Smoothed Particle Hydrodynamics Fluid Research Articles

Smoothed particle hydrodynamics simulations of microstructure induced stress overshoot in structured fluids

Stress overshoot/undershoot is an important phenomenon in structured fluids undergoing dynamic and transient flow. To accurately capture the flow process, it is important to have a better understanding of and include in the numerical modeling the microstructure evolution that leads to the stress overshoot/undershoot phenomenon. We present a procedure for incorporating a microstructure model into a Lagrangian framework based on the smoothed particle hydrodynamics fluid solver. The numerical simulation is performed for a typical structured fluid under an applied strain rate history flow. Good agreement between the numerical results and the experimental data lends credence to and validates the proposed procedure for simulations of complex mixture flows. Additionally, the interaction between a flow of structured fluid and a circular cylinder placed in a channel is investigated. The viscous force is found to overshoot together with the applied gradient pressure and decrease over time as the fluid approaches the equilibrium state.

An algorithm to couple smoothed particle hydrodynamics and finite element method for fluid–structure interaction problems

An algorithm for coupling the smoothed particle hydrodynamics (SPH) method and the finite element method (FEM) is proposed for fluid–structure interaction (FSI) problems. The SPH module solves the fluid motion, and the FEM module describes the deformation of structures. In the algorithm, a structure is considered as a solid boundary in the SPH module and dealt with using the dynamic boundary condition. Only three layers of SPH boundary particles are set to represent the structure surface, and the interaction forces between the SPH boundary and fluid particles, including the water pressure and the viscous shear stress, are quantified in a same way as the inter-fluid particle forces. Further, the computed forces on the SPH boundary particles exerted by the fluid are redistributed to the structure FEM nodes based on a well-defined projection scheme. In the FEM module, the deformation and motion of the structure under the exerted fluid forces are solved, and accordingly, the position and velocity of the SPH boundary particles are updated by interpolation from the new properties at the FEM nodes. The proposed SPH-FEM coupled model is validated in three FSI benchmarks. For the deformation of an elastic plate under hydrostatic water pressure, the relative difference between the computed and the analytical maximum vertical displacement at the plate midpoint is about 1.5%. For the deformation of an elastic gate subjected to a time-varying dam-break flow, the relative root mean squared errors in the computed vertical and horizontal displacement of the gate are, respectively, 5.5% and 2.2%. It is demonstrated that the proposed model performs well in simulating the deformation of structures under both hydrostatic water pressure and dynamic impacts of dam-break flows.

Modeling Solids in Nuclear Astrophysics with Smoothed Particle Hydrodynamics

Smoothed particle hydrodynamics (SPH) is a frequently applied tool in computational astrophysics to solve the fluid dynamics equations governing the systems under study. For some problems, for example when involving asteroids and asteroid impacts, the additional inclusion of material strength is necessary in order to accurately describe the dynamics. In compact stars, that is white dwarfs and neutron stars, solid components are also present. Neutron stars have a solid crust, which is the strongest material known in nature. However, their dynamical evolution, when modeled via SPH or other computational fluid dynamics codes, is usually described as a purely fluid dynamics problem. Here, we present the first 3D simulations of neutron star crustal toroidal oscillations including material strength with the Los Alamos National Laboratory SPH code FleCSPH. In the first half of the paper, we present the numerical implementation of solid material modeling together with standard tests. The second half is on the simulation of crustal oscillations in the fundamental toroidal mode. Here, we dedicate a large fraction of the paper to approaches that can suppress numerical noise in the solid. If not minimized, the latter can dominate the crustal motion in the simulations.

Evaluation of particle‐based smoothed particle hydrodynamics boundary handling approaches in computer animation

AbstractBoundary handling is an important aspect of fluid simulation, and several boundary handling approaches exist in smoothed particle hydrodynamics (SPH), which have individual strengths and weaknesses. However, comparing different boundary handling approaches is challenging as there is no common basis for evaluations, that is, no universal set of experiments with quantitative evaluation across different methods, especially within computer animation where many evaluations rely mainly on visual perception. This article proposes a set of experiments to aid the evaluation of the main categories of fluid‐boundary interactions that are important in computer animation, that is, no motion (resting) fluid, tangential and normal motion of a fluid with respect to the boundary, and a fluid impacting a corner. We propose ten experiments, comprising experimental setup and quantitative evaluation with optional visual inspections, that are arranged in four groups which focus on one of the main category of fluid‐boundary interactions. We use these experiments to evaluate three particle‐based boundary handling methods, that is, pressure mirroring, pressure boundaries, and moving least squares pressure extrapolation, in combination with two incompressible SPH fluid simulation methods, namely IISPH and DFSPH, to establish a quantifiable relation between different combinations of boundary handling with simulation approaches and the main categories of fluid‐boundary interactions. Finally, we summarize all results in a rating table and show how our experiments can be used to determine the promising method for specific requirements regarding a given constellation of fluid‐boundary interaction.

An efficient non-iterative smoothed particle hydrodynamics fluid simulation method with variable smoothing length

In classical smoothed particle hydrodynamics (SPH) fluid simulation approaches, the smoothing length of Lagrangian particles is typically constant. One major disadvantage is the lack of adaptiveness, which may compromise accuracy in fluid regions such as splashes and surfaces. Attempts to address this problem used variable smoothing lengths. Yet the existing methods are computationally complex and non-efficient, because the smoothing length is typically calculated using iterative optimization. Here, we propose an efficient non-iterative SPH fluid simulation method with variable smoothing length (VSLSPH). VSLSPH correlates the smoothing length to the density change, and adaptively adjusts the smoothing length of particles with high accuracy and low computational cost, enabling large time steps. Our experimental results demonstrate the advantages of the VSLSPH approach in terms of its simulation accuracy and efficiency.

Spatial adaptivity with boundary refinement for smoothed particle hydrodynamics fluid simulation

AbstractFluid simulation is well‐known for being visually stunning while computationally expensive. Spatial adaptivity can effectively ease the computational cost by discretizing the simulation space with varying resolutions. Adaptive methods nowadays mainly focus on the mechanism of refining the fluid surfaces to obtain more vivid splashes and wave effects. But such techniques hinder further performance gain under the condition where most of the vast fluid surface is tranquil. Moreover, energetic flow beneath the surface cannot be adequately captured with the interior of the fluid still being simulated under coarse discretization. This article proposes a novel boundary‐distance based adaptive method for smoothed particle hydrodynamics fluid simulation. The signed‐distance field constructed with respect to the coupling boundary is introduced to determine particle resolution in different spatial positions. The resolution is maximal within a specific distance to the boundary and decreases smoothly as the distance increases until a threshold is reached. The sizes of the particles are then adjusted towards the resolution via splitting and merging. Additionally, a wake flow preservation mechanism is introduced to keep the particle resolution at a high level for a period of time after a particle flows through the boundary object to prevent the loss of flow details. Experiments show that our method can refine fluid–solid coupling details more efficiently and effectively capture dynamic effects beneath the surface.

A coupled SPH-DEM approach for modeling of free-surface debris flows

A Lagrangian mesh-less model is proposed to simulate fluid–solid flows with multiple-sized solids, i.e., millimeter-sized particle and larger-sized debris. Considering the difference in the size of solid phases, a hybrid resolved and unresolved model is established based on the coupling method of smoothed particle hydrodynamics (SPH) and discrete element method (DEM). SPH is used to model fluid, and the locally averaged Navier–Stokes equations are adopted as governing equations. DEM is used to model the particle–particle interactions, and the unresolved description of hydrodynamic forces including drag and buoyancy is established. The large-sized debris is modeled as the rigid body, which is discretized by particle elements having both SPH and DEM characteristics, where SPH particle elements are involved in the closure of the SPH fluids, and DEM particle elements interact with the solid particles following the contact law. The numerical model is validated and verified by several examples, including single-particle sedimentation, collapse of cylinder columns, and debris dam break. Results show that the present model reproduces general features of the complex fluid–solid flow with free surfaces. The advantage of the hybrid model is that it can deal with the fluid–solid flow problem with both small particles and large objects at a suitable resolution, and it is especially good at dealing with the free surface flow problem. A discretization for the modeling of debris flows is proposed based on the coupled SPH-DEM method. The novelty of the work is a coupled resolved–unresolved scheme for the free surface flow with multi-sized solids. The present scheme allows using a uniform resolution by bridging the size difference between small-scale solid particles and large-scale debris. The unresolved model of fluid-particle flow is efficient because the fluid resolution can be configured comparably to the particle size. The unified nature of the model allows the combination of resolved and unresolved simulations in the same computational domain.

The role of time integration in energy conservation in Smoothed Particle Hydrodynamics fluid dynamics simulations

The choice of a time integration scheme is a crucial aspect of any transient fluid simulation, and Smoothed-Particle Hydrodynamics (SPH) is no exception. The influence of the time integration scheme on energy balance is here addressed. To do so, explicit expressions allowing to compute the deviations from the energy balance, induced by the time integration scheme, are provided. These expressions, computed a posteriori, are valid for different integration methods. Besides, a new formulation that improves energy conservation by enhancing stability, based on an implicit integration scheme, is proposed. Such formulation is tested with the simulation of a two-dimensional non-viscous impact of two jets, with no artificial dissipation terms. To the best of our knowledge, this is the first stable simulation of a non-dissipative system with a weakly-compressible SPH method. A viscous case, the Taylor–Green vortex, has also been simulated. Results show that an implicit time integration scheme also behaves better in a viscous context.

Dynamical response of a floating plate to water waves using a smoothed particle hydrodynamics algorithm for nonlinear elasticity

In this work, a newly developed Smoothed Particle Hydrodynamics (SPH) algorithm for nonlinear elasticity is combined with an incompressible SPH fluid solver to investigate the dynamics of a floating plate under impacts of regular water waves with a high steepness. Two scenarios of the plate's rigidity are investigated. The simulation results show that deformations of the stiffer plate mainly occur in a simple bending mode with small amplitudes, and the plate is almost submerged by a strong fluid flow over its surface. In the other scenario, the plate deforms more complexly with much higher deformation amplitudes but experiences a much weaker overwash. The more flexible plate is less resistant to wave motions and converts more wave energy into elastic deformations, and therefore, the overwash is less severe. A strong overflow exerts a pressure force onto the plate that alters the plate's dynamics and adds a viscous (damping) effect on the plate's elastic vibrations, especially in high-frequency modes. A rigorous examination of the numerical convergence and validation using the linear thin plate theory is also carried out. The new SPH algorithm for nonlinear elasticity shows its stability and reliability in evaluating finite and large elastic deformations. Therefore, it is promising for simulating elastic structures in fluid–structure interaction problems.

Adaptive smoothing length method based on weighted average of neighboring particle density for SPH fluid simulation

BackgroundIn the smoothed particle hydrodynamics (SPH) fluid simulation method, thesmoothing length affects not only the process of neighbor search but also the calculation accuracy of the pressure solver. Therefore, it plays a crucial role in ensuring the accuracy and stability of SPH. MethodsIn this study, an adaptive SPH fluid simulation method with a variable smoothing length is designed. In this method, the smoothing length is adaptively adjusted according to the ratio of the particle density to the weighted average of the density of the neighboring particles. Additionally, a neighbor search scheme and kernel function scheme are designed to solve the asymmetry problems caused by the variable smoothing length. ResultsThe simulation efficiency of the proposed algorithm is comparable to that of some classical methods, and the variance of the number of neighboring particles is reduced. Thus, the visual effect is more similar to the corresponding physical reality. ConclusionsThe precision of the interpolation calculation performed in the SPH algorithm is improved using the adaptive-smoothing length scheme; thus, the stability of the algorithm is enhanced, and a larger timestep is possible.

A New Experimental Study and SPH Comparison for the Sequential Dam-Break Problem

The floods following the event of a dam collapse can have a significant impact on the downstream environment and ecology. Due to the limited number of real-case data for dam-break floods, laboratory experiments and numerical models are used to understand the complex flow behavior and to analyze the impact of the dam-break wave for different scenarios. In this study, a newly designed experimental campaign was conducted for the sequential dam-break problem in a rectangular channel with a steep slope, and the obtained results were compared against those of a particle-based numerical model. The laboratory tests permitted a better understanding of the physical process, highlighting five successive stages observed in the downstream reservoirs: dam-break wave propagation, overtopping, reflection wave, run-up, and oscillations. Experimental data were acquired using a virtual wave probe based on an image processing technique. A professional camera and a smartphone camera were used to obtain the footage of the experiment to examine the effect of the resolution and frame rate on image processing. The numerical results were obtained through the Smoothed Particle Hydrodynamics (SPH) method using free DualSPHysics software. The experimental and numerical results were in good agreement generally. Hence, the presented data can be used as a benchmark in future studies to validate the SPH and other Computational Fluid Dynamics (CFD) methods.

Turbulent Details Simulation for SPH Fluids via Vorticity Refinement

AbstractA major issue in smoothed particle hydrodynamics (SPH) approaches is the numerical dissipation during the projection process, especially under coarse discretizations. High‐frequency details, such as turbulence and vortices, are smoothed out, leading to unrealistic results. To address this issue, we introduce a vorticity refinement (VR) solver for SPH fluids with negligible computational overhead. In this method, the numerical dissipation of the vorticity field is recovered by the difference between the theoretical and the actual vorticity, so as to enhance turbulence details. Instead of solving the Biot‐Savart integrals, a stream function, which is easier and more efficient to solve, is used to relate the vorticity field to the velocity field. We obtain turbulence effects of different intensity levels by changing an adjustable parameter. Since the vorticity field is enhanced according to the curl field, our method can not only amplify existing vortices, but also capture additional turbulence. Our VR solver is straightforward to implement and can be easily integrated into existing SPH methods.

An advanced hybrid smoothed particle hydrodynamics–fluid implicit particle method on adaptive grid for condensation simulation

AbstractIn this article, we propose a novel hybrid framework by combining smoothed particle hydrodynamics and adaptive narrow band fluid implicit particle method (NB‐FLIP) to faithfully model the multiphysical processes involving heat transfer and phase transition, and to precisely simulate the dynamics of condensed droplets moving along intricate objects. We first formulate a governing physical model built upon an improved phase transition model and an augmented on‐surface drop analysis method to achieve realistic condensation effects over intricate hydrophilic/hydrophobic interface. To achieve both high‐fidelity interactions and high‐resolution visual effects, we further develop an adaptive NB‐FLIP solver with octree‐dictated background grid in order to further enhance the performance of our framework. Experimental results have shown that our approach can be used to efficiently and realistically simulate the small‐scale interaction details between condensed drops and complex objects with arbitrary geometry.

Modeling of Waterjet Abrasion in Mining Processes Based on the Smoothed Particle Hydrodynamics (SPH) Method

Abrasive waterjet is widely used for mass-cutting during coal mining or other mining process. Such a cutting process involves complex fluid–solid coupling, which require an effective method capable of simulating the large deformation and spalling of materials. This paper uses method of smoothed particle hydrodynamics (SPH) to establish a model to simulate the cutting process of coal seams by abrasive waterjets. In our SPH model, both fluid and solid are discretized with SPH particles. These particles are different in physical properties representing waterjet, abrasive particles and target materials. The waterjet is treated as viscous fluid and the coal (as a target material) is modeled as a brittle solid material. All these SPH particles of various medium are governed by the Navier–Stokes (NS) equations. Our established SPH model is then applied to study the efficiency of coal cutting using different waterjet formations. The results show that the cutting efficiency of the abrasive waterjet is higher than that of the standard waterjet. Our SPH model is capable of reveal the detailed interactions of the micro waterjet abrasive particles with the particles on the surface of coal. It enables the study on the mechanisms of coal seam breaking and cutting processes. It provides an effective computational tool for improving the efficiency of coal mining and of the development of new techniques for coal mining.

An advanced study on discretization-error-based adaptivity in Smoothed Particle Hydrodynamics

This contribution is concerned with a novel, purely methodological strategy enabling to automatically adjust the local spatial resolution in Smoothed Particle Hydrodynamics (SPH). It is built upon the fact that the accuracy of the SPH interpolation is related to zeroth- and first-order moments. Ensuing from this knowledge, a suitable measure of the SPH spatial discretization error has been derived. Using this measure as an adaptivity criterion allows to dynamically adjust the local resolution in such a way that a uniform distribution of the spatial discretization error over the model domain is achieved. This is demonstrated in the present paper. To that end, the theoretical foundation of the proposed adaptivity criterion is discussed first. After that, its applicability to both SPH fluid and solid simulations is thoroughly examined.

On the accurate large-scale simulation of ferrofluids

We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets' field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

Implementation of Open Boundaries within a Two-Way Coupled SPH Model to Simulate Nonlinear Wave–Structure Interactions

A two-way coupling between the Smoothed Particle Hydrodynamics (SPH) solver DualSPHysics and the Fully Nonlinear Potential Flow solver OceanWave3D is presented. At the coupling interfaces within the SPH numerical domain, an open boundary formulation is applied. An inlet and outlet zone are filled with buffer particles. At the inlet, horizontal orbital velocities and surface elevations calculated using OceanWave3D are imposed on the buffer particles. At the outlet, horizontal orbital velocities are imposed, but the surface elevation is extrapolated from the fluid domain. Velocity corrections are applied to avoid unwanted reflections in the SPH fluid domain. The SPH surface elevation is coupled back to OceanWave3D, where the originally calculated free surface is overwritten. The coupling methodology is validated using a 2D test case of a floating box. Additionally, a 3D proof of concept is shown where overtopping waves are acting on a heaving cylinder. The two-way coupled model (exchange of information in two directions between the coupled models) has proven to be capable of simulating wave propagation and wave–structure interaction problems with an acceptable accuracy with error values remaining below the smoothing length h S P H .

Interlinked SPH Pressure Solvers for Strong Fluid-Rigid Coupling

We present a strong fluid-rigid coupling for Smoothed Particle Hydrodynamics (SPH) fluids and rigid bodies with particle-sampled surfaces. The approach interlinks the iterative pressure update at fluid particles with a second SPH solver that computes artificial pressure at rigid-body particles. The introduced SPH rigid-body solver models rigid-rigid contacts as artificial density deviations at rigid-body particles. The corresponding pressure is iteratively computed by solving a global formulation that is particularly useful for large numbers of rigid-rigid contacts. Compared to previous SPH coupling methods, the proposed concept stabilizes the fluid-rigid interface handling. It significantly reduces the computation times of SPH fluid simulations by enabling larger time steps. Performance gain factors of up to 58 compared to previous methods are presented. We illustrate the flexibility of the presented fluid-rigid coupling by integrating it into DFSPH, IISPH, and a recent SPH solver for highly viscous fluids. We further show its applicability to a recent SPH solver for elastic objects. Large scenarios with up to 90 M particles of various interacting materials and complex contact geometries with up to 90 k rigid-rigid contacts are shown. We demonstrate the competitiveness of our proposed rigid-body solver by comparing it to Bullet.

Multiphase SPH modeling of water boiling on hydrophilic and hydrophobic surfaces

A multiphase smoothed particle hydrodynamics (SPH) model was established to study the boiling phenomenon of a water film heated on a hydrophilic or hydrophobic surface. For the two-phase fluids of water vapor and liquid with continuous density gradient, conservation equations in Lagrangian formulation were discretized by SPH fluid particles. While the solid is treated by a new fluid-solid wetting surface model, which considered both the macroscopic interface curvature and the microscopic attractive forces. This SPH model enabled us to simulate the water boiling directly without empirical assumptions. After this model was well validated by three benchmark cases, we studied water boiling using two types of heating strategies. One strategy was partial heating with static or dynamic spots. The other was complete heating on an overall heating surface. Several fluid ρ-T phase diagrams were plotted with a detailed insight of the boiling development. We further simulated the critical heat flux (CHF) for both partial and total heating. The results illustrated the influences of the fluid thickness and the heating condition on the CHF value. The effects of wettability on boiling were also calculated. We found that a jumping boiling phenomenon would be observed on a relatively nonwettable surfaces, enhancing the heat exchange capability.

MLS pressure boundaries for divergence-free and viscous SPH fluids

In this paper we present a novel method to predict pressure values at boundary particles in incompressible divergence-free SPH simulations (DFSPH). Our approach employs Moving Least Squares (MLS) to predict the pressure at boundary particles. Therefore, MLS computes hyperplanes that approximate the pressure field at the interface between fluid and boundary particles. We compare this approach with three previous techniques. One previous technique mirrors the pressure from fluid to boundary particles. Another one extrapolates the pressure from fluid to boundary particles, but uses a gradient that is computed with Smoothed Particle Hydrodynamics (SPH). The third one solves a pressure Poisson equation (PPE) for boundary particles. In our experiments, we indicate artifacts in the three previous approaches. We show that these artifacts are significantly reduced with our approach resulting in simulation steps that can be twice as large. We motivate that gradient-based extrapolation is more accurate than mirroring. We further motivate that, due to particle deficiency at the boundary, the SPH gradient is error prone. This is less the case for our proposed MLS gradient. Moreover, our approach is computationally less expensive as solving a PPE for the boundary particles. We present challenging and complex scenarios to illustrate the capabilities of our method. In addition, we demonstrate that the proposed boundary handling is applicable to highly viscous fluids.