Realistic and stable simulation of turbulent details behind objects in smoothed‐particle hydrodynamics fluids

This paper presents a novel realistic and stable turbulence synthesis method to simulate the turbulent details generated behind objects in smoothed particle hydrodynamics (SPH) fluids. Firstly, by approximating the boundary layer theory on the fly in SPH fluids, we propose a vorticity production model to identify which fluid particles shed from object surfaces and which are seeded as vortex particles. Then, we employ an SPH‐like summation interpolant formulation of the Biot–Savart law to calculate the fluctuating velocities stemming from the generated vorticity field. Finally, the stable evolution of the vorticity field is achieved by combining an implicit vorticity diffusion technique and an artificial dissipation term. Moreover, in order to efficiently catch turbulent details for rendering, we propose an octree‐based adaptive surface reconstruction method for particle‐based fluids. The experiment results demonstrate that our turbulence synthesis method provides an effect way to model the obstacle‐induced turbulent details in SPH fluids and can be easily added to existing particle‐based fluid–solid coupling pipelines. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Procedural Synthesis using Vortex Particle Method for Fluid Simulation

We propose a fast and effective technique to improve sub‐grid visual details of the grid based fluid simulation. Our method procedurally synthesizes the flow fields coming from the incompressible Navier‐Stokes solver and the vorticity fields generated by vortex particle method for sub‐grid turbulence. We are able to efficiently animate smoke which is highly turbulent and swirling with small scale details. Since this technique does not solve the linear system in high‐resolution grids, it can perform fluid simulation more rapidly. We can easily estimate the influence of turbulent and swirling effect to the fluid flow.     

Creating and Preserving Vortical Details in SPH Fluid

We present a new method to create and preserve the turbulent details generated around moving objects in SPH fluid. In our approach, a high‐resolution overlapping grid is bounded to each object and translates with the object. The turbulence formation is modeled by resolving the local flow around objects using a hybrid SPH‐FLIP method. Then these vortical details are carried on SPH particles flowing through the local region and preserved in the global field in a synthetic way. Our method provides a physically plausible way to model the turbulent details around both rigid and deformable objects in SPH fluid, and can efficiently produce animations of complex gaseous phenomena with rich visual details.     

CPU与GPU并行计算的火焰模拟

采用基于粒子插值的SPH方法对火焰流体进行模拟,用GPU加速粒子状态地计算,同时用CPU并行地计算粒子邻接关系并控制粒子产生速率。在SPH模型中,较为高效地加入了漩涡场的计算,增加了粒子运动的细节。在粒子渲染过程中,采用了色度场、有向点扩散和颜色锐化技术,由离散的粒子空间分布得到了较为理想的连续火焰图像。由于该方法属于流体模拟的拉格朗日法,所以火焰具有物理真实性,又由于采用GPU为主CPU为辅的计算架构,使得模拟达到了实时。     

Incorporating stochastic turbulence in particle-based fluid simulation

We propose a new fluid modeling technique aimed at incorporating stochastic turbulence into a widely used Lagrangian fluid solver, the Smoothed Particle Hydrodynamics (SPH) method. We add to each SPH particle a swirling probability to model its likelihood to act as a swirling incentive particle (SIP). Particles are selected as a SIP randomly based on the probability, and a SIP spins its neighboring particles to rotate around itself by applying rotational force. The force is computed from a swirling vorticity of the SIP. We model the production, development, and spreading of the swirling probability and vorticity among all SPH particles. The algorithm inherently implements preferred turbulence evolution including vortex aggregation and decay. The turbulent effects are non-repeating and easily controlled by animators. Our method is fully integrated with the SPH scheme with minimal extra memory usage, computational load, and programming efforts.     

SPH fluid control with self‐adaptive turbulent details

Smoothed particle hydrodynamics (SPH)‐based fluid control is often involved in fluid animation. Because most of the existing SPH fluid control methods employ the strategy of control force to control fluid particles, the artificial viscosity introduced by control force would lead to the loss of fine‐scale details. Although the introduction of the low‐pass filter can add details, it may easily destroy the target shape. To remedy the previous problems, we sample the control particles with curvature information to represent the shape complexity. Because of the shape's complexity, we suppress the generation of turbulence in the high‐curvature areas and promote turbulence in the low‐curvature regions. Our self‐adaptive way to randomly generate turbulence can effectively prevent the lack of fluid dynamics caused by the artificial viscosity. Our new method can improve the visual quality of the fluid animation, and the shape control result is consistent to the target shape. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

An Efficient Boundary Handling with a Modified Density Calculation for SPH

We propose a new boundary handling method for smoothed particle hydrodynamics (SPH). Previous approaches required the use of boundary particles to prevent particles from sticking to the boundary. We address this issue by correcting the fundamental equations of SPH with the integration of a kernel function. Our approach is able to directly handle triangle mesh boundaries without the need for boundary particles. We also show how our approach can be integrated into a position‐based fluid framework.     

Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement

Capturing fine details of turbulence on a coarse grid is one of the main tasks in real‐time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined second vorticity confinement method, referred to as robust second vorticity confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second vorticity confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high‐resolution flow fields. As shown in our results, this approach produces stable high‐resolution turbulence very efficiently.     

Effects of Chemical Reaction on Two-Dimensional Turbulence

Direct numerical simulations of compressible two-dimensional homogeneous turbulent reacting flows are conducted to investigate the interactions between turbulence and chemical reaction. Both isothermal and exothermic nonpremixed reactions are considered. In isothermal reacting simulations, the turbulence is not affected by the reaction and is characterized by the large scale coherent vortices and vorticity-gradient sheet structures. The spatial structures of the density and temperature fields are similar to that of vorticity. However, mixing and reaction occur in the layer like (lamellar) structures which are mainly formed in the hyperbolic flow regions, where the vorticily-gradient sheets are present and the turbulent stretching dominates the circulation. Analysis of the simulations with exothermic reactions indicates that the heat of reaction has significant influence on thc spatial and the compositional structure of velocity, scalar and thermodynamic variables. The fluctuations of the density, the temperature, the pressure and the dilatation are substantially increased due to nonuniform heat release. The heat of reaction also modifies the small scale solenoidal velocity field. At early times, when the reaction is significant, the magnitude of the vorticity (enstrophy) is enhanced by the baroclinic vorticity generation. At late times, when the reaction is almost completed, the molecular dissipation is dominant and the magnitude of vorticity decays continuously. Examination of the energy transfer among the rotational and the compressive components of the kinetic energy and the internal energy indicates that the energy of reaction is transfered to the compressive component of the kinetic energy by the pressure-dilatation correlations. The turbulent advection then transfer the energy from the compressive component of the kinetic energy to its rotational component.     

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。     

A novel method for modeling Neumann and Robin boundary conditions in smoothed particle hydrodynamics

We present a novel smoothed particle hydrodynamics (SPH) method for diffusion equations subject to Neumann and Robin boundary conditions. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to implement in numerical methods when the boundary geometry is complex. The new method presented here is based on the approximation of the sharp boundary with a diffuse interface and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method. The paper discusses the details of the method and the criteria for the width of the diffuse interface. The method is used to simulate diffusion and reactions in a domain bounded by two concentric circles and reactive flow between two parallel plates and its accuracy is demonstrated through comparison with analytical and finite difference solutions. To further illustrate the capabilities of the model, a reactive flow in a porous medium was simulated and good convergence properties of the model are demonstrated.     

Smoothed particle hydrodynamics: Applications to heat conduction

In this paper, we modify the numerical steps involved in a smoothed particle hydrodynamics (SPH) simulation. Specifically, the second order partial differential equation (PDE) is decomposed into two first order PDEs. Using the ghost particle method, consistent estimation of near-boundary corrections for system variables is also accomplished. Here, we focus on SPH equations for heat conduction to verify our numerical scheme. Each particle carries a physical entity (here, this entity is temperature) and transfers it to neighboring particles, thus exhibiting the mesh-less nature of the SPH framework, which is potentially applicable to complex geometries and nanoscale heat transfer. We demonstrate here only 1D and 2D simulations because 3D codes are as simple to generate as 1D codes in the SPH framework. Our methodology can be extended to systems where the governing equations are described by PDEs.     

One-information suboptimal control repercussion on the fine structure of wall turbulence

The suboptimal control with the cost function directly connected to the wall shear and introduced for a while has been revisited through direct numerical simulations of high temporal and spatial resolution. Its effect on the fine structure of the wall turbulence has been analyzed in details, essentially through the spanwise vorticity transport mechanism. It is shown that only half of the viscous sublayer is mainly affected by the control. The actuation efficiency is limited in terms of the wall shear stress reduction, but is high as long as the turbulent wall activity is concerned. The wall shear stress is reduced due both to the reduction of the shear production in the viscous sublayer and to the contribution of the turbulent body force. The dissipation involving in the streamwise vorticity fluctuations transport equation increases significantly and overcomes the production in a thin layer near the wall leading to a drastic diminution of the turbulent wall shear stress fluctuations.     

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.     

A Physically Consistent Implicit Viscosity Solver for SPH Fluids

In this paper, we present a novel physically consistent implicit solver for the simulation of highly viscous fluids using the Smoothed Particle Hydrodynamics (SPH) formalism. Our method is the result of a theoretical and practical in‐depth analysis of the most recent implicit SPH solvers for viscous materials. Based on our findings, we developed a list of requirements that are vital to produce a realistic motion of a viscous fluid. These essential requirements include momentum conservation, a physically meaningful behavior under temporal and spatial refinement, the absence of ghost forces induced by spurious viscosities and the ability to reproduce complex physical effects that can be observed in nature. On the basis of several theoretical analyses, quantitative academic comparisons and complex visual experiments we show that none of the recent approaches is able to satisfy all requirements. In contrast, our proposed method meets all demands and therefore produces realistic animations in highly complex scenarios. We demonstrate that our solver outperforms former approaches in terms of physical accuracy and memory consumption while it is comparable in terms of computational performance. In addition to the implicit viscosity solver, we present a method to simulate melting objects. Therefore, we generalize the viscosity model to a spatially varying viscosity field and provide an SPH discretization of the heat equation.     

Wastewater treatment modelling with smoothed particle hydrodynamics

In this paper a novel hydrodynamic wastewater treatment (WWT) model based on smoothed particle hydrodynamics (SPH) is presented. The hydraulics of the wastewater treatment plant is modelled in detail with SPH. The SPH solver is coupled to the activated sludge model such that the influence on biokinetic processes is described. The key innovation of the present WWT model is that both the biokinetics and the wastewater hydraulics are simultaneously solved for non-steady flows. After validating the present method against the software ASIM 5, the capabilities are demonstrated for a full-scale treatment plant simulation. We investigate the stirrer and aeration induced mixing within the reactor compartments as well as the resulting concentrations of the biokinetic compounds. Following the establishment of a local coupling between the hydraulics and the biokinetics, the biokinetic concentrations within a treatment plant can be spatially resolved with a high resolution.     

Coherent structure formation,phase correlations,and finite-size effects in 2D turbulence

General conditions for the formation of long-lived coherent vortices in decaying and force-driven 2-D turbulence are investigated. It is shown by a series of numerical simulations that the emergence of closed streamlines leading to the trapped trajectories of vorticity is a necessary, but not sufficient condition for this phenomenon, so that these trapped trajectories may be considered only as seed vortices. Numerical experiments which demonstrate the relations between phase correlations, finite-size effects, and the formation of coherent vortices in 2-D decaying turbulence are presented. It is shown that there is a universal dimensionless time for the onset of intermittency in the flow which corresponds to the time of establishment of phase correlations. The stricter conditions for appearance of coherent vortices in forced turbulence in comparison with decaying turbulence are associated with phase mixing introduced by random forcing. The universal features of decaying turbulence are discussed in terms of phase portraits based on inviscid constants of motion and their decay rates.