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

<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.

A hybrid peridynamics–SPH simulation of soil fragmentation by blast loads of buried explosive

In this work, a nonlocal peridynamics---smoothed particle hydrodynamics (SPH) coupling formulation has been developed and implemented to simulate soil fragmentation induced by buried explosions. A peridynamics---SPH coupling strategy has been developed to model the soil---explosive gas interaction by assigning the soil as peridynamic particles and the explosive gas as SPH particles. Artificial viscosity and ghost particle enrichment techniques are utilized in the simulation to improve computational accuracy. A Monaghan type of artificial viscosity function is incorporated into both the peridynamics and SPH formulations in order to eliminate numerical instabilities caused by the shock wave propagation. Moreover, a virtual or ghost particle method is introduced to improve the accuracy of peridynamics approximation at the boundary. Three numerical simulations have been carried out based on the proposed peridynamics---SPH theory: (1) a 2D explosive gas expansion using SPH, (2) a 2D peridynamics---SPH coupling example, and (3) an example of soil fragmentation in a 3D soil block due to shock wave expansion. The simulation results reveal that the peridynamics---SPH coupling method can successfully simulate soil fragmentation generated by the shock wave due to buried explosion.

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

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.

Finite element-smoothed particle hydrodynamics adaptive method in simulating debris cloud

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.

Studying compact-star binaries and their mergers is integral to determining progenitors for observable transients. Today, compact-star mergers are typically studied via state-of-the-art computational fluid dynamics codes. One such numerical technique, smoothed particle hydrodynamics (SPH), is frequently chosen for its excellent mass, energy, and momentum conservation. The natural treatment of vacuum and the ability to represent highly irregular morphologies make SPH an excellent tool for the study of compact-star binaries and mergers. For many scenarios, including binary systems, the outcome of simulations is only as accurate as the initial conditions. For SPH, it is essential to ensure that the particles are distributed regularly, representing the initial density profile but without long-range correlations. Particle noise in the form of high-frequency local motion and low-frequency global dynamics must be damped out. Damping the latter can be as computationally intensive as the actual simulation. We discuss a new and straightforward relaxation method, halted-pendulum relaxation (HPR), to remove global oscillation modes of SPH particle configurations. In combination with effective external potentials representing gravitational and orbital forces, we show that HPR has an excellent performance in efficiently relaxing SPH particles to the desired density distribution and removing global oscillation modes. We compare the method to frequently used relaxation approaches and test it on a white dwarf binary model at its Roche-lobe overflow limit. We highlight the importance of our method in achieving accurate initial conditions and its effect on achieving circular orbits and realistic accretion rates when compared with other general relaxation methods.

Ferrofluids are oil-based liquids containing magnetic particles that interact with magnetic fields without solidifying. Leveraging the exploration of new applications of these promising materials (such as in optics, medicine and engineering) requires high fidelity modeling and simulation capabilities in order to accurately explore ferrofluids in silico. While recent work addressed the macroscopic simulation of large-scale ferrofluids using smoothed-particle hydrodynamics (SPH), such simulations are computationally expensive. In their work, the Kelvin force model has been used to calculate interactions between different SPH particles. The application of this model results in a force pointing outwards with respect to the fluid surface causing significant levitation problems. This drawback limits the application of more advanced and efficient SPH frameworks such as divergence-free SPH (DFSPH) or implicit incompressible SPH (IISPH). In this contribution, we propose a current loop magnetic force model which enables the fast macroscopic simulation of ferrofluids. Our new force model results in a force term pointing inwards allowing for more stable and fast simulations of ferrofluids using DFSPH and IISPH.

Macroscopic pedestrian models are theoretically simpler than microscopic models, and they can potentially be solved faster while producing reasonable predictions of crowd dynamics. Therefore, they can be very useful for applications such as large-scale simulation, real-time state estimation and crowd management. However, the numerical methods presently used to solve macroscopic pedestrian models, which are mostly grid-based, have some shortcomings that limit their applicability. More specifically, they usually include complex procedures for grid generation and remeshing, and they produce simulation results that may not be sufficiently accurate (for example, because of unclear boundaries between flow states). Smoothed Particle Hydrodynamics (SPH) constitutes an alternative numerical method that could potentially overcome these limitations. SPH is a meshfree method where a crowd is represented by a set of particles that possess material properties and move according to macroscopic laws. Relevant state variables at each particle are approximated using information about the material properties of the neighboring particles and a smoothing function. This paper puts forward for the first time a generic SPH framework for solving macroscopic pedestrian models; in addition, it demonstrates that an SPH-based simulation model can produce meaningful and accurate results by means of three case studies. The first case study shows that the proposed numerical method can approximate well the analytical solution of a simple macroscopic model applied to a queue-discharge scenario. The second case study demonstrates that the proposed numerical method can potentially reproduce density dispersion (a phenomenon observed in real crowds) more accurately than grid-based methods, due to its meshfree, Lagrangian, and particle-based nature. The third case study highlights the need to reformulate the acceleration equation of the basic macroscopic model in order to reproduce lane formation in bi-directional flows (also an observed phenomenon) using the proposed SPH framework, and this paper presents a solution to do so.

We have developed a microscopic blood model, that can express the deformation of an erythrocyte in micro-circulation, based on the Smoothed Particle Hydrodynamics (SPH) method. In the method, plasma fluid is discretized by SPH particles and an erythrocyte is modeled by internal SPH particles wrapped in elastic membrane particles. For verifying the model, in two dimensions, we numerically analyzed a popular phenomenon of erythrocyte; the tank tread motion of an erythrocyte under a constant shear field. The numerical results agreed well with the experimental data and the tank tread motion of erythrocyte was well realized by the model. From these results, it is confirmed that our blood model based on the SPH method can well express microscopic and rheological properties of erythrocytes.

Improved element-particle coupling strategy with δ-SPH and particle shifting for modeling sloshing with rigid or deformable structures

In this work, we present the application of an alternative numerical model for fluid dynamic analyses of structural systems within the Smoothed Particle Hydrodynamics (SPH) framework of DualSPHysics coupled to the Project Chrono library. The Discrete Elements Method-based (DEM) structure model relies on the Euler&ndash;Bernoulli theory and utilizes lumped elasticity and rigid body dynamics to reproduce the flexural behavior of two-dimensional beams. The structure and fluid domain are both discretized with SPH particles: the fluid dynamics obey a Weakly Compressible SPH (WCSPH) formulation, whereas the structure particles are assembled into DEM rigid elements, moving according to physically-based, properly developed rotational dynamics. The presented model is of interest for studying complex soil&ndash;, solid&ndash;, fluid&ndash;structure interactions, involving a system that includes all the aforementioned phases in a unitary context&mdash;very useful for studying engineered structures under the threat of hazardous natural events. Test cases are presented to validate the SPH-DEM coupled model in both accuracy and stability, starting from an equilibrium test, to the dynamic response, and ending with fluid&ndash;structure interaction simulations. This work proves that the developed theory can be used within a Lagrangian framework, using the features provided by a DEM solver, overtaking the intrinsic limitations, and hence applying the results of static theory to complex dynamic problems

In this paper, we present a dynamic refinement algorithm for the smoothed particle Hydrodynamics (SPH) method. An SPH particle is refined by replacing it with smaller daughter particles, which positions are calculated by using a square pattern centered at the position of the refined particle. We determine both the optimal separation and the smoothing distance of the new particles such that the error produced by the refinement in the gradient of the kernel is small and possible numerical instabilities are reduced. We implemented the dynamic refinement procedure into two different models: one for free surface flows, and one for post-failure flow of non-cohesive soil. The results obtained for the test problems indicate that using the dynamic refinement procedure provides a good trade-off between the accuracy and the cost of the simulations.