Monolithic Friction and Contact Handling for Rigid Bodies and Fluids Using SPH

We propose a novel monolithic pure SPH formulation to simulate fluids strongly coupled with rigid bodies. This includes fluid incompressibility, fluid–rigid interface handling and rigid–rigid contact handling with a viable implicit particle-based dry friction formulation. The resulting global system is solved using a new accelerated solver implementation that outperforms existing fluid and coupled rigid–fluid simulation approaches. We compare results of our simulation method to analytical solutions, show performance evaluations of our solver and present a variety of new and challenging simulation scenarios.     

Visual Simulation of Multiple Unmixable Fluids

We present a novel grid-based method for simulating multiple unmixable fluids moving and interacting. Unlike previous methods that can only represent the interface between two fluids （usually between liquid and gas）, this method can handle an arbitrary number of fluids through multiple independent level sets coupled with a constrain condition. To capture the fluid surface more accurately, we extend the particle level set method to a multi-fluid version. It shares the advantages of the particle level set method, and has the ability to track the interfaces of multiple fluids. To handle the dynamic behavior of different fluids existing together, we use a multiphase fluid formulation based on a smooth weight function.     

Remeshing-free Graph-based Finite Element Method for Fracture Simulation

Fracture produces new mesh fragments that introduce additional degrees of freedom in the system dynamics. Existing finite element method (FEM) based solutions suffer from increasing computational cost as the system matrix size increases. We solve this problem by presenting a graph-based FEM model for fracture simulation that is remeshing-free and easily scales to high-resolution meshes. Our algorithm models fracture on the graph induced in a volumetric mesh with tetrahedral elements. We relabel the edges of the graph using a computed damage variable to initialize and propagate fracture. We prove that non-linear, hyper-elastic strain energy density is expressible entirely in terms of the edge lengths of the induced graph. This allows us to reformulate the system dynamics for the relabelled graph without changing the size of the system dynamics matrix and thus prevents the computational cost from blowing up. The fractured surface has to be reconstructed explicitly only for visualization purposes. We simulate standard laboratory experiments from structural mechanics and compare the results with corresponding real-world experiments. We fracture objects made of a variety of brittle and ductile materials, and show that our technique offers stability and speed that is unmatched in current literature.     

Accelerating Liquid Simulation With an Improved Data-Driven Method

In physics-based liquid simulation for graphics applications, pressure projection consumes a significant amount of computational time and is frequently the bottleneck of the computational efficiency. How to rapidly apply the pressure projection and at the same time how to accurately capture the liquid geometry are always among the most popular topics in the current research trend in liquid simulations. In this paper, we incorporate an artificial neural network into the simulation pipeline for handling the tricky projection step for liquid animation. Compared with the previous neural-network-based works for gas flows, this paper advocates new advances in the composition of representative features as well as the loss functions in order to facilitate fluid simulation with free-surface boundary. Specifically, we choose both the velocity and the level-set function as the additional representation of the fluid states, which allows not only the motion but also the boundary position to be considered in the neural network solver. Meanwhile, we use the divergence error in the loss function to further emulate the lifelike behaviours of liquid. With these arrangements, our method could greatly accelerate the pressure projection step in liquid simulation, while maintaining fairly convincing visual results. Additionally, our neutral network performs well when being applied to new scene synthesis even with varied boundaries or scales.     

An Implicit SPH Formulation for Incompressible Linearly Elastic Solids

We propose a novel smoothed particle hydrodynamics (SPH) formulation for deformable solids. Key aspects of our method are implicit elastic forces and an adapted SPH formulation for the deformation gradient that—in contrast to previous work—allows a rotation extraction directly from the SPH deformation gradient. The proposed implicit concept is entirely based on linear formulations. As a linear strain tensor is used, a rotation‐aware computation of the deformation gradient is required. In contrast to existing work, the respective rotation estimation is entirely realized within the SPH concept using a novel formulation with incorporated kernel gradient correction for first‐order consistency. The proposed implicit formulation and the adapted rotation estimation allow for significantly larger time steps and higher stiffness compared to explicit forms. Performance gain factors of up to one hundred are presented. Incompressibility of deformable solids is accounted for with an ISPH pressure solver. This further allows for a pressure‐based boundary handling and a unified processing of deformables interacting with SPH fluids and rigids. Self‐collisions are implicitly handled by the pressure solver.     

Anisotropic Strain Limiting for Quadrilateral and Triangular Cloth Meshes

The cloth simulation systems often suffer from excessive extension on the polygonal mesh, so an additional strain‐limiting process is typically used as a remedy in the simulation pipeline. A cloth model can be discretized as either a quadrilateral mesh or a triangular mesh, and their strains are measured differently. The edge‐based strain‐limiting method for a quadrilateral mesh creates anisotropic behaviour by nature, as discretization usually aligns the edges along the warp and weft directions. We improve this anisotropic technique by replacing the traditionally used equality constraints with inequality ones in the mathematical optimization, and achieve faster convergence. For a triangular mesh, the state‐of‐the‐art technique measures and constrains the strains along the two principal (and constantly changing) directions in a triangle, resulting in an isotropic behaviour which prohibits shearing. Based on the framework of inequality‐constrained optimization, we propose a warp and weft strain‐limiting formulation. This anisotropic model is more appropriate for textile materials that do not exhibit isotropic strain behaviour.     

Stable and Fast Fluid–Solid Coupling for Incompressible SPH

The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum‐conserving velocity‐position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid–solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two‐way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios.     

一种新的有效模拟不可压缩流体的SPH方法

提出了一种基于光滑粒子流体动力学(SPH)来模拟不可压缩流体的有效方法.传统的SPH方法是针对可压缩流体设计的,而该方法是传统SPH方法的一个扩展.提出了一种新的可以满足不可压缩性的压强计算方法,讨论了压力和粘性力的新型计算方法.实验结果表明,提出的方法与以前的方法相比,能够更真实地模拟不可压缩流体.     

Fast and Controllable Simulation of the Shattering of Brittle Objects

We present a method for the rapid and controllable simulation of the shattering of brittle objects under impact. An object is represented as a set of point masses connected by distance-preserving linear constraints. This use of constraints, rather than stiff springs, gains us a significant advantage in speed while still retaining fine control over the fracturing behavior. The forces exerted by these constraints during impact are computed using Lagrange multipliers. These constraint forces are then used to determine when and where the object will break, and to calculate the velocities of the newly created fragments. We present the details of our technique together with examples illustrating its use.
An earlier version of this paper was presented at Graphics Interface 2000, held in Montreal, Canada.     

Primal‐Dual Optimization for Fluids

We apply a novel optimization scheme from the image processing and machine learning areas, a fast Primal‐Dual method, to achieve controllable and realistic fluid simulations. While our method is generally applicable to many problems in fluid simulations, we focus on the two topics of fluid guiding and separating solid‐wall boundary conditions. Each problem is posed as an optimization problem and solved using our method, which contains acceleration schemes tailored to each problem. In fluid guiding, we are interested in partially guiding fluid motion to exert control while preserving fluid characteristics. With our method, we achieve explicit control over both large‐scale motions and small‐scale details which is valuable for many applications, such as level‐of‐detail adjustment (after running the coarse simulation), spatially varying guiding strength, domain modification, and resimulation with different fluid parameters. For the separating solid‐wall boundary conditions problem, our method effectively eliminates unrealistic artefacts of fluid crawling up solid walls and sticking to ceilings, requiring few changes to existing implementations. We demonstrate the fast convergence of our Primal‐Dual method with a variety of test cases for both model problems.     

Compressed Neighbour Lists for SPH

We propose a novel compression scheme to store neighbour lists for iterative solvers that employ Smoothed Particle Hydrodynamics (SPH). The compression scheme is inspired by Stream VByte, but uses a non-linear mapping from data to data bytes, yielding memory savings of up to 87%. It is part of a novel variant of the Cell-Linked-List (CLL) concept that is inspired by compact hashing with an improved processing of the cell-particle relations. We show that the resulting neighbour search outperforms compact hashing in terms of speed and memory consumption. Divergence-Free SPH (DFSPH) scenarios with up to 1.3 billion SPH particles can be processed on a 24-core PC using 172 GB of memory. Scenes with more than 7 billion SPH particles can be processed in a Message Passing Interface (MPI) environment with 112 cores and 880 GB of RAM. The neighbour search is also useful for interactive applications. A DFSPH simulation step for up to 0.2 million particles can be computed in less than 40 ms on a 12-core PC.     

Real-Time Simulation of Aeolian Sand Movement and Sand Ripple Evolution: A Method Based on the Physics of Blown Sand

Simulation and visualization of aeolian sand movement and sand ripple evolution are a challenging subject. In this paper, we propose a physically based modeling and simulating method that can be used to synthesize sandy terrain in various patterns. Our method is based on the mechanical behavior of individual sand grains, which are widely studied in the physics of blown sand. We accounted significant mechanisms of sand transportation into the sand model, such as saltation, successive saltation and collapsing, while simplified the vegetation model and wind field model to make the simulation feasible and affordable. We implemented the proposed method on the programming graphics processing unit (GPU) to get real-time simulation and rendering. Finally, we proved that our method can reflect many characteristics of sand ripple evolution through several demonstrations. We also gave several synthesized desert scenes made from the simulated height field to display its significance on application.     

滴水涟漪的计算机动画模拟

模拟了近距离观察滴水涟漪的,用有限体积法求解二维的浅水波方程,在水表面受到扰动后自动产生波纹,为了增加真实感,加入了粒子系统,但与以往工作不同的是粒子被进一步分类成水滴、水柱、水粒和水泡。详细讨论了隐式曲面技术给这些液态物体造型,以便逼真地表现出这些液态物体的多变性。     

基于物理模型的烟雾实时模拟

本文提出了一种基于物理模型的烟雾的实时数值模拟方法.真实感和实时性是计算机图形学追求的两个目标.传统的动画技术生成的物体运动是虚拟的,并不能完全反映物体的真实运动.与传统的动画技术相比,基于物理的动画更能表现运动的真实性.在用非粘性不可压欧拉方程表示烟雾的物理模型的基础上,利用破开算子法将其分解成外力项、对流项和投影项分别进行求解,每一步都稳定,因而整个求解也就稳定.求解过程的稳定性保证了模拟可以用大时间步长,也就保证了模拟的实时性.与传统的方法相比,能同时满足计算机图形学的真实感和实时性要求.     

Vortex particle smoke simulation with an octree data structure

We propose an octree‐based presentation of vortex particles to simulate smoke and gaseous phenomena in a physical way. Vortex particle method prevails over grid‐based method in terms of less numerical dissipation and more detail features, but it suffers from heavy computational overhead due to per‐particle Biot–Savart integration over the entire simulation space. To alleviate this problem, we employ an octree background grid to separate the vortex particles into individual groups. Particles in groups are aggregated as a single super vortex particle to reduce computational cost. The proposed method produces comparable visual result as previous methods with much less computational overhead. Copyright © 2014 John Wiley & Sons, Ltd.     

The Matchstick Model for Anisotropic Friction Cones

Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g. the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP-based simulators using different solvers with both explicit and fully implicit time-integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.     

Techniques for Realistic Visualization of Fluids: A Survey

Visualization of fluids has wide applications in science, engineering and entertainment. Various methodologies of visualizing fluids have evolved which emphasize on capturing different aspects of the fluids accurately. In this survey the existing methods for realistic visualization of fluids are reviewed. The approaches are classified based on the key concept they rely on for fluid modeling. This classification allows for easy selection of the method to be adopted for visualization given an application. It also enables identification of alternative techniques for fluid modeling.     

Multi-Segment Foot for Human Modelling and Simulation

Realistic modelling of a human-like character is one of the main topics in computer graphics to simulate human motion physically and also look realistically. Of the body parts, a human foot interacts with the ground, and plays an essential role in weight transmission, balancing posture and assisting ambulation. However, in the previous researches, the foot model was often simplified into one or two rigid bodies connected by a revolute joint. We propose a new foot model consisting of multiple segments to reproduce human foot shape and its functionality accurately. Based on the new model, we develop a foot pose controller that can reproduce foot postures that are generally not obtained in motion capture data. We demonstrate the validity of our foot model and the effectiveness of our foot controller with a variety of foot motions in a physics-based simulation.     

微可压缩SPH流体的稳定性固体边界处理算法

固流耦合,即流体的固体边界处理一直是基于物理的流体模拟技术的研究重点.为解决SPH流体模拟中固流耦合存在的交界面处流体粒子衰减和穿透问题,提出一种固体采样边界粒子与动量守恒保持的位置-速度修正方案相结合的固流耦合方法.首先在预处理阶段对快速格子形状匹配(fast lattice shape matching,FLSM)模型表示的固体边界进行表面和内部边界粒子采样;然后在运行过程中计算流体粒子密度和受力时考虑边界固体粒子的相对贡献;最后利用动量守恒保持的位置-速度修正方案对流体粒子进行位置和速度的修正.为了提高计算速度以满足交互式应用需求,把每个迭代步长内的计算完全并行化后加载到GPU上进行加速处理.实验结果表明,该算法实现了微可压缩SPH流体与刚体以及弹性体的双向耦合,并可以高效、稳定地模拟固流耦合中的非穿透、液滴飞溅、溶解等复杂现象.     

SPH固流交互中的实时固体破碎动画模拟

目的 针对固流交互中的固体破碎现象模拟研究较少、物理模型复杂、多求解器耦合性差、真实感与实时性难以兼顾等问题,提出一种适用于光滑粒子流体动力学（smoothed particle hydrodynamics,SPH）固流交互统一粒子框架的实时固体破碎模拟方法。方法 首先,结合断裂力学理论与统一粒子框架下固体边界粒子的空间和物理特性,构建基于物理的能量分析模型。然后,通过实时分析固体与流体之间的能量转化和自身能量平衡,将满足条件的粒子作为破碎发生的启发点。最后,采用基于几何的碎块生成方法,将启发点集作为种子点构建Voronoi图,完成碎块的生成。为确保模拟系统实时性,将模拟系统进行并行优化并加载至图形处理器（graphics processing unit,GPU）并行执行。结果 通过在不同复杂度和粒子规模的实验场景中进行模拟得到的结果表明,本文方法能够稳定地模拟固体受到流体冲击后发生的破碎现象,破碎细节真实感良好,在百万级粒子规模下能够满足实时性要求,可大规模并行执行且GPU加速效果显著,加速收益随场景规模增大而增大。结论 与现有研究相比,本文方法充分结合物理与几何方法的优点,与SPH统一粒子框架具有更高的耦合性,能够稳定地模拟固流交互中的固体破碎现象,细节符合现实世界物理规律,真实感渲染效果良好,可应用于洪涝、海啸、溃坝和泥石流等自然灾害的交互式预演、电子游戏特效等领域。