This article proposes a novel simulation approach that combines implicit integration with the Bonded Discrete Element Method (BDEM) to achieve faster, more stable, and more accurate fracture simulation. The new method leverages the efficiency of implicit schemes in dynamic simulation and the versatility of BDEM in fracture modeling. Specifically, an optimization-based integrator for BDEM is introduced and combined with a manifold optimization approach to accelerate the solution process of the quaternion-constrained system. Our comparative experiments indicate that our method offers better scale consistency and more realistic collision effects than finite element method and material point method fragmentation approaches. Additionally, our method achieves a computational speedup of 2.1 to 9.8 times over explicit BDEM methods.

Physics-based fluid simulation has played an increasingly important role in the computer graphics community. Recent methods in this area have greatly improved the generation of complex visual effects and its computational efficiency. Novel techniques have emerged to deal with complex boundaries, multiphase fluids, gas–liquid interfaces, and fine details. The parallel use of machine learning, image processing, and fluid control technologies has brought many interesting and novel research perspectives. In this survey, we provide an introduction to theoretical concepts underpinning physics-based fluid simulation and their practical implementation, with the aim for it to serve as a guide for both newcomers and seasoned researchers to explore the field of physics-based fluid simulation, with a focus on developments in the last decade. Driven by the distribution of recent publications in the field, we structure our survey to cover physical background; discretization approaches; computational methods that address scalability; fluid interactions with other materials and interfaces; and methods for expressive aspects of surface detail and control. From a practical perspective, we give an overview of existing implementations available for the above methods.

Along with motion and deformation, fracture is a fundamental behaviour for solid materials, playing a critical role in physically-based animation. Many simulation methods including both continuum and discrete approaches have been used by the graphics community to animate fractures for various materials. However, compared with motion and deformation, fracture remains a challenging task for simulation, because the material's geometry, topology and mechanical states all undergo continuous (and sometimes chaotic) changes as fragmentation develops. Recognizing the discontinuous nature of fragmentation, we propose a discrete approach, namely the Bonded Discrete Element Method (BDEM), for fracture simulation. The research of BDEM in engineering has been growing rapidly in recent years, while its potential in graphics has not been explored. We also introduce several novel changes to BDEM to make it more suitable for animation design. Compared with other fracture simulation methods, the BDEM has some attractive benefits, e.g., efficient handling of multiple fractures, simple formulation and implementation, and good scaling consistency. But it also has some critical weaknesses, e.g., high computational cost, which demand further research. A number of examples are presented to demonstrate the pros and cons, which are then highlighted in the conclusion and discussion.

To maintain incompressibility in SPH fluid simulations is important for visual plausibility. However, it remains an outstanding challenge to enforce incompressibility in such recent multiple-fluid simulators as the mixture-model SPH framework. To tackle this problem, we propose a novel incompressible SPH solver, where the compressibility of fluid is directly measured by the deformation gradient. By disconnecting the incompressibility of fluid from the conditions of constant density and divergence-free velocity, the new incompressible SPH solver is applicable to both single- and multiple-fluid simulations. The proposed algorithm can be readily integrated into existing incompressible SPH frameworks developed for single-fluid, and is fully parallelizable on GPU. Applied to multiple-fluid simulations, the new incompressible SPH scheme significantly improves the visual effects of the mixture-model simulation, and it also allows exploitation for artistic controlling.

Porous materials are common in daily life. They include granular material (e.g. sand) that behaves like liquid flow when mixed with fluid and foam material (e.g. sponge) that deforms like solid when interacting with liquid. The underlying physics is further complicated when multiple fluids interact with porous materials involving coupling between rigid and fluid bodies, which may follow different physics models such as the Darcy's law and the multiple-fluid Navier-Stokes equations. We propose a unified particle framework for the simulation of multiple-fluid flows and porous materials. A novel virtual phase concept is introduced to avoid explicit particle state tracking and runtime particle deletion/insertion. Our unified model is flexible and stable to cope with multiple fluid interacting with porous materials, and it can ensure consistent mass and momentum transport over the whole simulation space.

Abstract We present a novel divergence free mixture model for multiphase flows and the related fluid‐solid coupling. The new mixture model is built upon a volume‐weighted mixture velocity so that the divergence free condition is satisfied for miscible and immiscible multiphase fluids. The proposed mixture velocity can be solved efficiently by adapted single phase incompressible solvers, allowing for larger time steps and smaller volume deviations. Besides, the drift velocity formulation is corrected to ensure mass conservation during the simulation. The new approach increases the accuracy of multiphase fluid simulation by several orders. The capability of the new divergence‐free mixture model is demonstrated by simulating different multiphase flow phenomena including mixing and unmixing of multiple fluids, fluid‐solid coupling involving deformable solids and granular materials.

In physically based-based animation, pure particle methods are popular due to their simple data structure, easy implementation, and convenient parallelization. As a pure particle-based method and using Galerkin discretization, the Moving Least Square Reproducing Kernel Method (MLSRK) was developed in engineering computation as a general numerical tool for solving PDEs. The basic idea of Moving Least Square (MLS) has also been used in computer graphics to estimate deformation gradient for deformable solids. Based on these previous studies, we propose a multiphase MLSRK framework that animates complex and coupled fluids and solids in a unified manner. Specifically, we use the Cauchy momentum equation and phase field model to uniformly capture the momentum balance and phase evolution/interaction in a multiphase system, and systematically formulate the MLSRK discretization to support general multiphase constitutive models. A series of animation examples are presented to demonstrate the performance of our new multiphase MLSRK framework, including hyperelastic, elastoplastic, viscous, fracturing and multiphase coupling behaviours etc.

Abstract Inspired by skeletal animation, a novel rigging‐skinning flow control scheme is proposed to animate fluids intuitively and efficiently. The new animation pipeline creates fluid animation via two steps: fluid rigging and fluid skinning. The fluid rig is defined by a point cloud with rigid‐body movement and incompressible deformation, whose time series can be intuitively specified by a rigid body motion and a constrained free‐form deformation, respectively. The fluid skin generates plausible fluid flows by virtually fluidizing the point‐cloud fluid rig with adjustable zero‐ and first‐order flow features and at fixed computational cost. Fluid rigging allows the animator to conveniently specify the desired low‐frequency flow motion through intuitive manipulations of a point cloud, while fluid skinning truthfully and efficiently converts the motion specified on the fluid rig into plausible flows of the animation fluid, with adjustable fine‐scale effects. Besides being intuitive, the rigging‐skinning scheme for fluid animation is robust and highly efficient, avoiding completely iterative trials or time‐consuming nonlinear optimization. It is also versatile, supporting both particle‐ and grid‐ based fluid solvers. A series of examples including liquid, gas and mixed scenes are presented to demonstrate the performance of the new animation pipeline.

Abstract The material point method (MPM) has attracted increasing attention from the graphics community, as it combines the strengths of both particle‐ and grid‐based solvers. Like the smoothed particle hydrodynamics (SPH) scheme, MPM uses particles to discretize the simulation domain and represent the fundamental unknowns. This makes it insensitive to geometric and topological changes, and readily parallelizable on a GPU. Like grid‐based solvers, MPM uses a background mesh for calculating spatial derivatives, providing more accurate and more stable results than a purely particle‐based scheme. MPM has been very successful in simulating both fluid flow and solid deformation, but less so in dealing with multiple fluids and solids, where the dynamic fluid‐solid interaction poses a major challenge. To address this shortcoming of MPM, we propose a new set of mathematical and computational schemes which enable efficient and robust fluid‐solid interaction within the MPM framework. These versatile schemes support simulation of both multiphase flow and fully‐coupled solid‐fluid systems. A series of examples is presented to demonstrate their capabilities and performance in the presence of various interacting fluids and solids, including multiphase flow, fluid‐solid interaction, and dissolution.

Surface flow phenomena, such as rain water flowing down a tree trunk and progressive water front in a shower room, are common in real life. However, compared with the 3D spatial fluid flow, these surface flow problems have been much less studied in the graphics community. To tackle this research gap, we present an efficient, robust and high-fidelity simulation approach based on the shallow-water equations. Specifically, the standard shallow-water flow model is extended to general triangle meshes with a feature-based bottom friction model, and a series of coherent mathematical formulations are derived to represent the full range of physical effects that are important for real-world surface flow phenomena. In addition, by achieving compatibility with existing 3D fluid simulators and by supporting physically realistic interactions with multiple fluids and solid surfaces, the new model is flexible and readily extensible for coupled phenomena. A wide range of simulation examples are presented to demonstrate the performance of the new approach.

3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods are compared.

This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.

This article presents a novel and flexible bubble modelling technique for multi-fluid simulations using a volume fraction representation. By combining the volume fraction data obtained from a primary multi-fluid simulation with simple and efficient secondary bubble simulation, a range of real-world bubble phenomena are captured with a high degree of physical realism, including large bubble deformation, sub-cell bubble motion, bubble stacking over the liquid surface, bubble volume change, dissolving of bubbles, etc. Without any change in the primary multi-fluid simulator, our bubble modelling approach is applicable to any multi-fluid simulator based on the volume fraction representation.

This article presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of real-world multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction, etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.

Fluid flows are highly nonlinear and nonstationary, with turbulence occurring and developing at different length and time scales. In real-life observations, the multiscale flow generates different visual impacts depending on the distance to the viewer. We propose a new fluid simulation framework that adaptively allocates computational resources according to the viewer's position. First, a 3D empirical mode decomposition scheme is developed to obtain the velocity spectrum of the turbulent flow. Then, depending on the distance to the viewer, the fluid domain is divided into a sequence of nested simulation partitions. Finally, the multiscale fluid motions revealed in the velocity spectrum are distributed nonuniformly to these view-dependent partitions, and the mixed velocity fields defined on different partitions are solved separately using different grid sizes and time steps. The fluid flow is solved at different spatial-temporal resolutions, such that higher frequency motions closer to the viewer are solved at higher resolutions and vice versa. The new simulator better utilizes the computing power, producing visually plausible results with realistic fine-scale details in a more efficient way. It is particularly suitable for large scenes with the viewer inside the fluid domain. Also, as high-frequency fluid motions are distinguished from low-frequency motions in the simulation, the numerical dissipation is effectively reduced.

The nonlinear and nonstationary nature of Navier-Stokes equations produces fluid flows that can be noticeably different in appearance with subtle changes. In this paper, we introduce a method that can analyze the intrinsic multiscale features of flow fields from a decomposition point of view, by using the Hilbert-Huang transform method on 3D fluid simulation. We show how this method can provide insights to flow styles and help modulate the fluid simulation with its internal physical information. We provide easy-to-implement algorithms that can be integrated with standard grid-based fluid simulation methods and demonstrate how this approach can modulate the flow field and guide the simulation with different flow styles. The modulation is straightforward and relates directly to the flow's visual effect, with moderate computational overhead.

Various types of video can be captured with fisheye lenses; their wide field of view is particularly suited to surveillance video. However, fisheye lenses introduce distortion, and this changes as objects in the scene move, making fisheye video difficult to interpret. Current still fisheye image correction methods are either limited to small angles of view, or are strongly content dependent, and therefore unsuitable for processing video streams. We present an efficient and robust scheme for fisheye video correction, which minimizes time-varying distortion and preserves salient content in a coherent manner. Our optimization process is controlled by user annotation, and takes into account a wide set of measures addressing different aspects of natural scene appearance. Each is represented as a quadratic term in an energy minimization problem, leading to a closed-form solution via a sparse linear system. We illustrate our method with a range of examples, demonstrating coherent natural-looking video output. The visual quality of individual frames is comparable to those produced by state-of-the-art methods for fisheye still photograph correction.

Abstract Gaseous fluids may move slowly, as smoke does, or at high speed, such as occurs with explosions. High‐speed gas flow is always accompanied by low‐speed gas flow, which produces rich visual details in the fluid motion. Realistic visualization involves a complex dynamic flow field with both low and high speed fluid behavior. In computer graphics, algorithms to simulate gaseous fluids address either the low speed case or the high speed case, but no algorithm handles both efficiently. With the aim of providing visually pleasing results, we present a hybrid algorithm that efficiently captures the essential physics of both low‐ and high‐speed gaseous fluids. We model the low speed gaseous fluids by a grid approach and use a particle approach for the high speed gaseous fluids. In addition, we propose a physically sound method to connect the particle model to the grid model. By exploiting complementary strengths and avoiding weaknesses of the grid and particle approaches, we produce some animation examples and analyze their computational performance to demonstrate the effectiveness of the new hybrid method.