Macroscopic pedestrian flow simulation using Smoothed Particle Hydrodynamics (SPH)

<strong class="journal-contentHeaderColor">Abstract.</strong> The Viscous-Plastic (VP) rheology with an elliptical yield curve and normal flow rule is implemented in a Lagrangian modelling framework using the Smoothed Particle Hydrodynamics (SPH) meshfree method. Results show, from perturbation analysis of SPH sea-ice dynamic equations, that the classical SPH particle density formulation expressed as a function of sea-ice concentration and mean ice thickness, leads to incorrect plastic wave speed. We propose a new formulation for particle density that gives a plastic wave speed in line with theory. In all cases, the plastic wave in the SPH framework is dispersive and depends on the smoothing length (i.e., the spatial resolution) and on the SPH kernel employed in contrast with its finite difference method (FDM) implementation counterpart. The steady-state solution for the simple 1D ridging experiment is in agreement with the analytical solution within an error of 1 %. SPH is also able to simulate a stable upstream ice arch in an idealized domain representing the Nares Strait in low wind regime (5.3 [m &middot; s^&minus;1]) with an ellipse aspect ratio of 2, an average thickness of 1 [m] and free-slip boundary conditions in opposition to the FDM implementation that requires higher shear strength to simulate it. In higher wind regime (7.5 [m &middot; s^&minus;1]) no stable ice arches are simulated &mdash; unless the thickness is increased &mdash; and the ice arch formation showed no dependence on the size of particles contrary to what is observed in the discrete element framework. Finally, the SPH framework is explicit, can take full advantage of parallel processing capabilities and show potential for pan-arctic climate simulations.

For the better management of available groundwater, it is essential to understand the flow behavior within the aquifer systems. The groundwater flow behavior in the complex aquifer system can be studied by solving the governing equations using either analytical or numerical methods. As the analytical solutions are available only for simple idealized cases, numerical methods such as finite difference method (FDM) and finite element method (FEM) are generally used. The Meshless method is a recently developed alternative numerical approach for the solution of existing problem. A variety of Meshless methods like point interpolation method, smooth particle hydrodynamics, Galerkin methods, etc. are under the development for the solution of many solid mechanics and fluid mechanics problems. Meshless method eliminates many of the drawbacks of grid-based methods such as difficulties in meshing and re-meshing as in FDM and FEM which require huge efforts in pre-processing and with Meshless method it translates in the lesser computational time and costs. In this paper, Meshless Local Petrov-Galerkin (MLPG) method with strong form of collocation with exponential/Gaussian radial basis function is used for solving the groundwater flow problem. A computer model in MATLAB has been developed in 1D and 2D for the solution of confined aquifer problems. The developed 1D model is verified with available analytical solution for a hypothetical problem and found to be satisfactory. Further, the 2D model is applied to two case studies and results are compared with the FEM based solutions and found to be satisfactory. The present study shows that the MLPG based Meshless method is very effective in the simulation of groundwater flow problems.

Smoothed particle hydrodynamics (SPH) is a meshfree method and has been widely used in the field of fluid dynamics. However, there is still a lack of robust approach to implement the far-field boundary condition in the simulation of free stream flow past the rigid body. To solve this problem, on the basis of Lastiwka et al.’s work, an improved non-reflecting boundary condition, called mixed characteristic boundary condition is proposed in this paper. The mixed characteristic boundary condition is tested by two-dimensional incompressible flows with a perturbation at the initial moment. The numerical results show that the mixed characteristic boundary condition can effectively suppress the reflection of waves on far-field boundaries. Finally, flows past a hydrofoil are simulated within the framework of the kernel gradient free SPH in two kinds of non-reflecting boundary condition. The results indicate that the present boundary condition is more robust and suitable for SPH than the one adopted by Lastiwka et al.

Friction stir welding (FSW) is a complex joining process which is governed by multiple intertwined physical phenomena. Besides friction, inelastic heat generation, and heat conduction, it involves high plastic deformations, resulting in a need for a numerical method being able to handle all these. Such a scheme is smoothed particle hydrodynamics (SPH), which is a mesh-free computational technique. Absence of a fixed mesh results in the ability of the method to deal with another challenge of friction stir welding, a coalescence of initially separate workpieces into one due to bonding mechanisms. The background of this phenomenon is a transition from contact between two pieces to one continuum due to enormous changes in several material condition, such as temperature, pressure, strain, and strain rate. This work deals with a new development related to bonding, which will provide deeper understanding about the physical weld formation during FSW. The SPH framework must be extended to consider this bonding mechanism. This involves the bonding criterion definition, the interaction type change, and the SPH–SPH contact formulation. Then, the implementation is tested for two different examples, a compression test and FSW.

Mathematical models that predict performance can aid in the understanding and development of solid oxide fuel cells (SOFCs). Of course, various modeling approaches exist involving different length scales. In particular, very significant advances are now taking place using microscopic models to understand the complex composite structures of electrodes and three-phase boundaries. Ultimately these advances should lead to predictions of cell behavior, which at present are measured empirically and inserted into macroscopic cell models. In order to achieve this ambitious goal, simulation tools based on these macroscopic models must be redesigned by matching them to the complex microscopic phenomena, which take place at the pore scale level. As a matter of fact, the macroscopic continuum approach essentially consists of applying some type of homogenization technique, which properly averages the underlying microscopic phenomena for producing measurable quantities. Unfortunately, these quantities in the porous electrodes of fuel cells are sometimes measurable only in principle. For this reason, this type of approach introduces additional uncertainties into the macroscopic models, which can significantly affect the numerical results, particularly their generality. This paper is part of an ongoing effort to address the problem by following an alternative approach. The key idea is to numerically simulate the underlying microscopic phenomena in an effort to bring the mathematical description nearer to actual reality. In particular, some recently developed mesoscopic tools appear to be very promising since the microscopic approach is, in this particular case, partially included in the numerical method itself. In particular, the models based on the lattice Boltzmann method (LBM) treat the problem by reproducing the collisions among particles of the same type, among particles belonging to different species, and finally among the species and the solid obstructions. Recently, a model developed by the authors was proposed which, based on LBM, models the fluid flow of reactive mixtures in randomly generated porous media by simulating the actual coupling interaction among the species. A parallel three–dimensional numerical code was developed in order to implement this model and to simulate the actual microscopic structures of SOFC porous electrodes. In this paper, a thin anode (50 micron) of Ni-metal / YSZ-electrolyte cermet for a high–temperature electrolyte supported SOFC was considered in the numerical simulations. The three–dimensional anode structure was derived by a regression analysis based on the granulometry law applied to some microscopic pictures obtained with an electron microscope. The numerical simulations show the spatial distribution of the mass fluxes for the reactants and the products of the electrochemical reactions. The described technique will allow one to design new improved materials and structures in order to statistically optimize these fluid paths.

A number of particle models that are suitable for simulating multiphase fluid flow and biogeochemical processes have been developed during the last few decades. Here we discuss three of them: a microscopic model – molecular dynamics; a mesoscopic model – dissipative particle dynamics; and a macroscopic model – smoothed particle hydrodynamics. Particle methods are robust and versatile, and it is relatively easy to add additional physical, chemical and biological processes into particle codes. However, the computational efficiency of particle methods is low relative to continuum methods. Multiscale particle methods and hybrid (particle–particle and particle–continuum) methods are needed to improve computational efficiency and make effective use of emerging computational capabilities. These new methods are under development.

The smoothed particle hydrodynamics (SPH) method was employed to simulate the heat transfer process in porous media at the pore scale. The effective thermal conductivity of a porous medium can be predicted through a simulation experiment of SPH. The accuracy of the SPH simulation experiment was verified by comparing the predicted values with reference values for ideal homogeneous media and multiphase layered media. 3D simulation experiments were implemented in granular media generated by the PFC method. Based on the SPH framework, a concise method was proposed to produce unsaturated media by simulating the wetting process in dry media. This approach approximates the formation of liquid bridges and water films on granules. Through simulation experiments, the empirical formula of the variation in thermal conductivity with the degree of saturation was tested. The results showed that the reciprocal of the normalized thermal conductivity and the reciprocal of the saturation are linearly related, which is in line with the empirical formula proposed by Cote and Konrad.

SummaryEnergy conservation and consistency are not easy to achieve simultaneously in smoothed particle hydrodynamics (SPH). In this study, an efficient strategy is proposed to achieve energy conservation in an SPH framework with a consistent basis function. Herein, at every particle pair interaction, a correction term is introduced such that energy conservation is restored locally and, at the same time, the total variation of different variables due to the correction term is minimum. The final form of the proposed formulation is such that no additional computational effort is required and the simplicity of SPH is preserved. The theoretical error estimate of the proposed formulation is performed. The proposed scheme is also compared with benchmark SPH formulations in terms of the L2 error norm for representative functional derivatives both in regular and irregular particle distributions. Finally, the efficacy of the proposed formulation in conserving energy and maintaining accuracy is demonstrated via few elastic, elastic‐plastic impact and fracture problems.

This chapter is devoted to the detailed study of the relation between a microscopic cellular automation and a macroscopic partial differential equation model for the movement of pedestrians. We describe the mathematical tools allowing to derive the macroscopic from the microscopic model. Such a connection between discrete, particle based and continuous, density based models can help to improve the understanding of basic properties of human crowds. We exemplify this by applying our results to typical cases. The first one is the formation of lanes in bi-directional flow. The second is the analysis of the fundamental diagram. Our analysis provides (at least qualitatively) a connection between these phenomena and model parameters. We conclude by pointing out a number of possible directions of future research.

A scalable parallel computing SPH framework for predictions of geophysical granular flows

Landslides exhibit complicated and destructive behaviour with disastrous consequences. A landslide event is preceded by slope failure, which is governed by laws of soil mechanics. Once initiated, landslides often propagate downslope at rapid rates, exhibiting fluid-like behaviour. Landslide propagation is therefore frequently characterised by laws of fluid dynamics. Numerical models are vital for an improved understanding of these catastrophic events. Existing models are incapable of adequately simulating the dynamics of both initiation and propagation. Smoothed Particle Hydrodynamics (SPH) is a meshless method that is able to capture large displacements and rapid velocities, and it has been frequently applied to simulate landslide propagation. However, SPH is susceptible to numerical instabilities, that are particularly detrimental with regards to simulations of soil. These must be eliminated for SPH to be an ideal tool for general landslide modelling. The majority of approaches at removing the numerical instabilities from SPH are not universal – some are applicable for small displacements problems only, while others require the tuning of artificial model parameters. In this research, a novel numerical model is developed capable of accurately simulating landslide behaviour – including initiation and propagation. The numerical model – Stress-Particle SPH – removes instabilities in a way that does not require artificial parameter tuning. The method is an extension of SPH, and involves calculating velocities and stresses on two separate sets of particles – nodes and stress-points. Previous literature suggests that the addition of stress-points have the potential to effectively stabilise SPH. Despite this, their implementation within SPH is relatively unexplored, and stress-points have only been applied to a limited range of problems. In this research, Stress-Particle SPH is extended for applicability to landslide behaviour, allowing the numerically stable simulation of high displacement problems with Stress-Particle SPH for the first time. The developments presented in this research offer the potential for SPH to tackle a broad range of problems beyond its current capabilities.

Helmholtz decomposition-based SPH

Liquid sloshing is a common phenomenon in the transporting of liquid tanks. Liquid waves lead to fluctuating forces on the tank wall. If these fluctuations are not predicted or controlled, they can lead to large forces and momentum. Baffles can control liquid sloshing fluctuations. One numerical method, widely used to model the liquid sloshing phenomena is Smoothed Particle Hydrodynamics (SPH). Because of its Lagrangian nature, SPH is suitable for simulating free surface flow. In the present study, a relatively accurate Incompressible SPH (ISPH) method improved by kernel gradient correction tensors, particle shifting algorithms, turbulence viscosity calculations, and free surface particle detectors is applied for the free surface flow modeling. In comparison to the other SPH Simulations and experimental data, these results show that the present algorithm is effective for simulating free surface problems. The present algorithm has been applied to simulate liquid sloshing phenomena, while the aim of this study is the investigation of vertical and horizontal baffle effects on the control and damping of liquid sloshing. Results show that for vertical baffles, baffle size has a major role in sloshing fluctuation damping. For horizontal baffles, also including size, the baffle base position has a significant role in liquid sloshing fluctuation damping. When horizontal baffle is near the free surface, sloshing fluctuation-damping increases.

As Computational Fluid Dynamics (CFD) methods evolve and mature, more engineering problems are being solved through computer simulation to reduce reliance on the costly and time-consuming experimental methods. This trend is also occurring in the gear manufacturing industry, where an increasing number of quality issues related to the oil quenching process are being investigated by CFD methods to find solutions. However, while the CFD theory and numerical methods have made significant advancements, gaps still exist between the academic research and industrial applications. In the case of the oil quenching processes, the prospect of using CFD methods to visualize and study the oil flow pattern in the gear quenching tank is promising yet challenging. The obstacle to simulating the oil quenching process using CFD methods lies not in the numerical method itself for solving the Navier-Stokes equation, but in building a computer simulation model that encompasses all the geometrical details of the quenching tank, fixtures, centrifugal pumps, and gears, including all the gear teeth. This task is particularly challenging for Finite Volume Method (FVM) CFD solvers, as the computation mesh could take days or weeks to build. In this research, a new solution method based on Smoothed Particle Hydrodynamics (SPH) is introduced to simulate the oil flow in the gear quenching tank. Since SPH is a mesh-free Lagrangian method, it not only greatly simplifies the mesh generation task for building the computational models but also handles the complex physics of the free surface flow and fluid-structure interaction with great ease. In addition, the oil flow in the gear quenching tank usually is driven by centrifugal pumps whose dynamics can be simulated directly in SPH methods, as opposed to FVM methods which require complicated moving mesh computation.

An overview of smoothed particle hydrodynamics for simulating multiphase flow