Simulation Of Granular Flows Research Articles

Machine Learning Aided Modeling of Granular Materials: A Review

AbstractArtificial intelligence (AI) has become a buzzy word since Google’s AlphaGo beat a world champion in 2017. In the past five years, machine learning as a subset of the broader category of AI has obtained considerable attention in the research community of granular materials. This work offers a detailed review of the recent advances in machine learning-aided studies of granular materials from the particle-particle interaction at the grain level to the macroscopic simulations of granular flow. This work will start with the application of machine learning in the microscopic particle-particle interaction and associated contact models. Then, different neural networks for learning the constitutive behaviour of granular materials will be reviewed and compared. Finally, the macroscopic simulations of practical engineering or boundary value problems based on the combination of neural networks and numerical methods are discussed. We hope readers will have a clear idea of the development of machine learning-aided modelling of granular materials via this comprehensive review work.

A Simplified Calibration Procedure for DEM Simulations of Granular Material Flow

The discrete element method (DEM) has emerged as an essential computational tool in geotechnical engineering for the simulation of granular materials, offering significant advantages over traditional continuum-based methods such as the finite element method (FEM) and the finite difference method (FDM). The DEM’s ability to model particle-level interactions, including contact forces, rotations, and particle breakage, allows for a more precise understanding of granular media behavior under various loading conditions. However, accurate DEM simulations require meticulous calibration of input parameters, such as particle density, stiffness, and friction, to effectively replicate real-world behavior. This study proposes a simplified calibration procedure, intended to be conducted prior to any granular material flow DEM modeling, based on three fundamental physical tests: bulk density, surface friction, and angle of repose. The ability of these tests, conducted on dry quartz sand, to accurately determine DEM micromechanical parameters, was validated through numerical simulation of cylinder tests with varying height-to-radius ratios. The results demonstrated that this calibration approach effectively reduced computational complexity while maintaining high accuracy, with validation errors of 0% to 12%. This research underscores the efficacy of simplified DEM calibration methods in enhancing the predictive reliability of simulations, particularly for sand modeling in geotechnical applications.

Drag Modeling Effects on Simulations of Supersonic Jet-Induced Cratering in a Soil

The impact of the drag model in the simulation of turbulent granular flows is studied using databases here created through simulations of supersonic jet-induced cratering in granular soil. The simulations are based on a previously developed model, which was shown to be hyperbolic, thus permitting the unhindered propagation of pressure waves critical to craters produced by supersonic plumes. The goal is to identify predicted quantities from these simulations that show sufficient differences among simulations performed with different drag models; these quantities would warrant future experimental investigations determining which model is correct. Among all drag models examined, only two models are found applicable to the regime of investigation. Examination of the databases is conducted from the viewpoint of global quantities and detailed quantities. The results show that isocontours and characteristic length scales are minimally affected by the employed drag law. In contrast, azimuthally averaged and root mean square ejecta-related quantities are more sensitive to the drag model employed, but only in the central part of the crater. This sensitivity is much larger for shallow craters having a parabolic cross section than for deep craters having a conical cross section, thus indicating the experimental configuration best suited to experimentally evaluating drag models.

Three-dimensional simulation of granular flow using a mesh-free numerical model

Three-dimensional simulation of granular flow using a mesh-free numerical model

Atomistic simulations of oblique collisions between crystalline and amorphous SiC nanoparticles: Mechanisms of deformation and scaling coefficients of restitutions

Systematic atomistic simulations of oblique collisions between spherical crystalline, 6H and 3C, and amorphous SiC nanoparticles (NPs) are performed in the bouncing and fragmentation regimes for the particles with diameters from 8 nm to 30 nm, impact velocities from 100 ms−1 to 5000 ms−1, and in the whole range of the geometric impact parameter. The critical sticking velocity of 6H-SiC NPs reduces from ∼490 ms−1 to ∼150 ms−1 when the NP diameter increases from 10 nm to 30 nm. Below the melting threshold, the collision of crystalline NPs induces the formation of localized zones of densified material, while the remaining parts of NPs are not affected by plastic deformations. The impact of amorphous NPs results in the plastic deformation of significant parts of the NP material and much larger irreversible losses of mechanical energy. The post-collision translational and rotational velocities of crystalline NPs as well as coefficients of restitution (CORs) demonstrate weak dependence on the NP size if the NP diameter is greater than 20 nm. At constant impact velocity, the normal COR only marginally varies for head-on and oblique collisions, when the collision angle is smaller than ∼53°. The tangential center-of-mass and point-of-contact CORs, as functions of the impact parameter, demonstrate extremal behavior with the minima at collision angles from ∼27° to ∼37°. The normal COR exhibits a linear decay as a function of the impact velocity where the slope coefficient is different below and above the melting threshold. The tangential CORs attain the minimum values at the impact velocity of ∼300 ms−1. The obtained results are summarized in the form of fitting equations for CORs as functions of the impact parameter and velocity, which can be readily used to predict the post-collision translational and angular velocities of NPs in large-scale simulations of granular gas flows.

Application of factorization machine with quantum annealing to hyperparameter optimization and metamodel‐based optimization in granular flow simulations

AbstractThis study examined the applicability of factorization machines with quantum annealing (FMQA) to the field of landslide risk assessment for two specific black‐box optimization problems, hyperparameter optimization (HPO) for metamodeling and metamodel‐based simulation optimization (MBSO) targeting granular flow simulation using discrete element method (DEM). These two optimization problems are solved successively: HPO is first performed to determine the hyperparameters of the Gaussian process regression (GPR) metamodel, which is then used as a low‐cost, fast approximate solver of granular flow simulations for MBSO. After conducting a series of granular flow simulations using DEM, a metamodel is created that outputs a risk index of interest, the run‐out distance, from its input parameters by employing GPR with two hyperparameters, length‐scale and signal variance. Subsequently, HPO is performed to obtain the optimal set of hyperparameters by applying FMQA and other optimization methods using another set of hyperparameters determined using the gradient‐ascent method as the reference solution. Finally, using the metamodel created by each optimization method as an approximate solver for DEM simulations, MBSO is performed to find the optimal target output, the maximum run‐out distance, in the space of physical input parameters for risk assessment. A comparison of the performance of FMQA with that of other methods shows that FMQA is competitive in terms of efficiency and stability with state‐of‐the‐art algorithms such as Bayesian optimization.

Subspace graph networks for real-time granular flow simulation with applications to machine-terrain interactions

Granular flows interacting with rigid bodies are key to machine-terrain interactions in robotics and related fields, and still pose several open problems. Continuum methods and deep learning, separately and in combination, show promise. This research advances machine learning methods for modeling rigid body-driven granular flows, for terrestrial industrial machine and planetary rover (where gravity is an important factor) applications. The original contribution of this research is the application of a subspace machine learning simulation approach for these engineering problems. To generate training datasets, a high-fidelity continuum method, the material point method (MPM) is utilized. Principal component analysis (PCA) is used to reduce the dimensionality of data. It is shown that the first few (8 in our datasets) principal components of our high-dimensional data keep almost the entire variance in data. A graph network simulator (GNS) is trained to learn the underlying subspace dynamics. The learned GNS is then able to predict particle positions and interaction forces with good accuracy, averaging 6×10−5 and 3×10−6 mean squared position error and 7% and 17% mean percentage force error, for excavation and wheel data, respectively. More importantly, PCA significantly enhances the time and memory efficiency of GNS in both training and rollout. This enables GNS to be trained using a single desktop graphics processing unit (GPU) with moderate video random-access memory (VRAM). This also makes the GNS real-time on large-scale 3D physics configurations (700x faster than our continuum method), which is the first demonstration of such significantly accelerated high-fidelity granular flow engineering simulations.

A machine learning-based simplified collision model for granular flows

This study aims to create an efficient, rapid, and reliable particle collision model utilizing machine learning techniques for granular flow simulations. A simplified surrogate collision model developed in the framework of a Hybrid Euler–Lagrange (HEL) technique was successfully applied to model particle interactions for flows with a low fraction of the granular phase. The precision of the simplified collision model was evaluated using experimental data obtained from the in-house, two-stream particle collision test rig, focusing on solid phase velocity profiles. The implemented model demonstrates strong concordance with the experimental results. The simulations carried out highlight the relation between the simulation time step and the collision rate, which affects the cost of the numerical simulation. The execution time for both the conventional Discrete Element Method (DEM) on a CPU and the streamlined collision HEL model saw a reduction exceeding 70%.

Application of Material Point Method and Mohr-Coulomb Strain Softening Constitutive Model in Simulations of Multiphase Granular Flows

Application of Material Point Method and Mohr-Coulomb Strain Softening Constitutive Model in Simulations of Multiphase Granular Flows

Investigation of granular flow run-out behavior under dilative and compressive Coriolis conditions using DEM simulation

Centrifuge modeling allows granular flows to be simulated under stresses characteristic of full-scale flows, while maintaining repeatability. However, the impact of the Coriolis effect on the run-out behavior of dry granular flows is not fully understood. In this study, using the discrete element method (DEM), we conducted simulations of dry granular flow both with and without Coriolis (dilative and compressive) conditions to analyze the impact of the Coriolis effect on granular run-out mobility, flow structure, and granular interaction. For unsteady flows, the dilative Coriolis force increased the moving distance of the flow centroid by 60%–70% and increased the maximum kinetic energy by 5%–17%, whereas those parameters were reduced by 30% and 2%–9%, respectively, under compressive Coriolis conditions. Results showed that selecting a lower centrifugal acceleration by reducing the rotational angular velocity in physical modeling is ineffective for realizing a weaker Coriolis effect. This study established that using a larger centrifuge could mitigate the Coriolis effect, but that this outcome became less notable as the centrifugal radius increased. Additionally, we suggest a preliminary relation that could be used to correct the results of experimental granular flow final run-out distance obtained using a geotechnical centrifuge.

Simulation of granular surface flows using incompressible non-Newtonian SPH (INNSPH) method

This study presents a comprehensive continuum approach to modeling granular surface flows using the Incompressible Non-Newtonian Smoothed Particle Hydrodynamics (INNSPH) method. The model integrates an incompressible SPH method, where pressure is computed by solving a pressure-Poisson equation with a non-Newtonian rheology. Projection-based SPH has a strong and rigorous theoretical basis can lead to stable and accurate simulations. This paper aims to develop a projection-based SPH method for modeling complex granular flows. INNSPH method combines incompressible SPH and μ(I) rheology models to simulate non-Newtonian viscoplastic fluid behavior in granular flows. Surface deposition, and velocity and pressure fields are estimated using a rheology model. Validation is performed by comparing simulation results, including surface profiles and run-out distances with experimental data, showing good agreement. INNSPH method is then employed to model a 2D column collapse and a dam-break scenario on horizontal and inclined planes for sands and glass beads. The method captures three distinct final deposition morphologies; truncated cone, conic, and Mexican hat shapes in collapsing columns. INNSPH computational efficiency enables simulations of large-scale granular flows, and its open-source nature facilitates collaboration and further modifications by researchers. The method provides a good understanding of granular flow dynamics in various industrial applications including powder technology.

Insights into the Movement and Diffusion Accumulation Characteristics of a Catastrophic Rock Avalanche Debris—A Case Study

In this study, the 1991 rock avalanche, in Touzhai, Zhaotong, Yunnan, China, was considered the study object. The investigation of the landslide accumulation body revealed that the Touzhai rock avalanche accumulation body has the characteristics of wide gradation and poor sorting. A combination of field investigations, indoor and outdoor experiments, and numerical simulations were used to invert the occurrence and spreading range of rock avalanche-debris flow hazards. To invert and analyze its dynamics and the crushing process, a three-dimensional discrete element modeling was performed on the real terrain data. Simulation results showed that the movement time of the numerically simulated Touzhai rock avalanche was approximately 200 s. After 50 s of movement, the peak velocity reached 32 m/s, and the velocity gradually decayed after the sliding mass rubbed violently against the valley floor and collided with the mountain. Due to the meandering nature of the gully, the sliding mass makes its way down the gully and constantly collides with the mountain, making particles appear to climb, with some particles being blocked by the valley. After 150 s of movement, the average velocity rate decreased substantially, and the landslide-avalanche debris reached the mouth of the trench. After 200 s of movement, the average sliding velocity tends to 0 m/s, where the avalanche debris tends to stop and accumulate. When the rock avalanche movement reaches the mouth of the gully, the avalanche debris spreads to the sides as it is no longer bounded by the hills on either side of the narrow gully, eventually forming a ‘trumpet-shaped’ accumulation, and the granular flow simulation matched the findings of the landslide site accumulation.

Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

A mesh-free particle method for continuum modelling of granular flow

Based on the continuum model for granular media developed in Dunatunga et al. we propose a mesh-free generalized finite difference method for the simulation of granular flows. The model is given by an elasto-viscoplastic model with a yield criterion using the μ(I) rheology from Jop et al. The numerical procedure is based on a mesh-free particle method with a least squares approximation of the derivatives in the balance equations combined with the numerical algorithm developed in Dunatunga et al. to compute the plastic stresses. The method is numerically tested and verified for several numerical experiments including granular column collapse and rigid body motion in granular materials. For comparison a nonlinear microscopic model from Lacaze et al. is implemented and results are compared to the those obtained from the continuum model for granular column collapse and rigid body coupling to granular flow.

Experimental and numerical analyses of gravity-driven granular flows between vertical parallel plates for solar thermal energy storage and transport

Gravity-driven granular flows between vertical parallel plates were considered at elevated temperatures to examine flow behavior and inform solar thermal energy storage and transport infrastructure design and performance. A series of experiments was performed at inlet temperatures of 23, 200, 400, 600, and 800 °C in a high-temperature granular flow experimental rig and spatial and temporal velocity and surface temperature fields were measured. Granular flows were observed to change as a function of temperature. The interaction between the particles and the wall significantly increased with decreases in channel widths. Particle velocities at the outlet of the channel were compared with results from numerical model using the discrete element method. Temperature-dependent flow properties directly related to the assembly were measured and used for granular flow simulation. Flow behavior within the channel was investigated from the simulated results by obtaining particle volume fractions and particle velocities. Wall temperature and outlet granular flow temperature were monitored during the flow experiment and temporal heat loss in the flow was calculated. The granular flow behavior and heat transfer analysis from both the experiment work and simulation provide important mass transfer information for heat transfer modeling at elevated temperature.

A new method for DEM simulation of dust-bearing granular flow – Modeling the effect of dust on the change in granule friction coefficient

The simulation of dust-bearing granular accumulation flow in the theoretical and practical aspects of the engineering field poses a significant challenge due to the massive computational requirements associated with cross-scale simulations. In this study, a novel approach is proposed to address this issue by developing a model that accounts for the impact of dust on granular flow through changes in the granule friction coefficient. Initially, the theoretical analysis was conducted to examine the effects of dust on granular flow. Subsequently, a method was developed to measure the equivalent friction coefficient of granules by combining theoretical analysis and experimental work. The proposed method was then employed to simulate the stability of a spherical granule pile in a drum influenced by dust content and compared against experimental results. The simulation results demonstrate agreement with the experimental results, indicating the feasibility of modeling the effect of dust on dust-bearing granular flow through the granule equivalent friction coefficient. The dust effect can be considered equivalent to a change in the granule friction coefficient, which facilitates the reduction of the computational load generated by the Discrete Element Method (DEM) method and enables cross-scale simulations.

Signed distance field enhanced fully resolved CFD-DEM for simulation of granular flows involving multiphase fluids and irregularly shaped particles

It is challenging to model granular particles with arbitrary shapes and related complications to fluid–particle interactions for granular flows which are widely encountered in nature and engineering. This paper presents an improved framework of the immersed boundary method (IBM)-based fully resolved computational fluid dynamics (CFD) and discrete element method (DEM), with an emphasis on irregular-shaped particles and the implications to particle–fluid interactions. The improved CFD-DEM framework is featured by two novel enhancements with signed distance field (SDF). First, an SDF-based formulation is employed to enable handling of granular particles with arbitrary shapes in DEM robustly and efficiently. Second, the IBM is modified to be consistent with SDF to fully resolve fluid–particle interactions in the presence of non-spherical particles. Such treatments leverage SDF as a generic interface to furnish a new SDF-CFD-DEM framework for universal modeling of arbitrarily shaped particles interacting with multiphase fluids with desired resolutions. Exemplified particle shape models include super-quadrics, spherical harmonics, polyhedron and level set, and new shape models can be flexibly developed by implementing the unified SDF-based shape interface. The proposed SDF-CFD-DEM is validated and showcased with examples including particle settling, drafting–kissing–tumbling, immersed granular collapse, and mudflow. The results demonstrate the good accuracy and robustness of the SDF-CFD-DEM and its potential for efficient computational modeling of multiphase granular flows involving granular particles with arbitrary shapes.

A novel Minkowski sum contact algorithm for arbitrarily shaped particles constructed by multiple dilated DEM models

Nonspherical granular materials are widely used in various industrial fields. Because the simulation of mixed granular flows consisting of arbitrarily shaped particles with smooth surfaces modeled by multiple discrete element models remains difficult for practical applications, a novel Minkowski sum contact algorithm in the CUDA-GPU architecture was proposed. In this algorithm, super-ellipsoidal equations, spherical harmonic functions, and polyhedrons were used to model differently shaped particles with smooth surfaces using the Fibonacci and Minkowski sum algorithms. Subsequently, single or multiple contact points between arbitrarily shaped particles were determined using the Minkowski sum contact algorithm. The automatic mesh simplification and GPU parallel computing methods were employed to improve the calculation efficiency of the discrete element method. The conservation, accuracy, and robustness of the proposed algorithm were verified by four sets of numerical examples: elastic collisions between particles, inelastic collisions between particles, accumulation of multiple particles, and dynamic granular flows. The relative DEM results show good agreement with the analytical solution, which indicates that the proposed Minkowski sum contact algorithm can accurately reflect the dynamic properties of arbitrarily shaped granular materials containing differently dilated DEM models.

Particle fluctuations and their effects on the rheological behavior of sheared granular flows

We present numerical simulations of plane-sheared granular flows in two pressure-controlled configurations and investigate the particle fluctuations over a wide range of the inertial number I. Quantities affecting the velocity fluctuations, including the granular temperature and the stress ratio, are shown to be intrinsically related and to exhibit similar I-dependent characteristics. We first propose a scaling law describing the one-to-one relationship between the granular temperature and I in both the inertial and collisional regimes, where the volume fraction plays an important role. This relation differs from the power-law dependence between the stress ratio and I. However, for low values of I, these two velocity fluctuation quantities deviate from the one-to-one relation, similar to the effective friction coefficient μ. Based on the obtained inverse power law, we propose a new unified model incorporating the stress ratio to describe the rheological behaviors in the quasistatic, inertial, and collisional regimes. The proposed model is more applicable than the one that integrates the granular temperature, allowing nonlocal effects to be roughly eliminated at low values of I and the rheological dependence on the volume fraction to be effectively removed at high values of I. This provides an alternative approach for developing rheological models for granular materials under complex flow conditions.

Efficient lattice Boltzmann simulation of free-surface granular flows with μ(I)-rheology

This paper presents a lattice Boltzmann framework for accurate and efficient simulation of free-surface granular flows. The granular assembly is treated as a viscoplastic fluid, whose apparent viscosity varies locally with the shear rate and pressure according to a regularized μ(I)-rheology. A single-phase free-surface model is employed to track the evolution of the particle-air interface. The lattice Boltzmann implementation is first validated by simulating a steady-state granular flow on a rough inclined plane and a good agreement with the analytical solution is achieved. The validated model is then applied to simulate a transient granular column collapse problem. Compared to a companion discrete element simulation, the lattice Boltzmann model with the μ(I)-rheology is able to capture the overall dynamic behaviors of granular column collapse. However, a different behavior is observed when a similar Bingham viscoplastic model with a fixed yield stress is applied, highlighting the pressure dependent nature of granular flows. The proposed lattice Boltzmann formulation is highly efficient compared to the conventional computational fluid dynamics, and has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular physics.