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.     

Implicit Integration for Particle‐based Simulation of Elasto‐Plastic Solids

We present a novel particle‐based method for stable simulation of elasto‐plastic materials. The main contribution of our method is an implicit numerical integrator, using a physically‐based model, for computing particles that undergo both elastic and plastic deformations. The main advantage of our implicit integrator is that it allows the use of large time steps while still preserving stable and physically plausible simulation results. As a key component of our algorithm, at each time step we compute the particle positions and velocities based on a sparse linear system, which we solve efficiently on the graphics hardware. Compared to existing techniques, our method allows for a much wider range of stiffness and plasticity settings. In addition, our method can significantly reduce the computation cost for certain range of material types. We demonstrate fast and stable simulations for a variety of elasto‐plastic materials, ranging from highly stiffelastic materials to highly plastic ones.     

Hybrid particle–grid fluid animation with enhanced details

Simulating large-scale fluid while retaining and rendering details still remains to be a difficult task in spite of rapid advancements of computer graphics during the last two decades. Grid-based methods can be easily extended to handle large-scale fluid, yet they are unable to preserve sub-grid surface details like spray and foam without multi-level grid refinement. On the other hand, the particle-based methods model details naturally, but at the expense of increasing particle densities. This paper proposes a hybrid particle–grid coupling method to simulate fluid with finer details. The interaction between particles and fluid grids occurs in the vicinity of “coupling band” where multiple particle level sets are introduced simultaneously. First, fluids free of interaction could be modeled by grids and SPH particles independently after initialization. A coupling band inside and near the interface is then identified where the grids interact with the particles. Second, the grids inside and far away from the interface are adaptively sampled for large-scale simulation. Third, the SPH particles outside the coupling band are enhanced by diffuse particles which render little computational cost to simulate spray, foam, and bubbles. A distance function is continuously updated to adaptively coarsen or refine the grids near the coupling band and provides the coupling weights for the two-way coupling between grids and particles. One characteristic of our hybrid approach is that the two-way coupling between these particles of spray and foam and the grids of fluid volume can retain details with little extra computational cost. Our rendering results realistically exhibit fluids with enhanced details like spray, foam, and bubbles. We make comprehensive comparisons with existing works to demonstrate the effectiveness of our new method.     

Two-way coupled SPH and particle level set fluid simulation

Grid-based methods have difficulty resolving features on or below the scale of the underlying grid. Although adaptive methods (e.g. RLE, octrees) can alleviate this to some degree, separate techniques are still required for simulating small-scale phenomena such as spray and foam, especially since these more diffuse materials typically behave quite differently than their denser counterparts. In this paper, we propose a two-way coupled simulation framework that uses the particle level set method to efficiently model dense liquid volumes and a smoothed particle hydrodynamics (SPH) method to simulate diffuse regions such as sprays. Our novel SPH method allows us to simulate both dense and diffuse water volumes, fully incorporates the particles that are automatically generated by the particle level set method in under-resolved regions, and allows for two way mixing between dense SPH volumes and grid-based liquid representations.     

A novel method for modeling of complex wall geometries in smoothed particle hydrodynamics

Smoothed particle hydrodynamics (SPH) has become increasingly important during recent decades. Its meshless nature, inherent representation of convective transport and ability to simulate free surface flows make SPH particularly promising with regard to simulations of industrial mixing devices for high-viscous fluids, which often have complex rotating geometries and partially filled regions (e.g., twin-screw extruders). However, incorporating the required geometries remains a challenge in SPH since the most obvious and most common ways to model solid walls are based on particles (i.e., boundary particles and ghost particles), which leads to complications with arbitrarily-curved wall surfaces. To overcome this problem, we developed a systematic method for determining an adequate interaction between SPH particles and a continuous wall surface based on the underlying SPH equations. We tested our new approach by using the open-source particle simulator “LIGGGHTS” and comparing the velocity profiles to analytical solutions and SPH simulations with boundary particles. Finally, we followed the evolution of a tracer in a twin-cam mixer during the rotation, which was experimentally and numerically studied by several other authors, and ascertained good agreement with our results. This supports the validity of our newly-developed wall interaction method, which constitutes a step forward in SPH simulations of complex geometries.     

Efficient high-quality volume rendering of SPH data

High quality volume rendering of SPH data requires a complex order-dependent resampling of particle quantities along the view rays. In this paper we present an efficient approach to perform this task using a novel view-space discretization of the simulation domain. Our method draws upon recent work on GPU-based particle voxelization for the efficient resampling of particles into uniform grids. We propose a new technique that leverages a perspective grid to adaptively discretize the view-volume, giving rise to a continuous level-of-detail sampling structure and reducing memory requirements compared to a uniform grid. In combination with a level-of-detail representation of the particle set, the perspective grid allows effectively reducing the amount of primitives to be processed at run-time. We demonstrate the quality and performance of our method for the rendering of fluid and gas dynamics SPH simulations consisting of many millions of particles.     

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.     

A splitting integration scheme for the SPH simulation of concentrated particle suspensions

Simulating nearly contacting solid particles in suspension is a challenging task due to the diverging behavior of short-range lubrication forces, which pose a serious time-step limitation for explicit integration schemes. This general difficulty limits severely the total duration of simulations of concentrated suspensions. Inspired by the ideas developed in [S. Litvinov, M. Ellero, X.Y. Hu, N.A. Adams, J. Comput. Phys. 229 (2010) 5457–5464] for the simulation of highly dissipative fluids, we propose in this work a splitting integration scheme for the direct simulation of solid particles suspended in a Newtonian liquid. The scheme separates the contributions of different forces acting on the solid particles. In particular, intermediate- and long-range multi-body hydrodynamic forces, which are computed from the discretization of the Navier–Stokes equations using the smoothed particle hydrodynamics (SPH) method, are taken into account using an explicit integration; for short-range lubrication forces, velocities of pairwise interacting solid particles are updated implicitly by sweeping over all the neighboring pairs iteratively, until convergence in the solution is obtained. By using the splitting integration, simulations can be run stably and efficiently up to very large solid particle concentrations. Moreover, the proposed scheme is not limited to the SPH method presented here, but can be easily applied to other simulation techniques employed for particulate suspensions.     

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。     

基于ARM SVE的光滑粒子流体动力学SIMD加速方法

光滑粒子流体动力学（SPH）是近年来兴起的一种无网格的粒子方法,SPH在处理大变形、运动物质表面以及自由表面等问题时优势明显,在数值模拟领域得到了非常广泛的应用,是一种典型的科学计算应用。作为一种显式的粒子方法,SPH在每一个迭代步都需要计算大量的粒子间相互作用,计算量非常大,如何提高SPH的计算效率成为研究热点。可伸缩矢量扩展（SVE）是ARM针对高性能计算推出的下一代SIMD指令集,基于SVE研究了SPH方法的SIMD加速方法,取得了显著的加速效果。     

Fast SPH simulation for gaseous fluids

This paper presents a fast smoothed particle hydro-dynamics (SPH) simulation approach for gaseous fluids. Unlike previous SPH gas simulators, which solve the transparent air flow in a fixed simulation domain, the proposed approach directly solves the visible gas without involving the transparent air. By compensating the density and force calculation for the visible gas particles, we completely avoid the need of computational cost on ambient air particles in previous approaches. This allows the computational resources to be exclusively focused on the visible gas, leading to significant performance improvement of SPH gas simulation. The proposed approach is at least ten times faster than the standard SPH gas simulation strategy and is able to reduce the total particle number by 25–400 times in large open scenes. The proposed approach also enables fast SPH simulation of complex scenes involving liquid–gas transition, such as boiling and evaporation. A particle splitting and merging scheme is proposed to handle the degraded resolution in liquid–gas phase transition. Various examples are provided to demonstrate the effectiveness and efficiency of the proposed approach.     

An Optimization-based SPH Solver for Simulation of Hyperelastic Solids

This paper proposes a novel method for simulating hyperelastic solids with Smoothed Particle Hydrodynamics (SPH). The proposed method extends the coverage of the state-of-the-art elastic SPH solid method to include different types of hyperelastic materials, such as the Neo-Hookean and the St. Venant-Kirchoff models. To this end, we reformulate an implicit integration scheme for SPH elastic solids into an optimization problem and solve the problem using a general-purpose quasi-Newton method. Our experiments show that the Limited-memory BFGS (L-BFGS) algorithm can be employed to efficiently solve our optimization problem in the SPH framework and demonstrate its stable and efficient simulations for complex materials in the SPH framework. Thanks to the nature of our unified representation for both solids and fluids, the SPH formulation simplifies coupling between different materials and handling collisions.     

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

In many scientific disciplines, the motion of finite‐sized objects in fluid flows plays an important role, such as in brownout engineering, sediment transport, oceanology or meteorology. These finite‐sized objects are called inertial particles and, in contrast to traditional tracer particles, their motion depends on their current position, their own particle velocity, the time and their size. Thus, the visualization of their motion becomes a high‐dimensional problem that entails computational and perceptual challenges. So far, no visualization explored and visualized the particle trajectories under variation of all seeding parameters. In this paper, we propose three coordinated views that visualize the different aspects of the high‐dimensional space in which the particles live. We visualize the evolution of particles over time, showing that particles travel different distances in the same time, depending on their size. The second view provides a clear illustration of the trajectories of different particle sizes and allows the user to easily identify differences due to particle size. Finally, we embed the trajectories in the space‐velocity domain and visualize their distance to an attracting manifold using ribbons. In all views, we support interactive linking and brushing, and provide abstraction through density volumes that are shown by direct volume rendering and isosurface slabs. Using our method, users gain deeper insights into the dynamics of inertial particles in 2D fluids, including size‐dependent separation, preferential clustering and attraction. We demonstrate the effectiveness of our method in multiple steady and unsteady 2D flows.     

Interaction of flexible multibody systems with fluids analyzed by means of smoothed particle hydrodynamics

The present work deals with a computational approach to fluid-structure interaction (FSI) problems by coupling of flexible multibody system dynamics and fluid dynamics. Since the methods for the numerical modeling are well known, both for the structural and the fluid part, the focus of this work lies on the coupling formalism. Moreover, the applicability of the presented approach to arbitrary geometries and high structural stiffness is studied, as well as an easy model setup. No restriction should be made on the topology of the structure or the complexity of motion.For the fluid part a meshless method, known as smoothed particle hydrodynamics (SPH) is applied, which fulfills the above requirements. While an explicit time integration scheme in SPH provides a fast simulation of the fluid dynamics, advanced methods from flexible multibody dynamics provide a variety of benefits for the simulation of the solid part. Amongst these are specialized structural finite elements for both small and large deformation bodies, joints, stable implicit time-integration schemes, and model reduction techniques.A rule for the interaction between fluids and structures is derived from imposing a distributed potential over boundary segments of the structures, which the fluid particles respond to. The work is concluded by illustrative examples, demonstrating the successful coupling of flexible multibody systems with fluids.     

Dynamically Enriched MPM for Invertible Elasticity

We extend the material point method (MPM) for robust simulation of extremely large elastic deformation. This facilitates the application of MPM towards a unified solver since its versatility has been demonstrated lately with simulation of varied materials. Extending MPM for invertible elasticity requires accounting for several of its inherent limitations. MPM as a meshless method exhibits numerical fracture in large tensile deformations. We eliminate it by augmenting particles with connected material domains. Besides, constant redefinition of the interpolating functions between particles and grid introduces accumulated error which behaves like artificial plasticity. We address this problem by utilizing the Lagrangian particle domains as enriched degrees of freedom for simulation. The enrichment is applied dynamically during simulation via an error metric based on local deformation of particles. Lastly, we novelly reformulate the computation in reference configuration and investigate inversion handling techniques to ensure the robustness of our method in regime of degenerated configurations. The power and robustness of our method are demonstrated with various simulations that involve extreme deformations.     

Hybrid Simulation of Miscible Mixing with Viscous Fingering

By modeling mass transfer phenomena, we simulate solids and liquids dissolving or changing to other substances. We also deal with the very small‐scale phenomena that occur when a fluid spreads out at the interface of another fluid. We model the pressure at the interfaces between fluids with Darcy's Law and represent the viscous fingering phenomenon in which a fluid interface spreads out with a fractal‐like shape. We use hybrid grid‐based simulation and smoothed particle hydrodynamics (SPH) to simulate intermolecular diffusion and attraction using particles at a computable scale. We have produced animations showing fluids mixing and objects dissolving.     

Coupling of rigid body dynamics and moving particle semi-implicit method for simulating isothermal multi-phase fluid interactions

The moving particle semi-implicit (MPS) method does not require grids for simulating fluid motions. Therefore, the MPS method can easily handle a large deformation of fluid. However, the MPS method has some difficulties in simulating transfer of momentum caused by a physical collision between different fluids because fluid particles have no mass or volume and only have weights for interacting with other particles. To overcome this inherent defect of the MPS method, rigid body dynamics is explicitly coupled with the MPS method in this study. In the first step, the MPS calculation is performed with particles which are considered to have no mass or volume. In the second step, rigid body dynamics comes into the calculation and considers the particles to have a slightly lesser diameter than the initial distance between particles. Then, physical contacts between particles are simulated with the dynamic energy conserved while the incompressibility of fluids is effectively maintained. In the single fluid region, the coupled method deals with the behavior of the particles. For the interface of the different fluids, only rigid body dynamics is used to simulate the transfer of the momentum caused by physical collisions of fluids. Through this coupling of rigid body dynamics and the MPS method, the overall stability related with the incompressibility of a fluid is comparatively increased in the single-phase fluid simulation. For the calculation of the multi-phase fluids behavior, fluids interactions can be easily treated with improving stability of the MPS calculation. In this study, collapse of water column and the isothermal fuel–coolant interaction (FCI), in which a water jet is directed into a denser fluid pool, were simulated to validate the coupling method of the MPS method and rigid body dynamics.     

GPU‐assisted real‐time coupling of blood flow and vessel wall

The vessel wall and the blood flow interact and influence each other, and real‐time coupling between them is of great importance to the virtual surgery as well as the research and diagnosis of vascular disease. On the basis of smoothed particle hydrodynamics (SPH), we present a new approach to solve non‐Newtonian viscous force of blood and a parallel mixed particles‐based coupling method for blood flow and vessel wall. Meanwhile, we also design a proxy particle‐based vessel wall force visualization method. Our method is as follows. Firstly, we solve the non‐Newtonian viscous forces of blood through the SPH method to discretize the Casson equation. Secondly, in each time step, we combine blood particles and sampling proxy particles on the blood vessel wall to form mixed particles and calculate the interaction forces through the SPH method between every pair of the neighboring mixed particles inside the graphics processing unit. Thirdly, the forces of the proxy particles will be mapped to the color display of the proxy particle. Experimental results demonstrate that our method is able to implement real‐time sizeable coupling of blood flow and vessel wall while mainly ensuring physical authenticity and it can also provide real‐time and obvious information about vessel wall force distribution. Copyright © 2015 John Wiley & Sons, Ltd.     

Temporal Blending for Adaptive SPH

In this paper, we introduce a fast and consistent smoothed particle hydrodynamics (SPH) technique which is suitable for convection–diffusion simulations of incompressible fluids. We apply our temporal blending technique to reduce the number of particles in the simulation while smoothly changing quantity fields. Our approach greatly reduces the error introduced in the pressure term when changing particle configurations. Compared to other methods, this enables larger integration time‐steps in the transition phase. Our implementation is fully GPU‐based to take advantage of the parallel nature of particle simulations.     

A SPH-based particle model for computational microrheology

In this article we present a particle method based on smoothed particle hydrodynamics for microrheology simulations of polymeric fluids. The viscoelasticity of the solvent is modelled via a standard Oldroyd-B model and thermal fluctuations, inherently present at the microscopic scale, are incorporated into the particle framework by application of the GENERIC formalism, ensuring the strict fulfilment of the Fluctuation?CDissipation theorem at the discrete level. Rigid structures of arbitrary shape suspended in the viscoelastic solvent are modelled by freezing SPH particles within a given solid domain and letting them interact with the solvent particles. The rheological properties of the Oldroyd-B fluid, namely frequency-dependent storage and loss moduli, are extracted via macroscopic deterministic simulations under small amplitude oscillatory (SAOS) flow and, alternatively, through standard microrheological simulations of a probe particle suspended in the same Brownian viscoelastic medium, by assuming the validity of a generalized Stokes?CEinstein relation (GSER). We check that good agreement with the analytical theory for the Oldroyd-B model is found in the deterministic SAOS flow over the entire regime of frequencies investigated. Concerning the microrheological measurements, good agreement is observed only up to a maximal frequencies corresponding to time scales considerably larger than the viscous time of the probe particle where the diffusive regime is fully established. At larger investigated frequencies, a crossover between diffusive and ballistic behaviour for the MSD of the probe is observed and validity of the GSER is questionable. The model presented here provides an optimal computational framework to complement experimental observations and to analyse quantitatively the basic assumptions involved in the theory of microrheology.