大规模流体场景的真实感与实时模拟

目的 基于物理的流体动画模拟是计算机图形学领域中的研究热点,针对实际应用中仍难以实现大规模流体场景的真实感与实时模拟,提出了基于shallow water方程的物理模拟方法。方法 首先,给出shallow water方程的稳定欧拉数值求解方法,解决模拟过程中存在的毛刺、陡坡水滴斑点等数值求解的不稳定性问题;其次,提出刚体和粒子系统与流体高度场的稳定耦合模型,实现双向固流耦合和流体表面细节的真实感模拟;最后,设计高度场的多精度网格算法以及粒子的隔点采样方法,加速大规模流体的物理模拟计算。结果 实验结果表明,本文方法解决了传统欧拉方法求解shallow water方程的流体模拟过程中存在的不稳定和计算复杂等问题,在300×300网格分辨率和2.2×10⁴粒子数的规模下,达到了20帧/s的实时模拟速度。结论 本文算法具有良好的高效性和稳定性,适用于电子游戏和视景仿真等实时应用领域中的大规模流体场景的真实感模拟。     

浅水动边界问题的位移法模拟

为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程（Shallow Water Equation based on Displacement,SWE D）.SWE D以位移为基本未知量,可以精确满足动边界处的零水深要求并精确捕捉动态边界位置,且解具有协调性.在Hamilton变分原理的框架下,分别采用有限元和保辛积分算法对该浅水方程进行空间离散和时间积分,可有效地处理不平水底情况,保证对非线性演化进行长时间仿真的精度.数值算例表明该方法适用于浅水动边界问题的数值模拟.     

An adaptive solver for the spherical shallow water equations

The shallow water equations (SWE), which describe the flow of a thin layer of fluid in two dimensions have been used by the atmospheric modelling community as a vehicle for testing promising numerical methods for solving atmospheric and oceanic problems. The SWE are important for the study of the dynamics of large-scale flows, as well for the development of new numerical schemes that are applied to more complex models. In this paper we present a finite difference p-adaptive method based on high order finite differences that is applied using an error indicator for solving the SWE on the sphere. A standard test set is used to evaluate the accuracy of the new method. The results obtained are compared with the pseudo-spectral method.     

Application of meshless SWE model to moving wet/dry front problems

Engineering with Computers - In this study, the 2D shallow water equations (SWE) are solved using a meshless method with the local polynomial approximation and the weighted-least-squares (WLS)...     

Robust and Efficient Wave Simulations on Deforming Meshes

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.     

Hydraulic Erosion Using Smoothed Particle Hydrodynamics

This paper presents a new technique for modification of 3D terrains by hydraulic erosion. It efficiently couples fluid simulation using a Lagrangian approach, namely the Smoothed Particle Hydrodynamics (SPH) method, and a physically-based erosion model adopted from an Eulerian approach. The eroded sediment is associated with the SPH particles and is advected both implicitly, due to the particle motion, and explicitly, through an additional velocity field, which accounts for the sediment transfer between the particles. We propose a new donor-acceptor scheme for the explicit advection in SPH. Boundary particles associated to the terrain are used to mediate sediment exchange between the SPH particles and the terrain itself. Our results show that this particle-based method is efficient for the erosion of dense, large, and sparse fluid. Our implementation provides interactive results for scenes with up to 25,000 particles.     

Mixing Fluids and Granular Materials

Fluid animations in computer graphics show interactions with various kinds of objects. However, fluid flowing through a granular material such as sand is still not possible within current frameworks. In this paper, we present the simulation of fine granular materials interacting with fluids. We propose a unified Smoothed Particle Hydrodynamics framework for the simulation of both fluid and granular material. The granular volume is simulated as a continuous material sampled by particles. By incorporating previous work on porous flow in this simulation framework we are able to fully couple fluid and sand. Fluid can now percolate between sand grains and influence the physical properties of the sand volume. Our method demonstrates various new effects such as dry soil transforming into mud pools by rain or rigid sand structures being eroded by waves.     

Solving the Shallow Water equations using 2D SPH particles for interactive applications

In this paper, we introduce a 2D particle-based approach to achieve realistic water surface behaviors for interactive applications. We formulate 2D particle-based Shallow Water equations using the Smoothed Particle Hydrodynamics. Particles defined with specific amount of water volume interplay with each other, which generates the horizon flow and the water surface motion. By the application of the particle-based Lagrangian framework to the 2D Shallow Water simulation, our method allows the water particles to move freely without being confined to a grid. The motion of the particles can represent global flow with dynamic waves covering a large area while avoiding extensive 3D fluid dynamics computation. The 2D particle-based Shallow Water equations are straightforward and computed fast with the GPU-based implementation. Experiments on a standard hardware demonstrate the performance of our approach which is running on the GPU, and the results show a realistic motion of the water surface at interactive rates.     

A Layered Particle‐Based Fluid Model for Real‐Time Rendering of Water

We present a physically based real‐time water simulation and rendering method that brings volumetric foam to the real‐time domain, significantly increasing the realism of dynamic fluids. We do this by combining a particle‐based fluid model that is capable of accounting for the formation of foam with a layered rendering approach that is able to account for the volumetric properties of water and foam. Foam formation is simulated through Weber number thresholding. For rendering, we approximate the resulting water and foam volumes by storing their respective boundary surfaces in depth maps. This allows us to calculate the attenuation of light rays that pass through these volumes very efficiently. We also introduce an adaptive curvature flow filter that produces consistent fluid surfaces from particles independent of the viewing distance.     

Boundary Detection in Particle‐based Fluids

This paper presents a novel method to detect free‐surfaces on particle‐based volume representation. In contrast to most particle‐based free‐surface detection methods, which perform the surface identification based on physical and geometrical properties derived from the underlying fluid flow simulation, the proposed approach only demands the spatial location of the particles to properly recognize surface particles, avoiding even the use of kernels. Boundary particles are identified through a Hidden Point Removal (HPR) operator used for visibility test. Our method is very simple, fast, easy to implement and robust to changes in the distribution of particles, even when facing large deformation of the free‐surface. A set of comparisons against state‐of‐the‐art boundary detection methods show the effectiveness of our approach. The good performance of our method is also attested in the context of fluid flow simulation involving free‐surface, mainly when using level‐sets for rendering purposes.     

基于SPH方法的滴水涟漪动画模拟

光滑粒子流体动力学（Smoothed Particle Hydrodynamics,SPH）方法是一种新近发展的可用于流体模拟的无网格数值方法。文中基于SPH方法的基本原理,利用SPH方法求解描述水流现象的二维浅水波方程,根据具体模型使用Mon-aghan人工粘性的变形形式,有效地防止了相互靠近粒子的穿透,消除了SPH方法在模拟流体动力学问题时产生的数值振荡。通过使用可变光滑长度,使邻近粒子的数量保持相对稳定,提高了求解的计算效率和精度。同时,对光滑长度进行了修正以获取对称光滑长度,保持了粒子间相互作用对称性。全面考虑了各种定解条件的设置,对水滴的运动进行了模拟,SPH模拟结果与有限差分法、有限体积法结果非常吻合,验证了方法的准确性,为SPH方法的进一步发展和广泛运用奠定了基础。     

基于CUDA的弱可压SPH流体建模与仿真

为了实现小尺度范围流体场景的实时、真实感模拟,采用弱可压SPH方法对水体进行建模,提出了流体计算的CPU GPU混合架构计算方法。针对邻域粒子查找算法影响流体计算效率的问题,采用三维空间网格对整个模拟区域进行均匀网格划分,利用并行前缀求和和并行计数排序实现邻域粒子的查找。最后,采用基于CUDA并行加速的Marching Cubes算法实现流体表面提取,利用环境贴图表现流体的反射和折射效果,实现流体表面着色。实验结果表明,所提出的流体建模和模拟算法能实现小尺度范围流体的实时计算和渲染,绘制出水的波动、翻卷和木块在水中晃动的动态效果,当粒子数达到1 048 576个时,GPU并行计算方法相较CPU方法的加速比为60.7。     

大时间步长下体积守恒的实时水体模拟

摘 要：基于物理的流体仿真可以真实地捕捉水的运动,一种常用的实时模拟方法是基于 二维浅水方程进行水体仿真。首先介绍了二维浅水方程,并提出一种新的求解方法,通过一种 体积守恒的隐式半拉格朗日方法进行计算,在保持稳定的同时允许较大的时间步长,然后额外 增加修正步以保证计算过程中体积守恒。此外提出了一种基于动量守恒的流固耦合方法,可以 实时地模拟出较为真实的水体,并且保证了水体体积始终守恒,效果良好。     

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

Recently, many techniques using computational fluid dynamics have been proposed for the simulation of natural phenomena such as smoke and fire. Traditionally, a single grid is used for computing the motion of fluids. When an object interacts with a fluid, the resolution of the grid must be sufficiently high because the shape of the object is represented by a shape sampled at the grid points. This increases the number of grid points that are required, and hence the computational cost is increased. To address this problem, we propose a method using multiple grids that overlap with each other. In addition to a large single grid (a global grid) that covers the whole of the simulation space, separate grids (local grids) are generated that surround each object. The resolution of a local grid is higher than that of the global grid. The local grids move according to the motion of the objects. Therefore, the process of resampling the shape of the object is unnecessary when the object moves. To accelerate the computation, appropriate resolutions are adaptively‐determined for the local grids according to their distance from the viewpoint. Furthermore, since we use regular (orthogonal) lattices for the grids, the method is suitable for GPU implementation. This realizes the real‐time simulation of interactions between objects and smoke.     

Markov-type velocity field for efficiently animating water stream

In computer graphics, one of the most challenging tasks is continuously varying phenomena such as waving, swaying, and flowing motions. In this paper, we present a novel hybrid model (physical-stochastic) to create an endless animation in which offline simulation is used to produce an infinitely varying real-time animated result. In this particular case, a water stream model is proposed. Most fully 3D physically based simulation methods for depicting fluid flows are very time and memory consuming. Thus, these methods are still reserved for offline simulations and small-domain real-time simulations, especially in the case of fluid flows with irregularly repeating patterns. The proposed model is based on the tracer particle technique, uses a non-static velocity field, and consists of two main phases. In the first phase, we construct the stochastic velocity field by using the physically based method. The second phase is the main part, in which we create real-time endless animation. Here, we introduce a new type of velocity field which we refer to as a Markov-type velocity field (MTVF). MTVF allows us to animate a water stream endlessly in real-time by avoiding the time-consuming process of solving the corresponding equations for every simulation step.     

Implementing lattice Boltzmann computation on graphics hardware

The Lattice Boltzmann Model (LBM) is a physically-based approach that simulates the microscopic movement of fluid particles by simple, identical, and local rules. We accelerate the computation of the LBM on general-purpose graphics hardware, by grouping particle packets into 2D textures and mapping the Boltzmann equations completely to the rasterization and frame buffer operations. We apply stitching and packing to further improve the performance. In addition, we propose techniques, namely range scaling and range separation, that systematically transform variables into the range required by the graphics hardware and thus prevent overflow. Our approach can be extended to acceleration of the computation of any cellular automata model.     

Visualizing Underwater Ocean Optics

Simulating the in‐water ocean light field is a daunting task. Ocean waters are one of the richest participating media, where light interacts not only with water molecules, but with suspended particles and organic matter as well. The concentration of each constituent greatly affects these interactions, resulting in very different hues. Inelastic scattering events such as fluorescence or Raman scattering imply energy transfers that are usually neglected in the simulations. Our contributions in this paper are a bio‐optical model of ocean waters suitable for computer graphics simulations, along with an improved method to obtain an accurate solution of the in‐water light field based on radiative transfer theory. The method provides a link between the inherent optical properties that define the medium and its apparent optical properties, which describe how it looks. The bio‐optical model of the ocean uses published data from oceanography studies. For inelastic scattering we compute all frequency changes at higher and lower energy values, based on the spectral quantum efficiency function of the medium. The results shown prove the usability of the system as a predictive rendering algorithm. Areas of application for this research span from underwater imagery to remote sensing; the resolution method is general enough to be usable in any type of participating medium simulation.     

A model for real-time on-surface flows

Simulating fluid flows for visualization purposes is known to be one of the most challenging fields of the computer graphics domain. While rendering vast liquid areas has been widely addressed this last decade, few papers have tackled the problematic of on-surface flows, even though real-time applications such as drive simulators or video games could greatly benefit from such methods. We present a novel empirical method for the animation of liquid droplets lying on a flat surface, the core of our technique being a simulation operating on a 2D grid which is implementable on GPU. The wetted surface can freely be oriented in space and is not limited to translucent materials, the liquid flow being governed by external forces, the viscosity parameter and the presence of obstacles. Furthermore, we show how to simply incorporate in our simulation scheme two enriching visual effects, namely absorption and ink transport. Rendering can be achieved from an arbitrary view point using a GPU image based raycasting approach and takes into account the refraction and reflection of light. Even though our method doesn’t benefit from the literature of fluid mechanics, we show that convincing animations in terms of realism can be achieved in real-time.     

Real‐time Animation of Sand‐Water Interaction

Recent advances in physically‐based simulations have made it possible to generate realistic animations. However, in the case of solid‐fluid coupling, wetting effects have rarely been noticed despite their visual importance especially in interactions between fluids and granular materials. This paper presents a simple particle‐based method to model the physical mechanism of wetness propagating through granular materials; Fluid particles are absorbed in the spaces between the granular particles and these wetted granular particles then stick together due to liquid bridges that are caused by surface tension and which will subsequently disappear when over‐wetting occurs. Our method can handle these phenomena by introducing a wetness value for each granular particle and by integrating those aspects of behavior that are dependent on wetness into the simulation framework. Using this method, a GPU‐based simulator can achieve highly dynamic animations that include wetting effects in real time.     

Local Poisson SPH For Viscous Incompressible Fluids

Enforcing fluid incompressibility is one of the time‐consuming aspects in SPH. In this paper, we present a local Poisson SPH (LPSPH) method to solve incompressibility for particle based fluid simulation. Considering the pressure Poisson equation, we first convert it into an integral form, and then apply a discretization to convert the continuous integral equation to a discretized summation over all the particles in the local pressure integration domain determined by the local geometry. To control the approximation error, we further integrate our local pressure solver into the predictive‐corrective framework to avoid the computational cost of solving a pressure Poisson equation globally. Our method can effectively eliminate the large density deviations mainly caused by the solid boundary treatment and free surface topological change, and show advantage of a higher convergence rate over the predictive‐corrective incompressible SPH (PCISPH).