the web search may be taken from different vantage points, under different illumination conditions, and with different cameras. Grayscale versions of these reference images are then used in decomposing the grayscale target image into its intrinsic reflectance and illumination components. We transfer color from the color reflectance image to the grayscale reflectance image, and obtain the final result by relighting with the illumination component of the target image. We demonstrate via several examples that our method generates results with excellent color consistency.

Even though the temporal information is lost, a still picture of moving animals hints at their motion. In this paper, we infer motion cycle of animals from the "motion snapshots" (snapshots of different individuals) captured in a still picture. By finding the motion path in the graph connecting motion snapshots, we can infer the order of motion snapshots with respect to time, and hence the motion cycle. Both "half-cycle" and "full-cycle" motions can be inferred in a unified manner. Therefore, we can animate a still picture of a moving animal group by morphing among the ordered snapshots. By refining the pose, morphology, and appearance consistencies, smooth and realistic animal motion can be synthesized. Our results demonstrate the applicability of the proposed method to a wide range of species, including birds, fishes, mammals, and reptiles.

A method is presented for separating corneal reflections in an image of human irises to estimate illumination from the surrounding scene. Previous techniques for reflection separation have demonstrated success in only limited cases, such as for uniform colored lighting and simple object textures, so they are not applicable to irises which exhibit intricate textures and complicated reflections of the environment. To make this problem feasible, we present a method that capitalizes on physical characteristics of human irises to obtain an illumination estimate that encompasses the prominent light contributors in the scene. Results of this algorithm are presented for eyes of different colors, including light colored eyes for which reflection separation is necessary to determine a valid illumination estimate.