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.     

水流动画模拟方法探讨

目前,对于水流动画模拟的研究已经取得了相当丰富的成果。基于物理模型的流体动画模拟的研究,需要计算流体力学和计算机图形学的交叉融合,根据其研究的背景与内容的不同,可分为两种类型。基于物理模型的流体动画模拟中描述流体运动的方法主要有两种,一种是Euler方法,另一种是Lagrange方法。Euler方法的主要缺点是难以处理流体的细节,Lagrange方法的优点就是能很好地表现流体的细节。由于Euler方法和Lagrange方法的这些特点,如果发展这两种方法的综合方法,则可取长补短。     

Efficient 2D Simulation on Moving 3D Surfaces

We present a method to simulate fluid flow on evolving surfaces, e.g., an oil film on a water surface. Given an animated surface (e.g., extracted from a particle-based fluid simulation) in three-dimensional space, we add a second simulation on this base animation. In general, we solve a partial differential equation (PDE) on a level set surface obtained from the animated input surface. The properties of the input surface are transferred to a sparse volume data structure that is then used for the simulation. We introduce one-way coupling strategies from input properties to our simulation and we add conservation of mass and momentum to existing methods that solve a PDE in a narrow-band using the Closest Point Method. In this way, we efficiently compute high-resolution 2D simulations on coarse input surfaces. Our approach helps visual effects creators easily integrate a workflow to simulate material flow on evolving surfaces into their existing production pipeline.     

基于一种新的网格结构的涡粒子模拟烟的方法

目的：流体模拟方法中的基于旋度的模拟方法相比于基于速度的模拟方法,能提供较多细节,但是通常难以处理不同的边界条件,比如固体边界和自由表面,而且通常难以保证模拟的稳定性。本文的目的就是为了解决基于旋度的模拟方法的边界问题和稳定性问题。方法：本文提出了一种新的网格结构,在这种网格结构下,旋度分量被错开放置在每个网格的棱的中心点。利用这种网格离散格式,本文提出了几种修改求解速度场方程组的策略,以应对不同的边界条件。结果：本文给出了多种场景下的流体模拟结果图,以及几种场景下的总动能变化图和时间效率表。结果显示,本文方法能够处理好不同边界条件,并保持模拟的稳定性。结论：本文提出了一种新的涡粒子流体模拟方法,该方法利用一种新的网格结构辅助模拟,在这种新的网格离散格式下,该方法解决了基于旋度的模拟方法的边界问题和稳定性问题。     

雷诺应力模型对旋流器内流场的数值模拟

深入研究了液-液水力旋流器的流动机理和分散油相的流动特点及处理方法，用计算流体动力学（CFD）的数值方法，采用雷诺应力（RSM）模型对油水分离旋流器的内部流场进行了数值模拟。分析了旋流器内部的体积浓度分布，压力分布，以及切向、轴向和径向速度分布的规律，揭示了油水两相流的分离特性。并且在不同流量下，计算出了旋流器的流量一效率曲线，计算结果与实验数据吻合较好，从而说明该湍流模型和数值算法的可靠性，同时也为进一步研究水力旋流器的分离机理、流场特性以及结构优化设计提供了一条有效的途径。     

Augmented Flow Simulation Based on Tight Coupling Between Video Reconstruction and Eulerian Models

Hybrid approaches such as combining video data with pure physics-based simulation have been popular in the recent decade for computer graphics. The key motivation is to clearly retain salient advantages from both data-driven method and model-centric numerical simulation, while overcoming certain difficulties of both. The Eulerian method, which has been widely employed in flow simulation, stores variables such as velocity and density on regular Cartesian grids, thereby it could be associated with (volumetric) video data on the same domain. This paper proposes a novel method for flow simulation, which is tightly coupling video-based reconstruction with physically-based simulation and making use of meaningful physical attributes during re-simulation. First, we reconstruct the density field from a single-view video. Second, we estimate the velocity field using the reconstructed density field as prior. In the iterative process, the pressure projection can be treated as a physical constraint and the results of each step are corrected by obtained velocity field in the Eulerian framework. Third, we use the reconstructed density field and velocity field to guide the Eulerian simulation with anticipated new results. Through the guidance of video data, we can produce new flows that closely match with the real scene exhibited in data acquisition. Moreover, in the multigrid Eulerian simulation, we can generate new visual effects which cannot be created from raw video acquisition, with a goal of easily producing many more visually interesting results and respecting true physical attributes at the same time. We demonstrate salient advantages of our hybrid method with a variety of animation examples.     

交错网格结构的涡粒子烟模拟

目的 流体模拟方法中的基于旋度的模拟方法相比于基于速度的模拟方法,能提供较多细节,但是通常难以处理不同的边界条件,比如固体边界和自由表面,而且通常难以保证模拟的稳定性。本文的目的就是为了解决基于旋度的模拟方法的边界问题和稳定性问题。方法 提出一种交错网格结构,在这种网格结构下,旋度分量被错开放置在每个网格的棱的中心点。利用这种网格离散格式,提出了几种修改求解速度场方程组的策略,以应对不同的边界条件。结果 给出多种场景下的流体模拟结果图,以及几种场景下的总动能变化图和时间效率表。结果显示,本文方法能够处理好不同边界条件,并保持模拟的稳定性。结论 本文提出了一种新的涡粒子流体模拟方法,该方法利用一种交错网格结构辅助模拟,在这种新的网格离散格式下,该方法解决了基于旋度的模拟方法的边界问题和稳定性问题。     

Real-time simulation of physically based on-surface flow

Although many papers have been published in the field of fluid simulation, little attention has been paid to on-surface flow involving wetting and stain transportation as well as erosion and deposition phenomena. In this paper, we introduce nonzero divergence in the mass equation of Navier–Stokes equations to simulate water penetration from on-surface flow into substrate material. Also, the volume of fluid method is adopted to track the free surface. With a computation of the actual amount of absorbed water we render the wetting effects with fully dry and fully wet texture images simultaneously. Using our model, the on-surface flow that accompanies water absorption can be simulated realistically in real time with OpenGL preview rendering. Experimental results illustrate that our model can be widely applied to solve various problems related to on-surface flow.     

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。     

SPH haptic interaction with multiple-fluid simulation

Physics-based fluid interaction plays an important role in computer animation, with wide applications in virtual reality, computer games, digital entertainment, etc. For example, in virtual reality education and games, we often need fluid interactions like acting as an alchemist to create a potion by stirring fluid in a crucible. The traditional input devices such as a mouse and keyboard can basically input 2D information without feedback. In recent years, the continuous development of haptic device not only can achieve six degrees-of-freedom input, but also can calculate the force in virtual scenes and feedback to the user to make a better virtual experience. How to use haptic device in different kinds of virtual fluid scenarios to provide better experience is an important issue in the field of virtual reality. On the other hand, the researches on multiple-fluid interaction especially based on smoothed particle hydrodynamics (SPH) method are very lacking. Therefore, we study the key techniques of haptic interaction with SPH multiple-fluid to compensate this defect in computer graphics community. Different from the single-phase flow, interaction with multiple-fluid flow has difficulties in the realization of properties of different phases. After adding the multiple-fluid simulation, it is also important to keep haptic interaction real time. Our research is based on the mixture model. We guarantee the authenticity of multiple-fluid mixing effect while changing the drift velocity solver to improve efficiency. We employ a unified particle model to achieve rigid body–liquid coupling, and use FIR filter to smooth feedback force to the haptic device. Our novel multiple-fluid haptic simulation can provide an interactive experience for mixing liquid in virtual reality.     

流体动画模拟的一种新方法

近年来基于物理的流体模拟成为计算机动画领域中的一个极具有挑战性的问题,针对有限差分方法和有限元方法对流体动画模拟的局限性,利用光滑流体动力学方法实现了流体的动画模拟,该方法不依赖网格,适合于计算具有极大变形的流体计算,溃坝坍塌现象的模拟实验表明：方法既能模拟流体的整体演进特征,又能表现流体飞溅、破碎的现象,能够真实有效地模拟水流运动情况。     

一种骨架驱动的近岸涌浪动画合成方法

大面积水面及波浪的快速建模与可控动画一直是计算机图形学研究的热点问题之一,但是由于天然波浪的复杂性与不规则性,现有的波浪模拟方法无法在计算效率与真实感之间很好的权衡.本文针对此问题,以近岸涌浪为对象,研究波浪形态特征的表示与提取方法,快速生成可控的波浪动画.首先以波浪视频为数据源,利用数学形态学算法从水面视频图像中提取出涌浪骨架特征;然后根据此特征控制涌浪形状与高度,重用高度场数据生成可控的更加多样的近岸涌浪运动形态,克服了流体动画计算效率低下且难以交互控制的缺点.实验表明本文提出的方法能够以简单直观的控制方式,快速实现用户期望的变形效果.     

Distribution Update of Deformable Patches for Texture Synthesis on the Free Surface of Fluids

We propose an approach for temporally coherent patch‐based texture synthesis on the free surface of fluids. Our approach is applied as a post‐process, using the surface and velocity field from any fluid simulator. We apply the texture from the exemplar through multiple local mesh patches fitted to the surface and mapped to the exemplar. Our patches are constructed from the fluid free surface by taking a subsection of the free surface mesh. As such, they are initially very well adapted to the fluid's surface, and can later deform according to the free surface velocity field, allowing a greater ability to represent surface motion than rigid or 2D grid‐based patches. From one frame to the next, the patch centers and surrounding patch vertices are advected according to the velocity field. We seek to maintain a Poisson disk distribution of patches, and following advection, the Poisson disk criterion determines where to add new patches and which patches should e flagged for removal. The removal considers the local number of patches: in regions containing too many patches, we accelerate the temporal removal. This reduces the number of patches while still meeting the Poisson disk criterion. Reducing areas with too many patches speeds up the computation and avoids patch‐blending artifacts. The final step of our approach creates the overall texture in an atlas where each texel is computed from the patches using a contrast‐preserving blending function. Our tests show that the approach works well on free surfaces undergoing significant deformation and topological changes. Furthermore, we show that our approach provides good results for many fluid simulation scenarios, and with many texture exemplars. We also confirm that the optical flow from the resulting texture matches the fluid velocity field. Overall, our approach compares favorably against recent work in this area.     

Wake Synthesis For Shallow Water Equation

In fluid animation, wake is one of the most important phenomena usually seen when an object is moving relative to the flow. However, in current shallow water simulation for interactive applications, this effect is greatly smeared out. In this paper, we present a method to efficiently synthesize these wakes. We adopt a generalized SPH method for shallow water simulation and two way solid fluid coupling. In addition, a 2D discrete vortex method is used to capture the detailed wake motions behind an obstacle, enriching the motion of SWE simulation. Our method is highly efficient since only 2D simulation is required. Moreover, by using a physically inspired procedural approach for particle seeding, DVM particles are only created in the wake region. Therefore, very few particles are required while still generating realistic wake patterns. When coupled with SWE, we show that these patterns can be seen using our method with marginal overhead.     

The Lattice-boltzmann method for simulating gaseous phenomena

We present a physically-based, yet fast and simple method to simulate gaseous phenomena. In our approach, the incompressible Navier-Stokes (NS) equations governing fluid motion have been modeled in a novel way to achieve a realistic animation. We introduce the lattice Boltzmann model (LBM), which simulates the microscopic movement of fluid particles by linear and local rules on a grid of cells so that the macroscopic averaged properties obey the desired NS equations. The LBM is defined on a 2D or 3D discrete lattice, which is used to solve fluid animation based on different boundary conditions. The LBM simulation generates, in real-time, an accurate velocity field and can incorporate an optional temperature field to account for the buoyancy force of hot gas. Because of the linear and regular operations in each local cell of the LBM grid, we implement the computation in commodity texture hardware, further improving the simulation speed. Finally, textured splats are used to add small scale turbulent details, achieving high-quality real-time rendering. Our method can also simulate the physically correct action of stationary or mobile obstacles on gaseous phenomena in real-time, while still maintaining highly plausible visual details.     

Hybrid atomistic�Ccontinuum simulations of fluid flows involving interfaces

In this work, we use an hybrid atomistic–continuum (HAC) simulation method to study transient and steady isothermal flows of Lennard-Jones fluids near interfaces. Our hybrid method is based on a domain decomposition algorithm. The flow domain is composed of two overlapping regions: an atomistic region described by molecular dynamics, and a continuum region described by a finite volume discretization of the incompressible Navier–Stokes equations. To show the interest of such an hybrid method to compute flows near fluid/solid interface, we first applied our hybrid scheme to the classical Couette flow, where the moving wall is modelled at the atomistic scale. In addition, we also studied an oscillatory shear flow. Then, to compute flows near fluid/fluid interface, we applied our method to a two-phase Couette flow (liquid/gas), where the interface is modelled at the molecular scale. We show that hybrid results can sometimes differ from those provided by analytical solutions deduced from continuum mechanics equations combined with usual boundary/interface relations. For the Couette and oscillatory shear flows, a good agreement is found between hybrid simulations and macroscopic analytical solutions, however, we noticed that the fluid in contact with the wall can be more entailed than what expected. For the liquid/gas Couette flow, the hybrid simulation exhibits an unexpected jump of the velocity in the interfacial region, corresponding to a partial slip between the two fluid phases. Those interesting results highlight the interest of using an HAC method to deal with systems for which surfaces/interfaces effects are important.     

ANGULAR VELOCITY INTERPOLATION USING QUATERNION

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Detail-preserving fluid control

We propose a new fluid control technique that uses scale-dependent force control to preserve small-scale fluid detail. Control particles define local force fields and can be generated automatically from either a physical simulation or a sequence of target shapes. We use a multi-scale decomposition of the velocity field and apply control forces only to the coarse-scale components of the flow. Small-scale detail is thus preserved in a natural way avoiding the artificial viscosity often introduced by force-based control methods. We demonstrate the effectiveness of our method for both Lagrangian and Eulerian fluid simulation environments.     

Application of lattice Boltzmann method in free surface flow simulation of micro injection molding

The filling flow in micro injection molding was simulated by using the lattice Boltzmann method (LBM). A tracking algorithm for free surface to handle the complex interaction between gas and liquid phases in LBM was used for the free surface advancement. The temperature field in the filling flow is also analyzed by combining the thermal lattice Boltzmann model and the free surface method. To simulate the fluid flow of polymer melt with a high Prandtl number and high viscosity, a modified lattice Boltzmann scheme was adopted by introducing a free parameter in the thermal diffusion equation to overcome the restriction of the thermal relaxation time. The filling flow simulation of micro injection molding was successfully performed in the study.     

High-quality and interactive animations of 3D time-varying vector fields

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering