Compressible Smoothed Particle Hydrodynamics Method Research Articles

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The cover image is based on the Research Article A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer by Hee Sang Yoo et al., https://doi.org/10.1002/nme.7148.

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

AbstractIn this article, we propose a simple, consistent, and robust Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics (EL‐WCSPH) for the simulation of hydrodynamics and convection heat transfer problems. First, the basic governing equation is formulated using the ALE‐SPH framework. The universal formulation is similar to the standard WCSPH, but the degree of Eulerian and Lagrangian schemes can be controlled by inserting a pre‐defined arbitrary parameter . To alleviate potential numerical errors and inconsistency, particle mass correction is proposed along with particle disorder correction. Then, an algorithm is introduced, in which only a slight modification is necessary compared to the standard WCSPH. Finally, extensive benchmark simulations are conducted to validate the proposed method. As a result, the proposed method is found to perform well in hydrodynamics problems with various flow conditions (pipe flow, lid‐driven problem, Taylor–Green vortex, vortex shedding problem, and water sloshing) and thermal‐hydraulics problems (natural convection in a square cavity).

Multiphase large-eddy simulations of human cough jet development and expiratory droplet dispersion

Violent respiratory events play critical roles in the transmission of respiratory diseases, such as coughing and sneezing, between infectious and susceptible individuals. In this work, large-scale multiphase flow large-eddy simulations have been performed to simulate the coughing jet from a human's mouth carrying pathogenic or virus-laden droplets by using a weakly compressible smoothed particle hydrodynamics method. We explicitly model the cough jet ejected from a human mouth in the form of a mixture of two-phase fluids based on the cough velocity profile of the exhalation flow obtained from experimental data and the statistics of the droplets’ sizes. The coupling and interaction between the two expiratory phases and ambient surrounding air are examined based on the interaction between the gas particles and droplet particles. First, the results reveal that the turbulence of the cough jet determines the dispersion of the virus-laden droplets, i.e. whether they fly up evolving into aerosols or fall down to the ground. Second, the droplet particles have significant effects on the evolution of the cough jet turbulence; for example, they increase the complexity and butterfly effect introduced by the turbulence disturbance. Our results show that the prediction of the spreading distance of droplet particles often goes beyond the social distancing rules recommended by the World Health Organization, which reminds us of the risks of exposure if we do not take any protecting protocol.

The effect of thixotropy on deformation of a single droplet under simple shear flow

In this paper, the deformation of an isolated single two-dimensional droplet under simple shear flow is studied regarding the thixotropic behavior. In doing so, a modified consistent weakly compressible smoothed particle hydrodynamics method is employed. It is assumed that the thixotropic fluid obeys the Moore model, and the surface tension is modeled by the continuum surface tension (CST) method. After verifying the utilized paradigm, it is applied to novel cases in which one of the fluids exhibits thixotropic behavior. The effects of Moore's model constants are examined through several numerical simulations. It is shown that the drop deformation is dramatically affected by thixotropic behavior. Generally speaking, the deformation of the Newtonian droplet is decreased by increasing the destruction-to-rebuild ratio of the surrounding thixotropic liquid. The same trend is found when the thixotropic droplet is exposed to the shear flow of a Newtonian fluid. Also, it is demonstrated that the presence of another droplet in the vicinity of the first droplet could dramatically change the flow domain. To the best of the author's knowledge, the effect of thixotropy is investigated on droplet deformation for the first time.

A hydraulic soil erosion model based on a weakly compressible smoothed particle hydrodynamics method

Hydraulic soil erosion is one of the most important natural phenomena driving terrain changes over time. It is associated with a variety of geoenvironmental hazards such as coastline retreat, soil loss and debris flows, and can have severe consequences. In this work, an erosion criterion was introduced to analyze the water–sediment interaction, and a hydraulic soil erosion model was then established based on the smoothed particle hydrodynamics (SPH) method. Numerical simulations of dam-break flow on a mobile bed and sediment flushing were carried out, and the performance of the hydraulic erosion model was evaluated. The numerical results matched the experimental data well, thus verifying the reliability and validity of the proposed model.

A corrected solid boundary treatment method for Smoothed Particle Hydrodynamics

Smoothed Particle Hydrodynamics method (SPH) has a good adaptability for simulating of free surface flow problems. However, there are some shortcomings of SPH which are still in open discussion. This paper presents a corrected solid boundary handling method for weakly compressible SPH. This improved method is very helpful for numerical stability and pressure distribution. Compared with other solid boundary handling methods, this corrected method is simpler for virtual ghost particle interpolation and the ghost particle evaluation relationship is clearer. Several numerical tests are given, like dam breaking, solitary wave impact and sloshing tank waves. The results show that the corrected solid boundary processing method can recover the spurious oscillations of pressure distribution when simulating the problems with complex geometry boundary.

Numerical study on mitigating tsunami force on bridges by an SPH model

This study applies the numerical model of GPUSPH, an implementation of the weakly compressible Smoothed Particle Hydrodynamics method on graphics processing units, to investigate tsunami forces on bridge superstructures and tsunami mitigation on bridges by using a service road bridge and an offshore breakwater. The capability of GPUSPH to predict tsunami forces on bridges is first validated by simulating a laboratory experiment on tsunami impacting a bridge with different configurations of superstructures. To address the uncertainty of tsunami generation with the gate falling method used in the laboratory, this study proposes a new tsunami wave generation method that makes use of the laboratory free-surface measurements to replicate the wave. Furthermore, the tsunami force, in particular, the first impact force, on bridges is reasonably predicted by GPUSPH. Next additional numerical experiments built upon the laboratory work are carried out to examine the efficiency of tsunami mitigation by an upwave service road bridge and an offshore breakwater. It is found that a two-girder service road bridge is effective in reducing tsunami forces on the main bridge. Furthermore, a breakwater can also reduce tsunami forces on a bridge, and there is an optimal distance between the breakwater and the bridge to achieve the best reduction effect. However, the tsunami mitigation structures experience a strong tsunami force, which may lead to the failure of these structures.

An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field.

Development of Moving Particle Explicit (MPE) method for incompressible flows

A new particle method is proposed for computing incompressible flows. Using Moving Particle Semi-implicit (MPS) and Smoothed Particle Hydrodynamics (SPH) approaches, a new Moving Particle Explicit (MPE) method is developed. The concept, like the MPS method, is based on the weighted averaging scheme. Introducing a directional particle number density, the derivation of spatial discretization is performed without imposing any simplification. As a consequence, the formulation becomes more generic and covers the MPS scheme. The solution algorithm is similar to the weakly compressible SPH method. Considering slight compressibility for an incompressible flow, the continuity equation for compressible flow together with an equation of state is used to decouple the velocity and pressure of the Navier–Stokes equations. Consequently, the method becomes fully explicit, and the problems related to solving a set of equations in an implicit procedure are removed. Easy application of the solution algorithm, in comparison with the MPS method, as well as the generic discretization scheme, makes the MPE method more efficient for simulating incompressible flows. The proposed method is validated using a Poiseuille flow and two dam break problems; furthermore, a submerged hydraulic jump is investigated to evaluate the method’s capability in simulating open boundary problems. In all cases, good agreement between numerical results and analytical/experimental data is observed.

Lagrangian simulation and analysis of the micromixing phenomena in a cylindrical paddle mixer using a modified weakly compressible smoothed particle hydrodynamics method

AbstractIn the present study, a robust modified weakly compressible smoothed particle hydrodynamics (SPH) method is introduced in order to examine the micromixing phenomena within a cylindrical paddle mixer. Because it has a Lagrangian nature and it is based on particles, smoothed particle hydrodynamics is an appropriate and convenient method for simulating the moving boundary problems and tracking the particles in the mixing process. The present study thus introduces a convenient SPH method for modelling the mixing process. The straight and cross‐shaped blades are considered, and the effects of the fixed rotation, planetary motion of the blade, and position of the blade on the mixing rate are studied. © 2014 Curtin University of Technology and John Wiley & Sons, Ltd.

On the Reynolds number sensitivity of smoothed particle hydrodynamics

ABSTRACTThis work investigates the Reynolds number sensitivity of the weakly compressible smoothed particle hydrodynamics method. A mode of instability previously reported for Poiseuille flow is systematically analysed for six relevant test cases. We discuss the influence of the presence of physical viscosity, investigate the origin of the instability for the Couette flow example and explore its implications on convergence properties. Moreover, a novel instability of slightly different nature, which arises in pipe flow with expanding diameter, is detected and a qualitative explanation is given. Since both types of instabilities also occur at Reynolds numbers well below the critical value, its origin is seen in high-frequency particle oscillations independent of any effects of turbulence. We further demonstrate for a flow over a sill and a weir that if there is no breakup of the fluid structure at low Reynolds numbers, then energy balance is accurately simulated even at high Reynolds numbers. Finally, the implications of the instability are addressed from a theoretical, computational and practical perspective.

A numerical investigation into the correction algorithms for SPH method in modeling violent free surface flows

A quantitative comparison of the usual and recent numerical treatments which are applied to the Smoothed Particle Hydrodynamics (SPH) method are presented together with a new free-surface treatment. A series of numerical treatments are studied to refine the numerical procedures of the SPH method particularly for violent flows with a free surface. Two dimensional dam-break and sway-sloshing problems in a tank are modeled by solving Euler's equation of motion utilizing weakly compressible SPH method (WCSPH). Initially, the dam-break benchmark problem is studied by adopting only conventional basic equations of SPH without any numerical remedy and then by considering numerical treatments of interest one after another. In the WCSPH method, the precise calculation of the densities of the particles is vital for the solution, accordingly a density correction algorithm is presented as a basic numerical treatment. Subsequently, Monaghan's (1994) [1] XSPH velocity variant algorithm, artificial particle displacement (APD) algorithm (Shaldoo et al., 2011) [2], and a hybrid combination of velocity updated XSPH (VXSPH) and APD algorithms are implemented separately, but all with the density correction algorithm as a default treatment. The effects of each of these treatments on the pressure and on the free surface profiles are analyzed by comparing our numerical findings with experimental and numerical results in the literature. After the detailed scrutiny on the dam-break problem, sway-sloshing problem is handled with the VXSPH+APD algorithm which has been noted to provide the most reliable and accurate results in the dam-break problem. For the sway-sloshing problem, the time histories of free surface elevations on the left side wall of the rectangular tank are compared with experimental and numerical results available in the literature. It was shown that the VXSPH+APD treatment significantly improves the accuracy of the numerical simulations for violent flows with a free surface and lead to the results which are in very good agreement with experimental and numerical findings of literature in terms of both the kinematic and the dynamic point of view.

Study of droplet deformation, heat-conduction and solidification using incompressible smoothed particle hydrodynamics method

This paper presents a numerical model based on incompressible smoothed particle hydrodynamics (SPH) method to simulate the deformation, heat-conduction and solidification process of a droplet impinging on a substrate. Continuum, momentum and energy equations of the fluid flow are solved using SPH method, with van der Waals force accounting for the surface tension and Fourier's law for heat conduction. Incompressible smoothed particle hydrodynamics method (ISPH) is used here instead of weakly compressible smoothed particle hydrodynamics method (WSPH), to satisfy the fluid incompressibility. Effects of rough and smooth substrates are also taken into account. Results show that the droplet begins to deform and spread, followed by solidification. Also, the temperature of droplet falls faster in the rough one, and this may attribute to the roughness.