SPH–DCDEM model for arbitrary geometries in free surface solid–fluid flows

doi:10.1016/j.cpc.2016.01.006

Computer Physics Communications

Volume 202, May 2016, Pages 131-140

https://doi.org/10.1016/j.cpc.2016.01.006 Get rights and content

Abstract

A unified discretization of rigid solids and fluids is introduced, allowing for resolved simulations of fluid–solid phases within a meshless framework. The numerical solution, attained by Smoothed Particle Hydrodynamics (SPH) and a variation of Discrete Element Method (DEM), the Distributed Contact Discrete Element Method (DCDEM) discretization, is achieved by directly considering solid–solid and solid–fluid interactions. The novelty of the work is centred on the generalization of the coupling of the DEM and SPH methodologies for resolved simulations, allowing for state-of-the-art contact mechanics theories to be used in arbitrary geometries, while fluid to solid and vice versa momentum transfers are accurately described. The methods are introduced, analysed and discussed. Initial validations on the DCDEM and the fluid coupling are presented, drawing from test cases in the literature. An experimental campaign serves as a validation point for complex, large scale solid–fluid flows, where a set of blocks in several configurations is subjected to a dam-break wave. Blocks are tracked and positions are then compared between experimental data and the numerical solutions. A Particle Image Velocimetry (PIV) technique allows for the quantification of the flow field and direct comparison with numerical data. The results show that the model is accurate and is capable of treating highly complex interactions, such as transport of debris or hydrodynamic actions on structures, if relevant scales are reproduced.

Introduction

The characterization of solid–fluid and solid–solid interactions in free-surface flows transporting or in contact with solid objects represents a problem common to several engineering disciplines such as coastal, offshore, maritime and fluvial engineering. Applications include assessment of the severity of hydrodynamic actions on structures, risk assessment of natural hazards, design of floating bodies or design of exposed structures. Simple conceptual models can be drawn with the common simplification of assuming the solid material as perfectly rigid and the fluid as Newtonian. The mathematical formulation of problems involving complex geometries and frequent solid–solid interactions becomes simple but actual solutions are necessarily numerical and, in general, difficult to calculate. A computational tool designed to solve these interactions must be computationally scalable, as it should be able to (i) model all physically relevant scales at which fluid–solid interactions may occur in a given case, or (ii) incorporate extra simplifications, admissible for its spatial range of application. For instance, in many engineering applications, solid objects are much larger than the smallest flow scales, which means that the involved Reynolds numbers become large, allowing for neglecting viscous modes of momentum transfer [1]. However, for the purpose of providing a general model, relevant modes of interaction are not always evident, in which case high spatial and temporal resolutions must be attainable. Furthermore, some simulations may require remarkably large domains. This stresses the need for high performance models and implementations.

Within the meshless framework, efforts have been made on unifying solid and fluid modelling. Attempts to couple Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) have recently taken place, mainly for the modelling of industrial processes. Unresolved models gain popularity in this area mainly due to the lower computational cost, since the solid grains have a similar size to the fluid resolution. The DEM particle data is averaged with the SPH operators to use in the fluid phase, typically introducing empirical formulas for drag estimation. Fernandez et al. [2] used a one-way coupled SPH–DEM model to model the behaviour of a slurry flow on a vibrating screen, using regular but non spherical DEM particles that do not experience fluid forces. Sun et al. [3] and Cleary [4] presented fully coupled models, validating them with rotating drums filled with solid–fluid mixtures. Robinson et al. [5] employed a parametrized drag force using the local values of porosity and bulk fluid variables to couple a DEM and SPH models, successfully recovering sedimentation behaviour for a collection of spherical solid particles. In contrast, resolved models allow to discard most of the empirical formulations dealing with the solid–fluid coupling. Koshizuka et al. [6] modelled a rigid body as a collection of Moving Particle Simulation (MPS) fluid particles, rigidified by default. Particles that constitute a rigid body had their relative position fixed and were regarded by the fluid particles as MPS particles. This has become the standard approach for resolved models due to its simplicity and elegance. Monaghan et al. [7] and Rogers et al. [8] employed the same principle when modelling the effects of wave interaction on rigid bodies with SPH and special considerations for the particles that belonged to the solid body, effectively including a form of frictional behaviour. For solid normal interactions, empirical continuum potential based forces were used, not based in contact mechanics theories. Maruzewski [9] modelled the solid as a rigid boundary with imposed motion, using the ghost particle technique. Hashemi et al. [10] and Amicarelli et al. [11] also used a ghost particle method when modelling free floating bodies, each including particular ah-hoc considerations for solid–solid interactions. The ghost particle approach encounters generalization issues for arbitrary geometries and is usually used for fairly regular boundaries. Potapov et al. [12] used the same technique to treat the solid–fluid interaction but treated the solid–solid contacts with DEM and was limited to use exclusively sphere or disc shaped bodies.

This work is aimed at describing and validating a numerical tool based on SPH and DEM able to describe the motion of arbitrarily shaped solids in viscous fluids with no special boundary treatment. The modelling tool employed is the DualSPHyics code [13] and, to fulfil the stated objectives, key innovations are introduced in what concerns solid–fluid and solid–solid interactions. The more relevant concern the generalization of the fundamental technique of Koshizuka et al. [6] and the inclusion of a state-of-the-art Distributed Contact DEM (DCDEM) formulation, similar in concept to those employed by both Zhang et al. [14] and Ren et al. [15]. A $δ$ -SPH [16] term is added to the continuity equation, controlling the density field fluctuations and contributing for the mitigation of known solid–fluid interface deficiencies [17], particularly the development of a hydrophobic area that results in a reorganization of the fluid particle positions. Boundary or any particle belonging to a rigid body regard other solid particles as DEM elements, expanding on the concept of DCDEM introduced by Cummins and Cleary [18]. This means that the DualSPHyics meshless framework is effectively used to solve the fluid phase, fluid–solid interaction and solid phase simultaneously.

DualSPHysics enables simulation of millions of particles at a reasonable computation time by using GPU cards (Graphics Processing Units) as the execution devices. This allows to somewhat alleviate the previously expressed concerns about requirements of scale and resolution, since the computations are made up to two orders of magnitude faster than on conventional CPU systems [19]. A Multi-GPU code was developed to further compensate the increased memory consumption of running large-scale, high-resolution simulations. [20] showed that very high efficiency was achieved for tens of GPUs using the Multi-GPU implementation of DualSPHysics. The implementation has been validated for interaction between fluid and fixed structures [21], [22], [23].

The experimental data from Zhang et al. [14] is used to establish the effectiveness of the DCDEM discretization and the DCDEM–SPH model, using a small scale fluid–solid dam-break and comparing the results acquired with a high speed camera. An extensive experimental campaign was developed with the objective of providing data to validate the model in larger scales, both in time and space. A highly unsteady flow acts on initially resting objects, causing the collapse of the structure formed by their initial position. They are then dragged while interacting with the bottom of the flume. The objects were tracked and the hydrodynamics of the impact are measured with a Particle Image Velocimetry (PIV) technique, allowing a characterization of the flow and movement of the objects. The results from the model show accurate recovery of the motion of the objects, as well as the hydrodynamic quantities involved.

Section snippets

Method formulation

In SPH, the fluid domain is represented by a set of nodal points where physical quantities such as position, velocity, density and pressure are approximated at. These points move with the fluid in a Lagrangian manner and their properties change with time due to the interactions with neighbouring nodes. The term Smoothed Particle Hydrodynamics arises from the fact that the nodes, for all intended means, carry the mass of a portion of the medium, hence being easily labelled as “particles”, and

Discretization of fluid governing equations with SPH

The proposed SPH formulation relies on the discretization of the Navier–Stokes (NS) and continuity equations. Written for a variable density and neglecting the divergence of the velocity field in the NS equations, these are $\frac{d v}{d t} = - \frac{\nabla p}{ρ} + \frac{μ}{ρ} \nabla^{2} v + g$ $\frac{d ρ}{d t} = - ρ \nabla v,$ where $v$ is the velocity field, $p$ is the pressure, $ρ$ is the density and $μ$ and $g$ are the kinematic viscosity and body forces per unit mass, respectively. The system is written in such a way as to avoid the necessity of solving a Poisson equation,

Discretization of rigid body equations and contact forces with DCDEM

Following the original idea of Koshizuka et al. [6], a rigid body $I$ is represented by a set of particles whose relative positions remain unchanged. The volume of $I$ is discretized by such collection of particles, for notation simplicity also called $I$ . These are subject to a different set of equations from the normal SPH particles. Newton’s equations for rigid body dynamics are used, and their discretization consists of summing the contributions from each particle as $M_{I} \frac{d V_{I}}{d t} = \sum_{k \in I} m_{k} \frac{d v_{k}}{d t}$ $I_{I} \frac{d Ω_{I}}{d t} = \sum_{k}$

DCDEM and SPH–DCDEM results

Zhang et al. [14] devised an experimental set up in order to validate a similar SPH–DEM model. Solid cylinders were stacked in an acrylic resin tank with a length of 26 cm, a width of 10 cm and a height of 26 cm. The solid cylinders were made of aluminium and had a density of $2.7 \times 10^{3} kg / m^{3}$ , diameter of 1.0 cm and length of 9.9 cm. The initial conditions are enforced by a vertical gate 6 cm from the left wall. 6, 8, 10 and 12 layers of cylinders were used. The position of the cylinders was

Conclusions and future work

A general SPH–DCDEM discretization, expanded to support the inclusion of arbitrarily shaped rigid solids, was presented and discussed. This allows for a unified description of two media, without using extra terms in the discretization to account for coupling and geometrical effects.

Reproducing the results from Zhang et al. [14] for dry cases and solid–fluid mixtures presents a compelling case for the accuracy and robustness of the proposed method. Various time scales are seamlessly

Acknowledgements

This research was partially supported by project PTDC/ECM/117660/2010, funded by the Portuguese Foundation for Science and Technology (FCT). First author acknowledges FCT for his Ph.D. grant, SFRH/BD/75478/2010.

This work was partially financed by Xunta de Galicia under project Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas (Grupos de Referencia Competitiva) co-funded by European Regional Development Fund (FEDER), and also financed by Ministerio de Economía

References (43)

J. Fernandez et al.
Miner. Eng.
(2011)
X. Sun et al.
J. Comput. Phys.
(2013)
M. Robinson et al.
Int. J. Multiph. Flow
(2014)
M. Hashemi et al.
Int. J. Non-Linear Mech.
(2012)
A.V. Potapov et al.
Powder Technol.
(2001)
A. Crespo et al.
Comput. Phys. Comm.
(2015)
S. Zhang et al.
J. Comput. Phys.
(2009)
D. Molteni et al.
Comput. Phys. Comm.
(2009)
A. Colagrossi et al.
J. Comput. Phys.
(2003)
S.J. Cummins et al.
Appl. Math. Model.
(2011)

J. Domínguez et al.

Comput. Phys. Comm.

(2013)

J. Domínguez et al.

Comput. Phys. Comm.

(2013)

C. Altomare et al.

Comput. Struct.

(2014)

C. Altomare et al.

Coast. Eng.

(2015)

R. Dalrymple et al.

Coast. Eng.

(2006)

J.P. Morris et al.

J. Comput. Phys.

(1997)

D. Price

J. Comput. Phys.

(2008)

H. Kruggel-Emden et al.

Powder Technol.

(2007)

M. Lemieux et al.

Powder Technol.

(2008)

H. Kruggel-Emden et al.

Chem. Eng. Sci.

(2008)

C. Shu et al.

J. Hydraul. Res.

(2011)

Cited by (114)

Development and test of FDEM–FLOW-3D—A CFD–DEM model for the fluid–structure interaction of Accropode<sup>TM</sup> blocks under wave loads
2024, Ocean Engineering
In this study, a new coupled Computational Fluid Dynamics-Discrete Element Method (CFD–DEM) model was developed to investigate the stability of Accropode^TM blocks on a sloping breakwater under wave loads. The widely used CFD software FLOW-3D was customized by integrating it with the combined Finite-Discrete Element Method (FDEM) code, which accurately simulates the complex contact and interlocking behavior between multiple polyhedron blocks. The coupling strategy employed in this model involved the FDEM code updating the contact forces and torques at each time step, while FLOW-3D simulated the wave-structure interaction, and then calculated the position and velocity of the blocks for the next time step. Key information exchange between the two codes was facilitated through shared files. To validate the stability and accuracy of the CFD–DEM model, a series of cases were conducted. The results showed good agreement with theoretical results, demonstrating the high accuracy of the model. Furthermore, a representative case involving the interaction between waves and Accropode^TM blocks on a sloping breakwater was analyzed to evaluate the capabilities of the CFD–DEM model. The time histories of block displacement, wave force, and contact force were examined. The findings revealed that blocks located within one wave height above and below the still water level experienced more disturbances compared to other blocks, which aligns with engineering practices. These results collectively demonstrate that the presented CFD–DEM model is capable of simulating the complex wave-structure interactions with a reasonable level of accuracy.
Two-phase modelling of erosion and deposition process during overtopping failure of landslide dams using GPU-accelerated ED-SPH
2024, Computers and Geotechnics
Erosion and deposition induced by overtopping flow strongly impacts the breaching evolution of landslide dams. However, these two processes are not yet sufficiently captured in current dam breaching models. In this paper, we simulate the Erosion and Deposition process during overtopping dam breaching using a novel Smooth Particle Hydrodynamics (ED-SPH) method. A new multi-function boundary is proposed to prevent the penetration of water and soil particles and ensure steady inflows. Dam break and movable erosion scenarios are simulated as a means to validate the model. Dam breach simulations using the ED-SPH method reveal that the proposed model can capture the complex dam soil erosion, entrainment, and depositions behaviors. The soil deposition hinders the eroded particle movement and reduces the water velocity at the water-soil interface. If soil deposition is not considered, as in many existing models, the breaching time decreases and the outburst flood discharge is magnified. We further investigate the re-erosion of deposited soils by varying the re-erosion coefficient. With decreasing the re-erosion coefficient, the peak discharge increases whereas the residual dam height decreases due to the blockage by the deposited soils.
Numerical simulation of dike failure using a GPU-based coupled DEM–SPH model
2023, Computers and Fluids
Dike failure includes a complex fluid–solid interaction process, which is one of the challenges in investigating dike failure problem. Given the characteristics of dike failure, a GPU-based coupled discrete element method (DEM)-smoothed particle hydrodynamics (SPH) model is proposed and adopted to simulate dike failure problems in this study. GPU parallel computing is involved in the proposed model and solid and fluid phases are modeled by DEM and SPH respectively. Overtopping-induced dike failure is numerically tested to validate the proposed model, and the computed motion of sediments and water and the dike surface profiles are in good agreement with experimental results. Then the proposed model is adopted to simulate seepage-induced dike failures, which have relatively covert behaviors compared with the overtopping-induced dike failure. The evolution of dike saturated zone and sediment displacement during this process is studied, and a sensitivity analysis of sediment diameter indicates that it has a great impact on the dike deformation. Finally, the effect of bottom drainage length on the development of seepage inside dike is investigated.
Three-dimensional numerical investigation of floating debris effects on bridge superstructures during tsunamis
2023, Ocean Engineering
Catastrophic tsunamis occur around the world and as coastal communities continue to grow, consideration of cascading tsunami-borne debris effects on coastal structures becomes increasingly important. The objective of the present study is to address the gap in existing knowledge by advancing the fundamental understanding of the debris-tsunami-structure interaction of floating containers and quantifying the forces on representative bridge superstructures. To this end, a coupled SPH-FE modeling approach is calibrated against data from prior experiments and then used for conducting an extensive three-dimensional investigation. The results demonstrate that the initial water level, the elevation of the bridge and the bore properties have a significant effect on the debris trajectory, velocity and pitching, as well as, the forces on the superstructure. Moreover, there exist three different patterns in the debris-flow-deck interaction of containers aligned transverse to the flow (i.e. parallel to the bridge), which affect the direction of debris forces and their spatial and temporal evolution. Overall, the debris generates impulsive forces in both horizontal and vertical directions and consequently increase the total loads by a factor of 2.67 and 1.85, on average in the two directions, revealing the critical need to consider such effects in tsunami design guidelines and risk assessment frameworks.
A resolved SPH-DEM coupling method for analysing the interaction of polyhedral granular materials with fluid
2023, Ocean Engineering
Hybrid fluid–particle systems are prevalent in nature and engineering practices, but accurately simulating the dynamic behaviour is challenging due to their inherent strong non-linearity. This study proposes a three-dimensional resolved numerical framework for analysing complex shape polyhedron–fluid interaction. The weakly compressible smoothed particle hydrodynamics (SPH) is employed to describe the complex hydrodynamic behaviour, and the discrete element method (DEM) is applied to solve the motion of irregular polyhedral granular materials. An accurate contact collision algorithm is implemented in the coupling model to address the dynamic response of polyhedral particles. The high-fidelity modelling of the complex morphology of granular materials is realised. Hence, the coupling code is developed based on two high-performance open-source platforms, and an efficient two-way coupling scheme is designed to manage the fluid–particle interaction under a unified time framework. The reliability and the applicability of the SPH-DEM solver are demonstrated through extensive validations based on existing experimental and numerical data involving violent free-surface flow impacting multiple rigid bodies and cube deposition. Furthermore, a more complex case of wave-flow impact on rock piles is conducted, exhibiting great potential to employ this model in real-life engineering problems.
Three-dimensional fully-Lagrangian DEM-SPH modeling of river ice interaction with control structures
2023, Cold Regions Science and Technology
Ice control structures (ICSs) play a vital role in preventing ice jams and safeguarding communities by either stabilizing ice cover or relocating jams upstream. Understanding and modeling the interaction between ice floes and these structures is crucial for assessing their effectiveness and optimizing their designs. However, simulating these complex multi-physics systems poses challenges for numerical techniques. In this paper, we introduce and evaluate a fully-Lagrangian mesh-free continuum-discrete model based on the Smoothed Particles Hydrodynamics (SPH) method and Discrete Element Method (DEM) for three-dimensional (3D) simulation of ice interactions with control structures. To validate and parameterize the numerical model, we conduct two sets of experiments using real and artificial ice materials: (1) dam-break wave-ice-structure interaction and (2) ice-ICS interaction in an open channel. By comparing numerical and experimental results we demonstrate the capability and relative accuracy of our model. Our findings indicate that real ice generally exhibits faster jam evolution and ice passage through the ICS compared to artificial ice. Moreover, we identify the Froude number and ice material type as important factors influencing jam formation, evolution, and ICS effectiveness. Through sensitivity analysis of material properties, we highlight the significant impact of friction and restitution coefficients.

View all citing articles on Scopus

¹: http://ephyslab.uvigo.es.

View full text

SPH–DCDEM model for arbitrary geometries in free surface solid–fluid flows

Abstract

Introduction

Section snippets

Method formulation

Discretization of fluid governing equations with SPH

Discretization of rigid body equations and contact forces with DCDEM

DCDEM and SPH–DCDEM results

Conclusions and future work

Acknowledgements

Miner. Eng.

J. Comput. Phys.

Int. J. Multiph. Flow

Int. J. Non-Linear Mech.

Powder Technol.

Comput. Phys. Comm.

J. Comput. Phys.

Comput. Phys. Comm.

J. Comput. Phys.

Appl. Math. Model.

Comput. Phys. Comm.

Comput. Phys. Comm.

Comput. Struct.

Coast. Eng.

Coast. Eng.

J. Comput. Phys.

J. Comput. Phys.

Powder Technol.

Powder Technol.

Chem. Eng. Sci.

J. Hydraul. Res.