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体积映射流固交互的稳定性及细节提升方法

针对现有的光滑粒子流体动力学(SPH)流固交互方法中存在的稳定性以及流体细节表现不佳的问题,提出一种改进的体积映射流固交互方法.首先采用无散度SPH方法对流体进行建模,保证流体的不可压缩性;然后引入体积映射方法处理固体边界,以隐式函数的形式表示边界而无需使用粒子,解决粒子采样的固体表面不平滑的问题;再引入移动最小二乘法对固体边界上的压强进行插值,避免压强镜像带来的误差,提升体积映射方法中压强和压强梯度计算的精确性,提高系统的稳定性;最后引入粒子重采样方法进行流体表面细化,充分表现流体表面区域的不同粒子特征,增强流固交互后的流体细节,提高真实感.在斯坦福大学公开的基本三维模型上的实验结果表明,所提方法能够真实、稳定地表现不可压缩流体与固体的交互现象,处理多个静态或动态固体的复杂场景,并且能够有效地刻画流体细节.     

固体入水的边界压力处理及表面粒子位置的修正

基于传统光滑粒子流体动力学(SPH)方法的边界力法、虚粒子法或耦合力法处理固体入水时,流 体与固体交互界面的粒子密度不连续、压力不稳定、固体边界处会发生部分流体粒子穿透或分离等现象,而流 体表面因为受到力的作用,表面破碎后,液面较粗糙。针对上述问题,结合边界力和虚粒子的优点,对耦合力 法进行改进,处理运动固体边界,阻止流体粒子穿透固体边界;改进交互界面的压力计算方法,提高计算精度, 稳定交互界面压力场;对流体表面的粒子位置进行校正,提升流体表面自由流动液面边界的模拟效果。通过经 典的二维固体入水实验,对该方法进行了验证,实验结果表明,本文方法在流体粒子与固体粒子交互后,交互 界面压力稳定,界面分离清晰无穿透,表面流体粒子分布均匀,流场的运动真实自然。     

SPH 流固耦合模拟自适应采样固壁虚粒子边界处理方法

固壁虚粒子边界处理方法是流体模拟中一种主要边界处理方法,但其不能确保流 体粒子不穿透固体边界,并且计算量较大。为防止流体粒子穿透边界,在边界附近设置一个阻 尼区,阻尼区内的流体粒子被边界施加一个弹性力和一个和流体粒子运动速度方向相反的阻尼 力,使得边界附近流体粒子更加稳定。为减少计算量,提出两种边界粒子自适应采样法：一种 是依据边界周围粒子数目的不同,边界粒子自适应地采样质量不同的大小粒子;另一种是依据 边界周围粒子数目的不同,边界粒子自适应的采样不同层数的相同质量粒子。与传统的固体边 界粒子采样方法相比,该方法减少了边界粒子数目,加快了模拟速度,节省了计算机内存,基 于GPU 加速技术实现的三维流体模拟,能够进行实时交互。     

基于完全拉格朗日粒子方法的物理动画模拟

自然界中不同类型物体和行为的真实感模拟是物理动画的重要内容,但实现基于统一数值方法的模拟仍是研究难点。基于光滑粒子动力学方法和连续介质力学物理模型,提出一种基于完全拉格朗日粒子方法的物理动画模拟算法,模拟刚性物体、弹性物体和不可压缩流体的动力学行为。此外,结合固体表面粒子的自适应采样方案和相对贡献计算方案,提出一种稳定的固流交互算法。实验结果表明,该方法适合于虚拟环境中不同类型物体运动和交互的统一建模和模拟。     

基于SPH 的雨滴打击不规则边界的模拟方法

为实现对雨滴打击树枝等不规则边界过程的模拟,研究了流体粒子在网格表示的 固体边界处的受力情况,提出了一种不需要粒子采样的边界受力模拟方法。采用高斯积分法则 对网格模型的三角面片进行积分,并就此对固液边界的粒子的密度进行修正,以积分的方法对 固体边界处的压力、粘性力等参数进行计算,从而保证边界粒子受力的连续性。同时,还提出 了一种吸引力模型,用来控制粒子在沿着物体表面滑落时的运动。实验结果表明,该方法在模 拟水滴铺展、收缩、沿着边界流动等现象时达到了较为真实的效果。     

液固交互过程中固体破碎现象的实时模拟

提出一种适用于液固交互过程中的固体破碎模拟方法.针对传统液固交互边界处理算法复杂,难以实时模拟固体破碎的缺陷,本文基于SPH算法,提出对液体与固体使用统一的粒子表示,将预测校正方案应用于处理液固交互过程中固体之间的碰撞问题,从而将固体破碎过程简化为固体碎片边界粒子生成的过程,并使用形状匹配算法对固体碎片进行形状约束.实验结果证明,采用文中方法能够实时模拟出液固交互过程中,细节丰富的固体破碎现象,效果真实.     

改进的流体模拟固体边界处理算法

流体模拟是计算机图形学的一个重要研究分支,流体的固体边界处理一直是流体 模拟的研究重点,光滑粒子流体动力学(SPH)方法中的镜像粒子法是处理固体边界的一个重要方 法。镜像粒子法通过靠近边界的流体粒子在边界外动态生成对应的镜像粒子来处理固体边界问 题,但随着边界复杂程度的提高,传统的镜像粒子法生成镜像粒子的复杂度也随之提高,模拟 效率随之降低。为此,文章对镜像粒子法进行改进,提出一种新的镜像粒子场量求值方法,有 效地降低了复杂边界情况下生成镜像粒子的复杂度,且使靠近边界的流体粒子场量更加均匀。 仿真实验结果表明,随着流体模拟粒子数的增加以及边界复杂程度的提高,该方法比传统镜像 粒子法效率高的优势也更加明显。     

基于位置的流体实时交互仿真

针对基于光滑粒子动力学方法的流体交互仿真过程中效率低,交互细节不够真实等问题,提出了采用基于位置的流体来模拟刚体工具与流体的交互方法. 该方法在传统的光滑粒子动力学算法的基础上进行改进,以基于CUDA并行计算平台实时模拟交互过程,并结合力觉交互设备实时输出交互力. 实验结果表明仿真过程中的交互力符合预期,在保证流体模拟的精度的前提下验证了交互力的连续性以及稳定性.     

一种SPH流体仿真边界校正方法

使用光滑粒子流体动力学方法进行流体仿真,并提出一种边界校正方法。使用快速泊松盘采样算法对容器边界进行采样,生成边界粒子,对边界粒子质量进行差值估算,计算边界粒子对流体粒子的作用力,以此来仿真流体与边界的相互作用。该方法可避免穿刺、滞留等现象的发生。通过实验验证了该算法的正确性。     

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.     

A Geometrically Consistent Viscous Fluid Solver with Two‐Way Fluid‐Solid Coupling

We present a grid‐based fluid solver for simulating viscous materials and their interactions with solid objects. Our method formulates the implicit viscosity integration as a minimization problem with consistently estimated volume fractions to account for the sub‐grid details of free surfaces and solid boundaries. To handle the interplay between fluids and solid objects with viscosity forces, we also formulate the two‐way fluid‐solid coupling as a unified minimization problem based on the variational principle, which naturally enforces the boundary conditions. Our formulation leads to a symmetric positive definite linear system with a sparse matrix regardless of the monolithically coupled solid objects. Additionally, we present a position‐correction method using density constraints to enforce the uniform distributions of fluid particles and thus prevent the loss of fluid volumes. We demonstrate the effectiveness of our method in a wide range of viscous fluid scenarios.     

A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

     

An Efficient Hybrid Incompressible SPH Solver with Interface Handling for Boundary Conditions

We propose a hybrid smoothed particle hydrodynamics solver for efficientlysimulating incompressible fluids using an interface handling method for boundary conditions in the pressure Poisson equation. We blend particle density computed with one smooth and one spiky kernel to improve the robustness against both fluid–fluid and fluid–solid collisions. To further improve the robustness and efficiency, we present a new interface handling method consisting of two components: free surface handling for Dirichlet boundary conditions and solid boundary handling for Neumann boundary conditions. Our free surface handling appropriately determines particles for Dirichlet boundary conditions using Jacobi‐based pressure prediction while our solid boundary handling introduces a new term to ensure the solvability of the linear system. We demonstrate that our method outperforms the state‐of‐the‐art particle‐based fluid solvers.     

真实感固流交互动画的统一物质点法模拟

固流交互模拟是基于物理的流体模拟技术的重要研究内容,其中如何解决非穿透 和滑移接触是难点。为此,提出一种真实感固流交互动画的统一物质点法模拟方法。首先,给 出一种基于物质点法的快速微可压缩流体模拟方法,并在统一背景欧拉网格上对固体和流体动 量方程进行求解;其次,检测固流接触区域并在其上构建局部多重背景网格,给出一种动量守 恒保持的速度修正方法对固体和流体各自网格结点进行速度修正,从而实现固流交互的非穿透 和滑移接触效果模拟。实验结果表明,该方法可以模拟稳定、真实的固流交互动画,适用于计 算机图形学和虚拟现实领域中的真实感模拟应用。     

SPH simulation of selective withdrawal from microcavity

The selective withdrawal of weakly compressible fluids is investigated by smoothed particle hydrodynamics (SPH) with a revised model of surface tension. In our model problem, fluid is withdrawn from a two-dimensional microcavity through a narrow outlet above the interface of two immiscible fluids. The outflow boundary is implemented by a particular zone of fluid particles with prescribed velocity, together with the introduction of artificial boundary particles. Based on the average number density of fluid particles, the effective contribution of boundary particles is corrected for the compressible context. It is found that there exists a critical withdrawal rate for each initial interface height, beyond which the lower phase becomes entrained in a thin spout along with the upper phase. Besides, the Froude number with redefinition for this kind of multiphase flow could serve as a criterion of flow behavior. Furthermore, larger surface tension, smaller dynamical viscosity and density of the upper phase all lead to longer threshold time of formation of the spout state, and thus are favorable to the withdrawal of upper phase both in terms of higher efficiency and larger quantity.     

Lagrangian particle model for multiphase flows

A Lagrangian particle model for multiphase multicomponent fluid flow, based on smoothed particle hydrodynamics (SPH), was developed and used to simulate the flow of an emulsion consisting of bubbles of a non-wetting liquid surrounded by a wetting liquid. In SPH simulations, fluids are represented by sets of particles that are used as discretization points to solve the Navier-Stokes fluid dynamics equations. In the multiphase multicomponent SPH model, a modified van der Waals equation of state is used to close the system of flow equations. The combination of the momentum conservation equation with the van der Waals equation of state results in a particle equation of motion in which the total force acting on each particle consists of many-body repulsive and viscous forces, two-body (particle-particle) attractive forces, and body forces such as gravitational forces. Similar to molecular dynamics, for a given fluid component the combination of repulsive and attractive forces causes phase separation. The surface tension at liquid-liquid interfaces is imposed through component dependent attractive forces. The wetting behavior of the fluids is controlled by phase dependent attractive interactions between the fluid particles and stationary particles that represent the solid phase. The dynamics of fluids away from the interface is governed by purely hydrodynamic forces. Comparison with analytical solutions for static conditions and relatively simple flows demonstrates the accuracy of the SPH model.