Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression...... of the grains. This is true even of the resilient (or reversible) deformations. It is also interesting because the Discrete Element Method models resilient and plastic deformations as well as failure in a single process.The paper describes two types of calculations. One on a small sample of angular elements...... subjected to a pulsating (repeated) biaxial loading and another of a larger sample of circular element subjected to a plate load. Both cases are two dimensional, i.e. plane strain.The repeated biaxial loading showed a large increase in plastic strain for the first load pulse at a given load level...
Energy Technology Data Exchange (ETDEWEB)
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Certain Discrete Element Methods in Problems of Fracture Mechanics
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available In this paper two discrete element methods (DEM are discussed. The free hexagon element method is considered a powerful discrete element method, which is broadly used in mechanics of granular media. It substitutes the methods for solving continuum problems. The great disadvantage of classical DEM, such as the particle flow code (material properties are characterized by spring stiffness, is that they have to be fed with material properties provided from laboratory tests (Young's modulus, Poisson's ratio, etc.. The problem consists in the fact that the material properties of continuum methods (FEM, BEM are not mutually consistent with DEM. This is why we utilize the principal idea of DEM, but cover the continuum by hexagonal elastic, or elastic-plastic, elements. In order to complete the study, another one DEM is discussed. The second method starts with the classical particle flow code (PFC - which uses dynamic equilibrium, but applies static equilibrium. The second method is called the static particle flow code (SPFC. The numerical experience and comparison numerical with experimental results from scaled models are discussed in forthcoming paper by both authors.
A Review of Discrete Element Method Research on Particulate Systems
Mahmood, A. A.; Elektorowicz, M.
2016-07-01
This paper summarizes research done using the Discrete Element Method (DEM) and explores new trends in its use on Particulate systems. The rationale for using DEM versus the traditional continuum-based approach is explained first. Then, DEM application is explored in terms of geotechnical engineering and mining engineering materials, since particulate media are mostly associated with these two disciplines. It is concluded that no research to date had addressed the issue of using the DEM to model the strength and weathering characteristics of peaty soil-slag-Portland cement-fly ash combinations.
Analysis of bender element test interpretation using the discrete element method
O’Donovan, J.; O’Sullivan, C.; Marketos, G.; Muir Wood, D.
2015-01-01
While bender element testing is now well-established as a laboratory technique to determine soil stiffness, a robust technique to interpret the data remains elusive. A discrete element method (DEM) model of a face-centred cubic packing of uniform spheres was created to simulate bender element tests
3D mode discrete element method with the elastoplastic model
Institute of Scientific and Technical Information of China (English)
2012-01-01
The three-dimensional mode-deformable discrete element method (3MDEM) is an extended distinct element approach under the assumptions of small strain,finite displacement,and finite rotation of blocks.The deformation of blocks is expressed by the combination of the deformation modes in 3MDEM.In this paper,the elastoplastic constitutive relationship of blocks is implemented on the 3MDEM platform to simulate the integrated process from elasticity to plasticity and finally to fracture.To overcome the shortcomings of the conventional criterion for contact fracturing,a new criterion based on plastic strain is introduced.This approach is verified by two numerical examples.Finally,a cantilever beam is simulated as a comprehensive case study,which went through elastic,elastoplastic,and discontinuous fracture stages.
7th International Conference on Discrete Element Methods
Feng, Yuntian; Mustoe, Graham
2017-01-01
This book presents the latest advances in Discrete Element Methods (DEM) and technology. It is the proceeding of 7th International Conference on DEM which was held at Dalian University of Technology on August 1 - 4, 2016. The subject of this book are the DEM and related computational techniques such as DDA, FEM/DEM, molecular dynamics, SPH, Meshless methods, etc., which are the main computational methods for modeling discontinua. In comparison to continua which have been already studied for a long time, the research of discontinua is relatively new, but increases dramatically in recent years and has already become an important field. This book will benefit researchers and scientists from the academic fields of physics, engineering and applied mathematics, as well as from industry and national laboratories who are interested in the DEM. .
An implicit finite element method for discrete dynamic fracture
Energy Technology Data Exchange (ETDEWEB)
Gerken, Jobie M. [Colorado State Univ., Fort Collins, CO (United States)
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Modeling rammed earth wall using discrete element method
Bui, T.-T.; Bui, Q.-B.; Limam, A.; Morel, J.-C.
2016-03-01
Rammed earth is attracting renewed interest throughout the world thanks to its "green" characteristics in the context of sustainable development. Several research studies have thus recently been carried out to investigate this material. Some of them attempted to simulate the rammed earth's mechanical behavior by using analytical or numerical models. Most of these studies assumed that there was a perfect cohesion at the interface between earthen layers. This hypothesis proved to be acceptable for the case of vertical loading, but it could be questionable for horizontal loading. To address this problem, discrete element modeling seems to be relevant to simulate a rammed earth wall. To our knowledge, no research has been conducted thus far using discrete element modeling to study a rammed earth wall. This paper presents an assessment of the discrete element modeling's robustness for rammed earth walls. Firstly, a brief description of the discrete element modeling is presented. Then the parameters necessary for discrete element modeling of the material law of the earthen layers and their interfaces law following the Mohr-Coulomb model with a tension cut-off and post-peak softening were given. The relevance of the model and the material parameters were assessed by comparing them with experimental results from the literature. The results showed that, in the case of vertical loading, interfaces did not have an important effect. In the case of diagonal loading, model with interfaces produced better results. Interface characteristics can vary from 85 to 100% of the corresponding earthen layer's characteristics.
Discrete Element Method Simulations for Complex Granular Flows
Guo, Yu; Curtis, Jennifer Sinclair
2015-01-01
This review article focuses on the modeling of complex granular flows employing the discrete element method (DEM) approach. The specific topic discussed is the application of DEM models for the study of the flow behavior of nonspherical, flexible, or cohesive particles, including particle breakage. The major sources of particle cohesion—liquid induced, electrostatics, van der Waals forces—and their implementation into DEM simulations are covered. These aspects of particle flow are of great importance in practical applications and hence are the significant foci of research at the forefront of current DEM modeling efforts. For example, DEM simulations of nonspherical grains can provide particle stress information needed to develop constitutive models for continuum-based simulations of large-scale industrial processes.
Applications of the discrete element method in mechanical engineering
Energy Technology Data Exchange (ETDEWEB)
Fleissner, Florian, E-mail: fleissner@itm.uni-stuttgart.de; Gaugele, Timo, E-mail: gaugele@itm.uni-stuttgart.de; Eberhard, Peter [University of Stuttgart, Institute of Engineering and Computational Mechanics (Germany)], E-mail: eberhard@itm.uni-stuttgart.de
2007-08-15
Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples.
Mechanics of a crushable pebble assembly using discrete element method
Energy Technology Data Exchange (ETDEWEB)
Annabattula, R.K., E-mail: ratna.annabattula@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany); Gan, Y., E-mail: yixiang.gan@sydney.edu.au [School of Civil Engineering, University of Sydney, 2006 NSW, Sydney (Australia); Zhao, S. [College of Mechanical and Electronics Engineering, Hebei University of Science and Technology, Shijiazhuang, Hebei 050018 (China); Kamlah, M., E-mail: marc.kamlah@kit.edu [Institute for Applied Materials (IAM-WBM), Karlsruhe Institute of Technology (KIT), D-76344 Eggenstein-Leopoldshafen (Germany)
2012-11-15
The influence of crushing of individual pebbles on the overall strength of a pebble assembly is investigated using discrete element method. An assembly comprising of 5000 spherical pebbles is assigned with random critical failure energies with a Weibull distribution in accordance with the experimental observation. Then, the pebble assembly is subjected to uni-axial compression ({epsilon}{sub 33}=1.5%) with periodic boundary conditions. The crushable pebble assembly shows a significant difference in stress-strain response in comparison to a non-crushable pebble assembly. The analysis shows that a ideal plasticity like behaviour (constant stress with increase in strain) is the characteristic of a crushable pebble assembly with sudden damage. The damage accumulation law plays a critical role in determining the critical stress while the critical number of completely failed pebbles at the onset of critical stress is independent of such a damage law. Furthermore, a loosely packed pebble assembly shows a higher crush resistance while the critical stress is insensitive to the packing factor ({eta}) of the assembly.
Matsumoto, Takuma; Ogata, Kazuyuki; Yahiro, Masanobu
2009-01-01
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
The use of discrete orthogonal projections in boundary element methods
Brandts, J.
2001-01-01
In recent papers by Sloan and Wendland Grigorie and Sloan and Grigorie Sloan and Brandts a formalismwas developed that serves many important and interesting applications in boundary element methods the commutator property for splines Based on superapproximation results this property is for exam
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Application of Discrete Element Methods to the Problem of Rock Bumps
Directory of Open Access Journals (Sweden)
P. P. Procházka
2002-01-01
Full Text Available This paper is a continuation of a previous paper by the authors. Applications of two discrete element methods (DEM to several fields of geotechnics are discussed. The free hexagon element method is considered a powerful discrete element method, and is widely used in mechanics of granular media. It substitutes the methods for solving continuum problems. In order to complete the study, other discrete element methods are discussed. The second method starts with the classical particle flow code (PFC, which uses dynamic equilibrium, but we apply static equilibrium in our case. The second method is called the static particle flow code (SPFC. The numerical experiences and comparison with experimental results from scaled models are discussed.
Level set discrete element method for three-dimensional computations with triaxial case study
Kawamoto, Reid; Andò, Edward; Viggiani, Gioacchino; Andrade, José E.
2016-06-01
In this paper, we outline the level set discrete element method (LS-DEM) which is a discrete element method variant able to simulate systems of particles with arbitrary shape using level set functions as a geometric basis. This unique formulation allows seamless interfacing with level set-based characterization methods as well as computational ease in contact calculations. We then apply LS-DEM to simulate two virtual triaxial specimens generated from XRCT images of experiments and demonstrate LS-DEM's ability to quantitatively capture and predict stress-strain and volume-strain behavior observed in the experiments.
Discrete-element method simulations: from micro to macro scales.
Heyes, D M; Baxter, J; Tüzün, U; Qin, R S
2004-09-15
Many liquid systems encountered in environmental science are often complex mixtures of many components which place severe demands on traditional computational modelling techniques. A meso scale description is required to account adequately for their flow behaviour on the meso and macro scales. Traditional techniques of computational fluid dynamics and molecular simulation are not well suited to tackling these systems, and researchers are increasingly turning to a range of relatively new computational techniques that offer the prospect of addressing the factors relevant to multicomponent multiphase liquids on length- and time-scales between the molecular level and the macro scale. In this category, we discuss the off-lattice techniques of 'smooth particle hydrodynamics' (SPH) and 'dissipative particle dynamics' (DPD), and the grid-based techniques of 'lattice gas' and 'lattice Boltzmann' (LB). We highlight the main conceptual and technical features underpinning these methods, their strengths and weaknesses, and provide a few examples of the applications of these techniques that illustrate their utility.
Discrete Element Method simulations of standing jumps in granular flows down inclines
Directory of Open Access Journals (Sweden)
Méjean Ségolène
2017-01-01
Full Text Available This paper describes a numerical set-up which uses Discrete Element Method to produce standing jumps in flows of dry granular materials down a slope in two dimensions. The grain-scale force interactions are modeled by a visco-elastic normal force and an elastic tangential force with a Coulomb threshold. We will show how it is possible to reproduce all the shapes of the jumps observed in a previous laboratory study: diffuse versus steep jumps and compressible versus incompressible jumps. Moreover, we will discuss the additional measurements that can be done thanks to discrete element modelling.
Modeling of asphalt by means of discrete element method – an initial study
DEFF Research Database (Denmark)
Feng, Huan; Hededal, Ole; Stang, Henrik
type of numerical simulation method which allows the finite displacement and rotation of discrete particles, making it an excellent tool to simulate the complex micro interaction between aggregate particles within an asphalt mixture, [3],[4] . In this research, PFC3D – a commercial DEM program...... of conducting time-consuming and lab-costly procedures. The use of numerical models, capable of reducing greatly the testing cost, has shown great potential in characterizing asphalt-aggregate mixtures for both material evaluation and structural design purposes, [1],[2]. Discrete element method (DEM) is one...... – will be applied. The work presented here will focus on the discrete element method as a tool for modelling composite materials, i.e. determination of a representative volume; boundary conditions; characterisation of the components mastic (binder + filler) and aggregates; and establishment of virtual test samples...
Stochastic structural model of rock and soil aggregates by continuum-based discrete element method
Institute of Scientific and Technical Information of China (English)
WANG; Yuannian; ZHAO; Manhong; LI; Shihai; J.G.; Wang
2005-01-01
This paper first presents a stochastic structural model to describe the random geometrical features of rock and soil aggregates. The stochastic structural model uses mixture ratio, rock size and rock shape to construct the microstructures of aggregates,and introduces two types of structural elements (block element and jointed element) and three types of material elements (rock element, soil element, and weaker jointed element)for this microstructure. Then, continuum-based discrete element method is used to study the deformation and failure mechanism of rock and soil aggregate through a series of loading tests. It is found that the stress-strain curve of rock and soil aggregates is nonlinear, and the failure is usually initialized from weaker jointed elements. Finally, some factors such as mixture ratio, rock size and rock shape are studied in detail. The numerical results are in good agreement with in situ test. Therefore, current model is effective for simulating the mechanical behaviors of rock and soil aggregates.
A stable and optimal complexity solution method for mixed finite element discretizations
Brandts, J.; Stevenson, R.
2001-01-01
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inho- mogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally g
A stable and optimal complexity solution method for mixed finite element discretizations
Brandts, J.; Stevenson, R.
2002-01-01
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inho- mogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first, finally g
Flow Dynamics of green sand in the DISAMATIC moulding process using Discrete element method (DEM)
DEFF Research Database (Denmark)
Hovad, Emil; Larsen, P.; Walther, Jens Honore
2015-01-01
The DISAMATIC casting process production of sand moulds is simulated with DEM (discrete element method). The main purpose is to simulate the dynamics of the flow of green sand, during the production of the sand mould with DEM. The sand shot is simulated, which is the first stage of the DISAMATIC...
DEFF Research Database (Denmark)
Hovad, Emil; Spangenberg, Jon; Larsen, P.
2016-01-01
The discrete element method (DEM) is applied to simulate the dynamics of the flow of green sand while filling a mould using the DISAMATIC process. The focus is to identify relevant physical experiments that can be used to characterize the material properties of green sand in the numerical model...
Dynamic Analysis of Deep-Ocean Mining Pipe System by Discrete Element Method
Institute of Scientific and Technical Information of China (English)
LI Yan; LIU Shao-jun; LI Li
2007-01-01
The dynamic analysis of a pipe system is one of the most crucial problems for the entire mining system.A discrete element method (DEM) is proposed for the analysis of a deep-ocean mining pipe system,including the lift pipe,pump,buffer and flexible hose.By the discrete element method,the pipe is divided into some rigid elements that are linked by flexible connectors.First,two examples representing static analysis and dynamic analysis respectively are given to show that the DEM model is feasible.Then the three-dimensional DEM model is used for dynamic analysis of the mining pipe system.The dynamic motions of the entire mining pipe system under different work conditions are discussed.Some suggestions are made for the actual operation of deep-ocean mining systems.
Application of the extended discrete element method (XDEM) in the melting of a single particle
Baniasadi, Mehdi; Baniasadi, Maryam; Peters, Bernhard
2017-07-01
In this contribution, a new method referred to as Extended Discrete Element Method (XDEM) is usedto model melting of a single particle in the fluid media. The XDEM as a Lagrangian-Eulerian framework is the extension of Discrete Element Method (DEM) by considering thermodynamic state such as temperature distribution and is able to link with Computational Fluid Dynamics (CFD) for fluid phase. In order to provide more accurate results, multiscale method was used. The model is validated by comparing predicted results with existing experimental data for melting of a single ice particle in a water bath. In addition, the model has the capability to be extended to the packed bed of particles with different size and properties to produce different liquid phases.
Nye, Ben; Kulchitsky, Anton V; Johnson, Jerome B
2014-01-01
This paper describes a new method for representing concave polyhedral particles in a discrete element method as unions of convex dilated polyhedra. This method offers an efficient way to simulate systems with a large number of (generally concave) polyhedral particles. The method also allows spheres, capsules, and dilated triangles to be combined with polyhedra using the same approach. The computational efficiency of the method is tested in two different simulation setups using different efficiency metrics for seven particle types: spheres, clusters of three spheres, clusters of four spheres, tetrahedra, cubes, unions of two octahedra (concave), and a model of a computer tomography scan of a lunar simulant GRC-3 particle. It is shown that the computational efficiency of the simulations degrades much slower than the increase in complexity of the particles in the system. The efficiency of the method is based on the time coherence of the system, and an efficient and robust distance computation method between polyhedra as particles never intersect for dilated particles. PMID:26300584
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
Numerical simulation of liquefaction behaviour of granular materials using Discrete Element Method
Indian Academy of Sciences (India)
T G Sitharam; S V Dinesh
2003-09-01
In this paper, numerical simulation of 3-dimensional assemblies of 1000 polydisperse sphere particles using Discrete Element Method (DEM) is used to study the liquefaction behaviour of granular materials. Numerical simulations of cyclic triaxial shear tests under undrained conditions are performed at different confining pressures under constant strain amplitude. Results obtained in these numerical simulations indicate that with increase in confining pressure there is an increase in liquefaction resistance.
Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal Evolution of the MIZ
2015-09-30
dynamic and thermodynamic processes governing the seasonal evolution of the marginal ice zone (MIZ) and (b) forecasting conditions in the MIZ in...STATEMENT A. Approved for public release; distribution is unlimited. Evaluating the Discrete Element Method as a Tool for Predicting the Seasonal ...spatial variability of the surface stress fields to icepack evolution. • Evaluate the DEM’s effectiveness in simulating the seasonal evolution of the
Directory of Open Access Journals (Sweden)
F. Nicot
2002-01-01
Full Text Available The search of improvement of protective techniques against natural phenomena such as snow avalanches continues to use classic methods for calculating flexible structures. This paper deals with a new method to design avalanche protection nets. This method is based on a coupled analysis of both net structure and snow mantle by using a Discrete Element Method. This has led to the development of computational software so that avalanche nets can be easily designed. This tool gives the evolution of the forces acting in several parts of the work as a function of the snow situation.
Mesoscale dynamic coupling of finite- and discrete-element methods for fluid-particle interactions.
Srivastava, S; Yazdchi, K; Luding, S
2014-08-06
A new method for two-way fluid-particle coupling on an unstructured mesoscopically coarse mesh is presented. In this approach, we combine a (higher order) finite-element method (FEM) on the moving mesh for the fluid with a soft sphere discrete-element method for the particles. The novel feature of the proposed scheme is that the FEM mesh is a dynamic Delaunay triangulation based on the positions of the moving particles. Thus, the mesh can be multi-purpose: it provides (i) a framework for the discretization of the Navier-Stokes equations, (ii) a simple tool for detecting contacts between moving particles, (iii) a basis for coarse-graining or upscaling, and (iv) coupling with other physical fields (temperature, electromagnetic, etc.). This approach is suitable for a wide range of dilute and dense particulate flows, because the mesh resolution adapts with particle density in a given region. Two-way momentum exchange is implemented using semi-empirical drag laws akin to other popular approaches; for example, the discrete particle method, where a finite-volume solver on a coarser, fixed grid is used. We validate the methodology with several basic test cases, including single- and double-particle settling with analytical and empirical expectations, and flow through ordered and random porous media, when compared against finely resolved FEM simulations of flow through fixed arrays of particles.
Pennec, Fabienne; Alzina, Arnaud; Tessier-Doyen, Nicolas; Naitali, Benoit; Smith, David S.
2012-11-01
This work is about the calculation of thermal conductivity of insulating building materials made from plant particles. To determine the type of raw materials, the particle sizes or the volume fractions of plant and binder, a tool dedicated to calculate the thermal conductivity of heterogeneous materials has been developped, using the discrete element method to generate the volume element and the finite element method to calculate the homogenized properties. A 3D optical scanner has been used to capture plant particle shapes and convert them into a cluster of discret elements. These aggregates are initially randomly distributed but without any overlap, and then fall down in a container due to the gravity force and collide with neighbour particles according to a velocity Verlet algorithm. Once the RVE is built, the geometry is exported in the open-source Salome-Meca platform to be meshed. The calculation of the effective thermal conductivity of the heterogeneous volume is then performed using a homogenization technique, based on an energy method. To validate the numerical tool, thermal conductivity measurements have been performed on sunflower pith aggregates and on packed beds of the same particles. The experimental values have been compared satisfactorily with a batch of numerical simulations.
Failure analysis of pebble bed reactors during earthquake by discrete element method
Energy Technology Data Exchange (ETDEWEB)
Keppler, Istvan, E-mail: keppler.istvan@gek.szie.hu [Department of Mechanics and Engineering Design, Szent István University, Páter K.u.1., Gödöllő H-2103 (Hungary)
2013-05-15
Highlights: ► We evaluated the load acting on the central reflector beam of a pebble bed reactor. ► The load acting on the reflector beam highly depends on fuel element distribution. ► The contact force values do not show high dependence on fuel element distribution. ► Earthquake increases the load of the reflector, not the contact forces. -- Abstract: Pebble bed reactors (PBR) are graphite-moderated, gas-cooled nuclear reactors. PBR reactors use a large number of spherical fuel elements called pebbles. From mechanical point of view, the arrangement of “small” spherical fuel elements in a container poses the same problem, as the so-called silo problem in powder technology and agricultural engineering. To get more exact information about the contact forces arising between the fuel elements in static and dynamic case, we simulated the static case and the effects of an earthquake on a model reactor by using discrete element method. We determined the maximal contact forces acting between the individual fuel elements. We found that the value of the maximal bending moment in the central reflector beam has a high deviation from the average value even in static case, and it can significantly increase in case of an earthquake. Our results can help the engineers working on the design of such types of reactors to get information about the contact forces, to determine the dust production and the crush probability of fuel elements within the reactor, and to model different accident scenarios.
Institute of Scientific and Technical Information of China (English)
LUO Zhen-dong; ZHOU Yan-jie; ZHU Jiang
2007-01-01
The vapor deposition chemical reaction processes, which are of extremely extensive applications, can be classified as a mathematical modes by the following governing nonlinear partial differential equations containing velocity vector,temperature field,pressure field,and gas mass field.The mixed finite element(MFE)method is employed to study the system of equations for the vapor deposition chemical reaction processes.The semidiscrete and fully discrete MFE formulations are derived.And the existence and convergence(error estimate)of the semidiscrete and fully discrete MFE solutions are deposition chemical reaction processes,the numerical solutions of the velocity vector,the temperature field,the pressure field,and the gas mass field can be found out simultaneonsly.Thus,these researches are not only of important theoretical means,but also of extremely extensive applied vistas.
Directory of Open Access Journals (Sweden)
Zainorizuan Mohd Jaini
2013-12-01
Full Text Available Innovative technologies have resulted in more effective ceramic composite as high rate loading-resistance and protective layer. The ceramic composite layer consists of ceramic frontal plate that bonded by softer-strong reinforced polymer network, consequently gains the heterogeneous condition. These materials serve specific purposes of defeating high rate loading and maintaining the structural integrity of the layer. Further due to the lack of a constituent material and tedious problem in heterogonous material modelling, a numerical homogenization is employed to analyse the isotropic material properties of ceramic composite layer in homogenous manner. The objective of this study is to derive a constitutive law of the ceramic composite using the multi-scale analysis. Two-dimensional symmetric macrostructure of the ceramic composite was numerically modelled using the hybrid finite-discrete element method to investigate the effective material properties and strength profile. The macrostructure was modelled as brittle material with nonlinear material properties. The finite element method is incorporated with a Rankine-Rotating Crack approach and discrete element to model the fracture onset. The prescribed uniaxial and biaxial loadings were imposed along the free boundaries to create different deformations. Due to crack initiation on the macrostructure, the averaged stresses were calculated to plot the stress-strain curves and the effective yield stress surface. From the multi-scale analysis, the rate-dependency of Mohr-Coulomb constitutive law was derived for the ceramic composite layer.
Determination of contact parameters for discrete element method simulations of granular systems
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Both linear-spring-dashpot (LSD) and non-linear Hertzian-spring-dnshpot (HSD) contact models are commonly used for the calculation of contact forces in Discrete Element Method (DEM) simulations of granular systems.Despite the popularity of these models, determination of suitable values for the contact parameters of the simulated particles such as stiffness, damping coefficient, coefficient of restitution, and simulation time step,is not altogether obvious.In this work the relationships between these contact parameters for a model system where a particle impacts on a flat base are examined.Recommendations are made concerning the determination of these contact parameters for use in DEM simulations.
Damping of rotating beams with particle dampers: Discrete element method analysis
Els, D. N. J.
2013-06-01
The performance of particle dampers (PDs) under centrifugal loads was investigated. A test bench consisting of a rotating cantilever beam with a particle damper at the tip was developed (D. N. J. Els, AIAA Journal 49, 2228-2238 (2011)). Equal mass containers with different depths, filled with a range of uniform-sized steel ball bearings, were used as particle dampers. The experiments were duplicated numerically with a discrete element method (DEM) model, calibrated against the experimental data. The DEM model of the rotating beam with a PD at the tip captured the performance of the PD very well over a wide range of tests with different configurations and rotation velocities.
Directory of Open Access Journals (Sweden)
Enan Chi
2015-06-01
Full Text Available The fracture and fragmentation of rock materials are basic and important problem in geomechanics and blasting engineering. An approach, which can simulate the process of fracture and fragmentation of rock materials, is introduced in this work. A beam–particle model is first introduced in the frame of the discrete element method. In the beam–particle model, the neighboring elements are connected by beams. Consequently, a beam network is formed in the particle system. The strength characteristics of rock materials are reflected by the beam network. The strength criterion was then built to verify whether a beam exists or not. The process of rock fracture and fragmentation is described by the gradual disappearance of beams. Finally, two cases were presented to indicate the validity of the method proposed in this work.
A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method.
Brocklehurst, Paul; Adeniran, Ismail; Yang, Dongmin; Sheng, Yong; Zhang, Henggui; Ye, Jianqiao
2015-01-01
Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca(2+) concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.
Institute of Scientific and Technical Information of China (English)
马涛; 张德育; 张垚; 赵永利; 黄晓明
2016-01-01
The objective of this work is to model the microstructure of asphalt mixture and build virtual test for asphalt mixture by using Particle Flow Code in three dimensions (PFC3D) based on three-dimensional discrete element method. A randomly generating algorithm was proposed to capture the three-dimensional irregular shape of coarse aggregate. And then, modeling algorithm and method for graded aggregates were built. Based on the combination of modeling of coarse aggregates, asphalt mastic and air voids, three-dimensional virtual sample of asphalt mixture was modeled by using PFC3D. Virtual tests for penetration test of aggregate and uniaxial creep test of asphalt mixture were built and conducted by using PFC3D. By comparison of the testing results between virtual tests and actual laboratory tests, the validity of the microstructure modeling and virtual test built in this study was verified. Additionally, compared with laboratory test, the virtual test is easier to conduct and has less variability. It is proved that microstructure modeling and virtual test based on three-dimensional discrete element method is a promising way to conduct research of asphalt mixture.
Novel Discrete Element Method for 3D non-spherical granular particles.
Seelen, Luuk; Padding, Johan; Kuipers, Hans
2015-11-01
Granular materials are common in many industries and nature. The different properties from solid behavior to fluid like behavior are well known but less well understood. The main aim of our work is to develop a discrete element method (DEM) to simulate non-spherical granular particles. The non-spherical shape of particles is important, as it controls the behavior of the granular materials in many situations, such as static systems of packed particles. In such systems the packing fraction is determined by the particle shape. We developed a novel 3D discrete element method that simulates the particle-particle interactions for a wide variety of shapes. The model can simulate quadratic shapes such as spheres, ellipsoids, cylinders. More importantly, any convex polyhedron can be used as a granular particle shape. These polyhedrons are very well suited to represent non-rounded sand particles. The main difficulty of any non-spherical DEM is the determination of particle-particle overlap. Our model uses two iterative geometric algorithms to determine the overlap. The algorithms are robust and can also determine multiple contact points which can occur for these shapes. With this method we are able to study different applications such as the discharging of a hopper or silo. Another application the creation of a random close packing, to determine the solid volume fraction as a function of the particle shape.
Derakhshani, S. M.; Schott, D. L.; Lodewijks, G.
2013-06-01
Dust emissions can have significant effects on the human health, environment and industry equipment. Understanding the dust generation process helps to select a suitable dust preventing approach and also is useful to evaluate the environmental impact of dust emission. To describe these processes, numerical methods such as Computational Fluid Dynamics (CFD) are widely used, however nowadays particle based methods like Discrete Element Method (DEM) allow researchers to model interaction between particles and fluid flow. In this study, air flow over a stockpile, dust emission, erosion and surface deformation of granular material in the form of stockpile are studied by using DEM and CFD as a coupled method. Two and three dimensional simulations are respectively developed for CFD and DEM methods to minimize CPU time. The standard κ-ɛ turbulence model is used in a fully developed turbulent flow. The continuous gas phase and the discrete particle phase link to each other through gas-particle void fractions and momentum transfer. In addition to stockpile deformation, dust dispersion is studied and finally the accuracy of stockpile deformation results obtained by CFD-DEM modelling will be validated by the agreement with the existing experimental data.
Discrete-element modelling: methods and applications in the environmental sciences.
Richards, Keith; Bithell, Mike; Dove, Martin; Hodge, Rebecca
2004-09-15
This paper introduces a Theme Issue on discrete-element modelling, based on research presented at an interdisciplinary workshop on this topic organized by the National Institute of Environmental e-Science. The purpose of the workshop, and this collection of papers, is to highlight the opportunities for environmental scientists provided by (primarily) off-lattice methods in the discrete-element family, and to draw on the experiences of research communities in which the use of these methods is more advanced. Applications of these methods may be conceived in a wide range of situations where dynamic processes involve a series of fundamental entities (particles or elements) whose interaction results in emergent macroscale structures. Indeed, the capacity of these methods to reveal emergent properties at the meso- and macroscale, that reflect microscale interactions, is a significant part of their attraction. They assist with the definition of constitutive material properties at scales beyond those at which measurement and theory have been developed, and help us to understand self-organizing behaviours. The paper discusses technical issues including the contact models required to represent collision behaviour, computational aspects of particle tracking and collision detection, and scales at which experimental data are required and choices about modelling style must be made. It then illustrates the applicability of DEM and other forms of individual-based modelling in environmental and related fields as diverse as mineralogy, geomaterials, mass movement and fluvial sediment transport processes, as well as developments in ecology, zoology and the human sciences where the relationship between individual behaviour and group dynamics can be explored using a partially similar methodological framework.
Directory of Open Access Journals (Sweden)
T. Lukas
2014-12-01
Full Text Available The combined finite–discrete element method (FDEM belongs to a family of methods of computational mechanics of discontinua. The method is suitable for problems of discontinua, where particles are deformable and can fracture or fragment. The applications of FDEM have spread over a number of disciplines including rock mechanics, where problems like mining, mineral processing or rock blasting can be solved by employing FDEM. In this work, a novel approach for the parallelization of two-dimensional (2D FDEM aiming at clusters and desktop computers is developed. Dynamic domain decomposition based parallelization solvers covering all aspects of FDEM have been developed. These have been implemented into the open source Y2D software package and have been tested on a PC cluster. The overall performance and scalability of the parallel code have been studied using numerical examples. The results obtained confirm the suitability of the parallel implementation for solving large scale problems.
A hybrid mortar virtual element method for discrete fracture network simulations
Benedetto, Matías Fernando; Berrone, Stefano; Borio, Andrea; Pieraccini, Sandra; Scialò, Stefano
2016-02-01
The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN) is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to "weakly" impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries.
Spellings, Matthew; Anderson, Joshua A; Glotzer, Sharon C
2016-01-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks-Chandler-Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
Spellings, Matthew; Marson, Ryan L.; Anderson, Joshua A.; Glotzer, Sharon C.
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks-Chandler-Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests
Richardson, Derek C; Murdoch, Naomi; Michel, Patrick
2013-01-01
We present a new particle-based (discrete element) numerical method for the simulation of granular dynamics, with application to motions of particles on small solar system body and planetary surfaces. The method employs the parallel N-body tree code pkdgrav to search for collisions and compute particle trajectories. Collisions are treated as instantaneous point-contact events between rigid spheres. Particle confinement is achieved by combining arbitrary combinations of four provided wall primitives, namely infinite plane, finite disk, infinite cylinder, and finite cylinder, and degenerate cases of these. Various wall movements, including translation, oscillation, and rotation, are supported. We provide full derivations of collision prediction and resolution equations for all geometries and motions. Several tests of the method are described, including a model granular "atmosphere" that achieves correct energy equipartition, and a series of tumbler simulations that show the expected transition from tumbling to ...
Energy Technology Data Exchange (ETDEWEB)
Spellings, Matthew [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Marson, Ryan L. [Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Anderson, Joshua A. [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Glotzer, Sharon C., E-mail: sglotzer@umich.edu [Chemical Engineering, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States); Materials Science & Engineering, University of Michigan, 2300 Hayward St., Ann Arbor, MI 48109 (United States); Biointerfaces Institute, University of Michigan, 2800 Plymouth Rd., Ann Arbor, MI 48109 (United States)
2017-04-01
Faceted shapes, such as polyhedra, are commonly found in systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystal nucleation and growth, vacancy motion, and glassy dynamics are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We provide an implementation of this method intended for simulation of hard, faceted nanoparticles, with a conservative Weeks–Chandler–Andersen (WCA) interparticle potential, coupled to a thermodynamic ensemble. This method is a natural extension of classical molecular dynamics and enables rigorous thermodynamic calculations for faceted particles.
Predicting the Dynamic Behavior of Asphalt Concrete Using Three-dimensional Discrete Element Method
Institute of Scientific and Technical Information of China (English)
CHEN Jun; PAN Tongyan; CHEN Jingya; HUANG Xiaoming; LU Yang
2012-01-01
A user-defined three-dimensional (3D) discrete element model was presented to predict the dynamic modulus and phase angle of asphalt concrete (AC).The 3D discrete element method (DEM) model of AC was constructed employing a user-defined computer program developed using the "Fish" language in PFC3D.Important microstructural features of AC were modeled,including aggregate gradation,air voids and mastic.The irregular shape of aggregate particle was modeled using a clump of spheres.The developed model was validated through comparing with experimental measurements and then used to simulate the cyclic uniaxial compression test,based on which the dynamic modulus and phase angle were calculated from the output stressstrain relationship.The effects of air void content,aggregate stiffness and volumetric fraction on AC modulus were further investigated.The experimental results show that the 3D DEM model is able to accurately predict both dynamic modulus and phase angle of AC across a range of temperature and loading frequencies.The userdefined 3D model also demonstrated significant improvement over the general existing two-dimensional models.
THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS
Institute of Scientific and Technical Information of China (English)
LiuKaixin; GaoLingtian
2003-01-01
A three-dimensional discrete element model of the connective type is presented. Moreover, a three- dimensional numerical analysis code, which can carry out the transitional process from connective model (for continuum) to contact model (for non-continuum), is developed for simulating the mechanical process from continuum to non-continuum. The wave propagation process in a concrete block (as continuum) made of cement grout under impact loading is numerically simulated with this code. By comparing its numerical results with those by LS-DYNA, the calculation accuracy of the model and algorithm is proved. Furthermore, the failure process of the concrete block under quasi-static loading is demonstrated, showing the basic dynamic transitional process from continuum to non-continuum. The results of calculation can be displayed by animation. The damage modes are similar to the experimental results. The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum. It also shows that the discrete element method (DEM) will have broad prospects for development and application.
Martin, Hugo; Mangeney, Anne; Farin, Maxime; Richard, Patrick
2016-04-01
The mechanical behavior of granular flows is still an open issue. In particular, quantitative agreement between the detailed dynamics of the flow and laboratory experiments is necessary to better constrain the performance and limits of the models. We propose here to compare quantitatively the flow profiles and the force during granular column collapse simulated using Discrete Element Models and laboratory experiments. These small scale experiments are performed with dry granular material released initially from a cylinder on a sloping plane. The flow profiles and the acoustic signal generated by the granular impacts and stresses on the plane are recorded systematically [Farin et al., 2015]. These experiments are simulated using the Discrete Element Method Modys [Richard et al., 2000]. We show that the effect of the removing gate should be taken into account in the model in order to quantatively reproduce the flow dynamics. Furthermore we compare the simulated and observed acoustic signals that are generated by the fluctuating stresses exerted by the grains on the substrate in different frequency bands. [1] P. Richard et Luc Oger. 2000 Etude de la géométrie de milieux granulaires modèles tridimensionnels par simulation numérique. [2] Farin, M., Mangeney, A., Toussaint, R., De Rosny, J., Shapiro, N., Dewez, T., Hibert, C., Mathon, C., Sedan, O., Berger. 2015, Characterization of rockfalls from seismic signal: insights from laboratory experiments
Zhao, Xuzhe
High efficiency hydrogen storage method is significant in development of fuel cell vehicle. Seeking for a high energy density material as the fuel becomes the key of wide spreading fuel cell vehicle. LiBH4 + MgH 2 system is a strong candidate due to their high hydrogen storage density and the reaction between them is reversible. However, LiBH4 + MgH 2 system usually requires the high temperature and hydrogen pressure for hydrogen release and uptake reaction. In order to reduce the requirements of this system, nanoengineering is the simple and efficient method to improve the thermodynamic properties and reduce kinetic barrier of reaction between LiBH4 and MgH2. Based on ab initio density functional theory (DFT) calculations, the previous study has indicated that the reaction between LiBH4 and MgH2 can take place at temperature near 200°C or below. However, the predictions have been shown to be inconsistent with many experiments. Therefore, it is the first time that our experiment using ball milling with aerosol spraying (BMAS) to prove the reaction between LiBH4 and MgH2 can happen during high energy ball milling at room temperature. Through this BMAS process we have found undoubtedly the formation of MgB 2 and LiH during ball milling of MgH2 while aerosol spraying of the LiBH4/THF solution. Aerosol nanoparticles from LiBH 4/THF solution leads to form Li2B12H12 during BMAS process. The Li2B12H12 formed then reacts with MgH2 in situ during ball milling to form MgB 2 and LiH. Discrete element modeling (DEM) is a useful tool to describe operation of various ball milling processes. EDEM is software based on DEM to predict power consumption, liner and media wear and mill output. In order to further improve the milling efficiency of BMAS process, EDEM is conducted to make analysis for complicated ball milling process. Milling speed and ball's filling ratio inside the canister as the variables are considered to determine the milling efficiency. The average and maximum
Particle stratification and penetration of a linear vibrating screen by the discrete element method
Institute of Scientific and Technical Information of China (English)
Xiao Jianzhang; Tong Xin
2012-01-01
A simulation of stratification and penetration was performed over a range of structural parameters that included screen width,aperture size,inclination angle,and wire diameter.The discrete element method (DEM) was used for the simulations.The terms stratification and penetration are defined and the change in fine particle concentration is discussed.Mathematical models relating fine particle ratio to time are established using the least squares method.The effect of structural parameters on fine particle ratio is analyzed.Stratification and penetration rate are discussed by considering the time derivative of the fine particle ratio.The conclusions are:an increase in inclination or wire diameter has a positive effect on particle stratifying; The optimal screen width is 40 mm for particle stratification; The inclination angle has a negative effect on the penetration; The effect of wire diameter and screen width on the penetration rate is negligible.
Discrete Element Method, a Tool to Investigate Complex Material Behaviour in Material Forming
Iordanoff, Ivan; Iliescu, Daniel; Charles, Jean-Luc; NÉAUPORT, Jérome
2010-01-01
International audience; Discrete Model is based on the description of the physical state (velocity, position, temperature, magnetic moment, electric potential ..) of a large number of discrete elements that form the media to be studied. It is not based on a continuous description of the media. Then, it is particularly well adapted to describe media evolution driven by discontinuous phenomena : - multi fracturation problems like abrasion process and composite machining, - description of multi ...
Numerical simulation of two-dimensional spouted bed with draft plates by discrete element method
Institute of Scientific and Technical Information of China (English)
Yongzhi ZHAO; Yi CHENG; Maoqiang JIANG; Yong JIN
2008-01-01
A discrete element method (DEM)-computa-tional fluid dynamics (CFD) two-way coupling method was employed to simulate the hydrodynamics in a two-dimensional spouted bed with draft plates. The motion of particles was modeled by the DEM and the gas flow was modeled by the Navier-Stokes equation. The interactions between gas and particles were considered using a two-way coupling method. The motion of particles in the spouted bed with complex geometry was solved by com-bining DEM and boundary element method (BEM). The minimal spouted velocity was obtained by the BEM-DEM-CFD simulation and the variation of the flow pat-tern in the bed with different superficial gas velocity was studied. The relationship between the pressure drop of the spouted bed and the superficial gas velocity was achieved from the simulations. The radial profile of the averaged vertical velocities of particles and the profile of the aver-aged void fraction in the spout and the annulus were stat-istically analyzed. The flow characteristics of the gas-solid system in the two-dimensional spouted bed were clearly described by the simulation results.
Discrete element method of improved performance of railway ballast bed using elastic sleeper
Institute of Scientific and Technical Information of China (English)
高亮; 罗奇; 徐旸; 井国庆; 蒋函珂
2015-01-01
With the development of high-speed and heavy-haul railway in China, problems like insufficient thickness of ballast bed and overlarge track stiffness are obvious. Ballast may break into small particles and their contact status will deteriorate under cyclic loading, resulting in ballast degradation. Discrete element method (DEM) was used to research improved performance of ballast bed using elastic sleeper. Clusters were generated by bonding spheres to model real ballasts, while broken bonds were utilized to distinguish breakage. Two kinds of ballast beds with elastic sleeper and conventional sleeper were established, respectively. After applying cyclic loading to the models, differences of mechanical properties between two models were analyzed by contrasting their dynamic behavior indexes, such as particle contact force, sleeper settlement, vibration velocity and acceleration, breakage characteristic. The results illustrate that compared with conventional sleeper, elastic sleeper increases sleeper settlement, while reduces ballast vibration and contact force between particles, which could depress ballast breakage.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The phenomenon of the soil plug usually rising inside the suction foundations during suction penetration was quantitatively described and predicted. The formation process of the soil plug was simulated and calculated by DEM (discrete element method) model. The seepage flow, the self-weight of soil, the friction on the chamber wall as well as the suction inside the chamber are considered as the main external forces in the process. The results are compared with a set of laboratory model tests performed by using three soil types (sand, silty clay and clay) in the Bohai Sea area. The heights of soil plug from numerical estimations are lower than those from model test results, mainly because the suction pressure and friction resistance are applied in an ideal way under the numerical simulation.
Huang, Yueqin; Cheng, Yi Pik; Coop, Matthew
2017-06-01
The Discrete Element Method (DEM) was used to simulate the mechanical behaviour of a reservoir sandstone. Triaxial tests were carried out using 3D-DEM to simulate the stress-strain behaviour of a sandstone with comparisons made between the numerical tests and the laboratory tests. The influence of isotropic unloading was investigated, which was found to have impacts on bond breakages and was successfully captured in the 3D shearing processes. It was found that bond breakages correlated strongly with the stress-strain behaviour of the sandstone affecting the peak strength. It was also found that unloading affected the bond breakages, which then changed the mechanical behaviour of sandstone. The tangent stiffnesses of simulated virgin and cored samples under different confining stresses were compared. From the tangent stiffnesses, gross yield envelopes and the yielding surfaces for unloaded samples and virgin samples were plotted and analysed in detail.
Approximation of mechanical properties of sintered materials with discrete element method
Dosta, Maksym; Besler, Robert; Ziehdorn, Christian; Janßen, Rolf; Heinrich, Stefan
2017-06-01
Sintering process is a key step in ceramic processing, which has strong influence on quality of final product. The final shape, microstructure and mechanical properties, e.g. density, heat conductivity, strength and hardness are depending on the sintering process. In order to characterize mechanical properties of sintered materials, in this contribution we present a microscale modelling approach. This approach consists of three different stages: simulation of the sintering process, transition to final structure and modelling of mechanical behaviour of sintered material with discrete element method (DEM). To validate the proposed simulation approach and to investigate products with varied internal structures alumina powder has been experimentally sintered at different temperatures. The comparison has shown that simulation results are in a very good agreement with experimental data and that the novel strategy can be effectively used for modelling of sintering process.
Institute of Scientific and Technical Information of China (English)
AN Xi-Zhong
2007-01-01
The crystallization, corresponding to the fcc structure (with packing density p ≈ 0.74), of smooth equal hard spheres under batch-wised feeding and three-dimensional interval vibration is numerically obtained by using the discrete element method. The numerical experiment shows that the ordered packing can be realized by proper control of the dynamic parameters such as batch of each feeding § and vibration amplitude A. The radial distribution function and force network are used to characterize the ordered structure. The defect formed during vibrated packing is characterized as well The results in our work fill the gap of getting packing density between random close packing and fcc packing in phase diagram which provides an effective way of theoretically investigating the complex process and mechanism of hard sphere crystallization and its dynamics.
Discrete element method study of fuel relocation and dispersal during loss-of-coolant accidents
Govers, K.; Verwerft, M.
2016-09-01
The fuel fragmentation, relocation and dispersal (FFRD) during LOCA transients today retain the attention of the nuclear safety community. The fine fragmentation observed at high burnup may, indeed, affect the Emergency Core Cooling System performance: accumulation of fuel debris in the cladding ballooned zone leads to a redistribution of the temperature profile, while dispersal of debris might lead to coolant blockage or to debris circulation through the primary circuit. This work presents a contribution, by discrete element method, towards a mechanistic description of the various stages of FFRD. The fuel fragments are described as a set of interacting particles, behaving as a granular medium. The model shows qualitative and quantitative agreement with experimental observations, such as the packing efficiency in the balloon, which is shown to stabilize at about 55%. The model is then applied to study fuel dispersal, for which experimental parametric studies are both difficult and expensive.
Institute of Scientific and Technical Information of China (English)
Ji Xu; Jing hai Li; Hua biao Qi; Xiao jian Fang; Li qiang Lu; Wei Ge; Xiao wei Wang; Ming Xu; Fei guo Chen; Xian feng He
2011-01-01
Real-time simulation of industrial equipment is a huge challenge nowadays.The high performance and fine-grained parallel computing provided by graphics processing units (GPUs) bring us closer to our goals.In this article,an industrial-scale rotating drum is simulated using simplified discrete element method (DEM) without consideration of the tangential components of contact force and particle rotation.A single GPU is used first to simulate a small model system with about 8000 particles in real-time,and the simulation is then scaled up to industrial scale using more than 200 GPUs in a 1D domain-decomposition parallelization mode.The overall speed is about 1/11 of the real-time.Optimization of the communication part of the parallel GPU codes can speed up the simulation further,indicating that such real-time simulations have not only methodological but also industrial implications in the near future.
Han, Xuesong
2014-09-01
Machining technology about ceramics has been developed very fast over recent years due to the growing industrial demand of higher machining accuracy and better surface quality of ceramic elements, while the nature of hard and brittle ceramics makes it difficult to acquire damage-free and ultra-smooth surface. Ceramic bulk can be treated as an assemblage of discrete particles bonded together randomly as the micro-structure of ceramics consists of crystal particles and pores, and the inter-granular fracture of the ceramics can be naturally represented by the separation of particles due to breakage of bonds. Discrete element method (DEM) provides a promising approach for constructing an effective model to describe the tool-workpiece interaction and can serve as a predicting simulation tool in analyzing the complicated surface generation mechanism and is employed in this research to simulate the mechanical polishing process of ceramics and surface integrity. In this work, a densely packed particle assembly system of the polycrystalline Si3N4 has been generated using bonded-particle model to represent the ceramic workpiece numerically. The simulation results justify that the common critical depth of cut cannot be used as the effective parameters for evaluating brittle to ductile transformation in ceramic polishing process. Therefore, a generalized criterion of defining the range of ductile regime machining has been developed based on the numerical results. Furthermore, different distribution of pressure chain is observed with different depth of cut which ought to have intense relationship with special structure of ceramics. This study also justified the advantage of DEM model in its capability of revealing the mechanical behaviors of ceramics at micro-scale.
Energy Technology Data Exchange (ETDEWEB)
Herbold, E. B. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Walton, O. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Homel, M. A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-10-26
This document serves as a final report to a small effort where several improvements were added to a LLNL code GEODYN-L to develop Discrete Element Method (DEM) algorithms coupled to Lagrangian Finite Element (FE) solvers to investigate powder-bed formation problems for additive manufacturing. The results from these simulations will be assessed for inclusion as the initial conditions for Direct Metal Laser Sintering (DMLS) simulations performed with ALE3D. The algorithms were written and performed on parallel computing platforms at LLNL. The total funding level was 3-4 weeks of an FTE split amongst two staff scientists and one post-doc. The DEM simulations emulated, as much as was feasible, the physical process of depositing a new layer of powder over a bed of existing powder. The DEM simulations utilized truncated size distributions spanning realistic size ranges with a size distribution profile consistent with realistic sample set. A minimum simulation sample size on the order of 40-particles square by 10-particles deep was utilized in these scoping studies in order to evaluate the potential effects of size segregation variation with distance displaced in front of a screed blade. A reasonable method for evaluating the problem was developed and validated. Several simulations were performed to show the viability of the approach. Future investigations will focus on running various simulations investigating powder particle sizing and screen geometries.
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Numerical sedimentation particle-size analysis using the Discrete Element Method
Bravo, R.; Pérez-Aparicio, J. L.; Gómez-Hernández, J. J.
2015-12-01
Sedimentation tests are widely used to determine the particle size distribution of a granular sample. In this work, the Discrete Element Method interacts with the simulation of flow using the well known one-way-coupling method, a computationally affordable approach for the time-consuming numerical simulation of the hydrometer, buoyancy and pipette sedimentation tests. These tests are used in the laboratory to determine the particle-size distribution of fine-grained aggregates. Five samples with different particle-size distributions are modeled by about six million rigid spheres projected on two-dimensions, with diameters ranging from 2.5 ×10-6 m to 70 ×10-6 m, forming a water suspension in a sedimentation cylinder. DEM simulates the particle's movement considering laminar flow interactions of buoyant, drag and lubrication forces. The simulation provides the temporal/spatial distributions of densities and concentrations of the suspension. The numerical simulations cannot replace the laboratory tests since they need the final granulometry as initial data, but, as the results show, these simulations can identify the strong and weak points of each method and eventually recommend useful variations and draw conclusions on their validity, aspects very difficult to achieve in the laboratory.
Discrete element method analysis of lateral resistance of fouled ballast bed
Institute of Scientific and Technical Information of China (English)
徐旸; 高亮; 张艳荣; 尹辉; 蔡小培
2016-01-01
The lateral resistance of sleeper plays an important role in ensuring the stability of a railway track, which may change in the operation of railway, due to the fouling in the ballast bed. In this work, discrete element method was adopted to investigate the effect of fouling on the lateral resistance of sleeper. The shape information of ballast was captured by method of three-dimensional vision reconstruction. In order to calibrate the mechanical parameters and verify the models, a lateral resistance field test was carried out by using a custom-made device. The contact force distributions in the different parts of sleeper as well as the interaction between ballast and sleeper were discussed in depth. The results show that fouling of ballast bed evidently reduces the lateral resistance of sleeper and the decreasing degree is also related to the fouled position of ballast bed, in the order of shoulder > bottom > side. Therefore, the effect of fouling, especially the fouling in the ballast shoulder, on the lateral resistance of sleeper, should be taken into account in ballast track maintenance work.
A Review of Discrete Element Method (DEM) Particle Shapes and Size Distributions for Lunar Soil
Lane, John E.; Metzger, Philip T.; Wilkinson, R. Allen
2010-01-01
As part of ongoing efforts to develop models of lunar soil mechanics, this report reviews two topics that are important to discrete element method (DEM) modeling the behavior of soils (such as lunar soils): (1) methods of modeling particle shapes and (2) analytical representations of particle size distribution. The choice of particle shape complexity is driven primarily by opposing tradeoffs with total number of particles, computer memory, and total simulation computer processing time. The choice is also dependent on available DEM software capabilities. For example, PFC2D/PFC3D and EDEM support clustering of spheres; MIMES incorporates superquadric particle shapes; and BLOKS3D provides polyhedra shapes. Most commercial and custom DEM software supports some type of complex particle shape beyond the standard sphere. Convex polyhedra, clusters of spheres and single parametric particle shapes such as the ellipsoid, polyellipsoid, and superquadric, are all motivated by the desire to introduce asymmetry into the particle shape, as well as edges and corners, in order to better simulate actual granular particle shapes and behavior. An empirical particle size distribution (PSD) formula is shown to fit desert sand data from Bagnold. Particle size data of JSC-1a obtained from a fine particle analyzer at the NASA Kennedy Space Center is also fitted to a similar empirical PSD function.
Optimizing the Pipe Diameter of the Pipe Belt Conveyor Based on Discrete Element Method
Guo, Yong-cun; Wang, Shuang; Hu, Kun; Li, De-yong
2016-03-01
In order to increase the transport volume of the pipe belt conveyor and reduce lateral pressure of the supporting roller set, this study aims to optimize the pipe diameter of the pipe belt conveyor. A mechanical model of the pipe belt conveyor with six supporting roller sets in the belt bearing section was built based on the infinitesimal method, and the formula for calculating the lateral pressure of each supporting roller was deduced on the basis of reasonable assumption. Simulated analysis was carried out on the operation process of the pipe belt conveyor by using the discrete element method. The result showed that, when the other conditions were certain, as the pipe diameter increased, the average lateral pressure of the supporting roller set increased, with a gradually decreasing increment, which was consistent with the calculated result of the theoretical formula. An optimized pipe diameter under the current conditions was obtained by fitting the curve of the formula for calculating the transport volume of the pipe belt conveyor and its simulation curve. It provided a certain reference value for improving the transport efficiency and prolonging the service life of the pipe belt conveyor.
Institute of Scientific and Technical Information of China (English)
Qi Zhao; Andrea Lisjak; Omid Mahabadi; Qinya Liu; Giovanni Grasselli
2014-01-01
Hydraulic fracturing (HF) technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS) monitoring is one of the most effective approaches to eval-uate such stimulation process. In this paper, the combined finite-discrete element method (FDEM) is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value), fractal dimension (D-value), and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Energy Technology Data Exchange (ETDEWEB)
Zhou, Jing [Universiyt of Utah; Huang, Hai [Idaho National Lab. (INL), Idaho Falls, ID (United States); Deo, Milind
2015-10-01
The interaction between hydraulic fractures (HF) and natural fractures (NF) will lead to complex fracture networks due to the branching and merging of natural and hydraulic fractures in unconventional reservoirs. In this paper, a newly developed hydraulic fracturing simulator based on discrete element method is used to predict the generation of complex fracture network in the presence of pre-existing natural fractures. By coupling geomechanics and reservoir flow within a dual lattice system, this simulator can effectively capture the poro-elastic effects and fluid leakoff into the formation. When HFs are intercepting single or multiple NFs, complex mechanisms such as direct crossing, arresting, dilating and branching can be simulated. Based on the model, the effects of injected fluid rate and viscosity, the orientation and permeability of NFs and stress anisotropy on the HF-NF interaction process are investigated. Combined impacts from multiple parameters are also examined in the paper. The numerical results show that large values of stress anisotropy, intercepting angle, injection rate and viscosity will impede the opening of NFs.
Discrete Element Method simulations of the saturation of aeolian sand transport
Pähtz, Thomas; Carneiro, Marcus V; Araújo, Nuno A M; Herrmann, Hans J
2015-01-01
The saturation length of aeolian sand transport ($L_s$), characterizing the distance needed by wind-blown sand to adapt to changes in the wind shear, is essential for accurate modeling of the morphodynamics of Earth's sandy landscapes and for explaining the formation and shape of sand dunes. In the last decade, it has become a widely-accepted hypothesis that $L_s$ is proportional to the characteristic distance needed by transported particles to reach the wind speed (the ``drag length''). Here we challenge this hypothesis. From extensive numerical Discrete Element Method simulations, we find that, for medium and strong winds, $L_s\\propto V_s^2/g$, where $V_s$ is the saturated value of the average speed of sand particles traveling above the surface and $g$ the gravitational constant. We show that this proportionality is consistent with a recent analytical model, in which the drag length is just one of four similarly important length scales relevant for sand transport saturation.
Maxwell, R; Ata, S; Wanless, E J; Moreno-Atanasio, R
2012-09-01
Three dimensional Discrete Element Method (DEM) computer simulations have been carried out to analyse the kinetics of collision of multiple particles against a stationary bubble and the sliding of the particles over the bubble surface. This is the first time that a computational analysis of the sliding time and particle packing arrangements of multiple particles on the surface of a bubble has been carried out. The collision kinetics of monodisperse (33 μm in radius) and polydisperse (12-33 μm in radius) particle systems have been analysed in terms of the time taken by 10%, 50% and 100% of the particles to collide against the bubble. The dependencies of these collision times on the strength of hydrophobic interactions follow relationships close to power laws. However, minimal sensitivity of the collision times to particle size was found when linear and square relationships of the hydrophobic force with particles radius were considered. The sliding time for single particles has corroborated published theoretical expressions. Finally, a good qualitative comparison with experiments has been observed with respect to the particle packing at the bottom of the bubble after sliding demonstrating the usefulness of computer simulations in the studies of particle-bubble systems.
Podlozhnyuk, Alexander; Pirker, Stefan; Kloss, Christoph
2016-09-01
Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle-particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle-wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.
Parallel computing of discrete element method on multi-core processors
Institute of Scientific and Technical Information of China (English)
Yusuke Shigeto; Mikio Sakai
2011-01-01
This paper describes parallel simulation techniques for the discrete element method (DEM) on multi-core processors.Recently,multi-core CPU and GPU processors have attracted much attention in accelerating computer simulations in various fields.We propose a new algorithm for multi-thread parallel computation of DEM,which makes effective use of the available memory and accelerates the computation.This study shows that memory usage is drastically reduced by using this algorithm.To show the practical use of DEM in industry,a large-scale powder system is simulated with a complicated drive unit.We compared the performance of the simulation between the latest GPU and CPU processors with optimized programs for each processor.The results show that the difference in performance is not substantial when using either GPUs or CPUs with a multi-thread parallel algorithm.In addition,DEM algorithm is shown to have high scalability in a multi-thread parallel computation on a CPU.
Directory of Open Access Journals (Sweden)
Qi Zhao
2014-12-01
Full Text Available Hydraulic fracturing (HF technique has been extensively used for the exploitation of unconventional oil and gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formations by fluid injection, which creates an interconnected fracture network and increases the hydrocarbon production. Meanwhile, microseismic (MS monitoring is one of the most effective approaches to evaluate such stimulation process. In this paper, the combined finite-discrete element method (FDEM is adopted to numerically simulate HF and associated MS. Several post-processing tools, including frequency-magnitude distribution (b-value, fractal dimension (D-value, and seismic events clustering, are utilized to interpret numerical results. A non-parametric clustering algorithm designed specifically for FDEM is used to reduce the mesh dependency and extract more realistic seismic information. Simulation results indicated that at the local scale, the HF process tends to propagate following the rock mass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to the maximum in-situ stress.
Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures
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Behzad Majidi
2016-05-01
Full Text Available Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger’s model is developed using the discrete element method (DEM on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then used to estimate the Burger’s model parameters and calibrate the DEM model. The DSR tests were then simulated by a three-dimensional model. Very good agreement was observed between the experimental data and simulation results. Coke aggregates were modeled by overlapping spheres in the DEM model. Coke/pitch mixtures were numerically created by adding 5, 10, 20, and 30 percent of coke aggregates of the size range of 0.297–0.595 mm (−30 + 50 mesh to pitch. Adding up to 30% of coke aggregates to pitch can increase its complex shear modulus at 60 Hz from 273 Pa to 1557 Pa. Results also showed that adding coke particles increases both storage and loss moduli, while it does not have a meaningful effect on the phase angle of pitch.
Directory of Open Access Journals (Sweden)
Spyridon Liakas
2017-08-01
Full Text Available The particulate discrete element method (DEM can be employed to capture the response of rock, provided that appropriate bonding models are used to cement the particles to each other. Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors. Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional (2D models. In situ rock formations are often heterogeneous, thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis. In situ stress states are basically three-dimensional (3D, and therefore it is important to develop 3D models for this purpose. This paper revisits an earlier experimental study on heterogeneous specimens, of which the relative proportions of weaker material (siltstone and stronger, harder material (sandstone were varied in a controlled manner. Using a 3D DEM model with the parallel bond model, virtual heterogeneous specimens were created. The overall responses in terms of variations in strength and stiffness with different percentages of weaker material (siltstone were shown to agree with the experimental observations. There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations, suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
Podlozhnyuk, Alexander; Pirker, Stefan; Kloss, Christoph
2017-01-01
Particle shape representation is a fundamental problem in the Discrete Element Method (DEM). Spherical particles with well known contact force models remain popular in DEM due to their relative simplicity in terms of ease of implementation and low computational cost. However, in real applications particles are mostly non-spherical, and more sophisticated particle shape models, like superquadric shape, must be introduced in DEM. The superquadric shape can be considered as an extension of spherical or ellipsoidal particles and can be used for modeling of spheres, ellipsoids, cylinder-like and box(dice)-like particles just varying five shape parameters. In this study we present an efficient C++ implementation of superquadric particles within the open-source and parallel DEM package LIGGGHTS. To reduce computational time several ideas are employed. In the particle-particle contact detection routine we use the minimum bounding spheres and the oriented bounding boxes to reduce the number of potential contact pairs. For the particle-wall contact an accurate analytical solution was found. We present all necessary mathematics for the contact detection and contact force calculation. The superquadric DEM code implementation was verified on test cases such as angle of repose and hopper/silo discharge. The simulation results are in good agreement with experimental data and are presented in this paper. We show adequacy of the superquadric shape model and robustness of the implemented superquadric DEM code.
Simulation of growth normal fault sandbox tests using the 2D discrete element method
Chu, Sheng-Shin; Lin, Ming-Lang; Huang, Wen-Chao; Nien, Wei-Tung; Liu, Huan-Chi; Chan, Pei-Chen
2015-01-01
A fault slip can cause the deformation of shallow soil layers and destroy infrastructures. The Shanchiao Fault on the west side of the Taipei Basin is one such fault. The activities of the Shanchiao Fault have caused the quaternary sediment beneath the Taipei Basin to become deformed, damaging structures, traffic construction, and utility lines in the area. Data on geological drilling and dating have been used to determine that a growth fault exists in the Shanchiao Fault. In an experiment, a sandbox model was built using noncohesive sandy soil to simulate the existence of a growth fault in the Shanchiao Fault and forecast the effect of the growth fault on shear-band development and ground differential deformation. The experimental results indicated that when a normal fault contains a growth fault at the offset of the base rock, the shear band develops upward beside the weak side of the shear band of the original-topped soil layer, and surfaces considerably faster than that of the single-topped layer. The offset ratio required is approximately one-third that of the single-cover soil layer. In this study, a numerical simulation of the sandbox experiment was conducted using a discrete element method program, PFC2D, to simulate the upper-covering sand layer shear-band development pace and the scope of a growth normal fault slip. The simulation results indicated an outcome similar to that of the sandbox experiment, which can be applied to the design of construction projects near fault zones.
A parallel Discrete Element Method to model collisions between non-convex particles
Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony
2017-06-01
In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2015-01-01
In this paper, the viscoelastic behavior of asphalt mixture was studied by using discrete element method. The dynamic properties of asphalt mixture were captured by implementing Burger’s contact model. Different ways of taking into account of the normal and shear material properties of asphalt mi...
Modeling reservoir geomechanics using discrete element method : Application to reservoir monitoring
Energy Technology Data Exchange (ETDEWEB)
Alassi, Haitham Tayseer
2008-09-15
Understanding reservoir geomechanical behavior is becoming more and more important for the petroleum industry. Reservoir compaction, which may result in surface subsidence and fault reactivation, occurs during reservoir depletion. Stress changes and possible fracture development inside and outside a depleting reservoir can be monitored using time-lapse (so-called '4D') seismic and/or passive seismic, and this can give valuable information about the conditions of a given reservoir during production. In this study we will focus on using the (particle-based) Discrete Element Method (DEM) to model reservoir geomechanical behavior during depletion and fluid injection. We show in this study that DEM can be used in modeling reservoir geomechanical behavior by comparing results obtained from DEM to those obtained from analytical solutions. The match of the displacement field between DEM and the analytical solution is good, however there is mismatch of the stress field which is related to the way stress is measured in DEM. A good match is however obtained by measuring the stress field carefully. We also use DEM to model reservoir geomechanical behavior beyond the elasticity limit where fractures can develop and faults can reactivate. A general technique has been developed to relate DEM parameters to rock properties. This is necessary in order to use correct reservoir geomechanical properties during modeling. For any type of particle packing there is a limitation that the maximum ratio between P- and S-wave velocity Vp/Vs that can be modeled is 3 . The static behavior for a loose packing is different from the dynamic behavior. Empirical relations are needed for the static behavior based on numerical test observations. The dynamic behavior for both dense and loose packing can be given by analytical relations. Cosserat continuum theory is needed to derive relations for Vp and Vs. It is shown that by constraining the particle rotation, the S-wave velocity can be
Investigation of Crack Propagation in Rock using Discrete Sphero-Polyhedral Element Method
Behraftar, S.; Galindo-torres, S. A.; Scheuermann, A.; Li, L.; Williams, D.
2014-12-01
In this study a micro-mechanical model is developed to study the fracture propagation process in rocks. The model is represented by an array of bonded particles simulated by the Discrete Sphero-Polyhedral Element Model (DSEM), which was introduced by the authors previously and has been shown to be a suitable technique to model rock [1]. It allows the modelling of particles of general shape, with no internal porosity. The motivation behind using this technique is the desire to microscopically investigate the fracture propagation process and study the relationship between the microscopic and macroscopic behaviour of rock. The DSEM method is used to model the Crack Chevron Notch Brazilian Disc (CCNBD) test suggested by the International Society of Rock Mechanics (ISRM) for determining the fracture toughness of rock specimens. CCNBD samples with different crack inclination angles, are modelled to investigate their fracture mode. The Crack Mouth Opening Displacement (CMOD) is simulated and the results are validated using experimental results obtained from a previous study [2]. Fig. 1 shows the simulated and experimental results of crack propagation for different inclination angles of CCNBD specimens. The DSEM method can be used to predict crack trajectory and quantify crack propagation during loading. References: 1. Galindo-Torres, S. A., et al. "Breaking processes in three-dimensional bonded granular materials with general shapes." Computer Physics Communications 183.2 (2012): 266-277. 2. Erarslan, N., and D. J. Williams. "Mixed-mode fracturing of rocks under static and cyclic loading." Rock mechanics and rock engineering 46.5 (2013): 1035-1052.
Fish Passage though Hydropower Turbines: Simulating Blade Strike using the Discrete Element Method
Energy Technology Data Exchange (ETDEWEB)
Richmond, Marshall C.; Romero Gomez, Pedro DJ
2014-12-08
mong the hazardous hydraulic conditions affecting anadromous and resident fish during their passage though turbine flows, two are believed to cause considerable injury and mortality: collision on moving blades and decompression. Several methods are currently available to evaluate these stressors in installed turbines, i.e. using live fish or autonomous sensor devices, and in reduced-scale physical models, i.e. registering collisions from plastic beads. However, a priori estimates with computational modeling approaches applied early in the process of turbine design can facilitate the development of fish-friendly turbines. In the present study, we evaluated the frequency of blade strike and nadir pressure environment by modeling potential fish trajectories with the Discrete Element Method (DEM) applied to fish-like composite particles. In the DEM approach, particles are subjected to realistic hydraulic conditions simulated with computational fluid dynamics (CFD), and particle-structure interactions—representing fish collisions with turbine blades—are explicitly recorded and accounted for in the calculation of particle trajectories. We conducted transient CFD simulations by setting the runner in motion and allowing for better turbulence resolution, a modeling improvement over the conventional practice of simulating the system in steady state which was also done here. While both schemes yielded comparable bulk hydraulic performance, transient conditions exhibited a visual improvement in describing flow variability. We released streamtraces (steady flow solution) and DEM particles (transient solution) at the same location from where sensor fish (SF) have been released in field studies of the modeled turbine unit. The streamtrace-based results showed a better agreement with SF data than the DEM-based nadir pressures did because the former accounted for the turbulent dispersion at the intake but the latter did not. However, the DEM-based strike frequency is more
Modeling of crack propagation in weak snowpack layers using the discrete element method
Directory of Open Access Journals (Sweden)
J. Gaume
2015-01-01
Full Text Available Dry-snow slab avalanches are generally caused by a sequence of fracture processes including (1 failure initiation in a weak snow layer underlying a cohesive slab, (2 crack propagation within the weak layer and (3 tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e. to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited. For instance, it is not uncommon to perform field measurements with widespread crack propagation on one day, while a few days later, with very little changes to the snowpack, crack propagation does not occur anymore. Thus far, there is no clear theoretical framework to interpret such observations, and it is not clear how and which snowpack properties affect dynamic crack propagation. To shed more light on this issue, we performed numerical propagation saw test (PST experiments applying the discrete element (DE method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, the relation between mechanical parameters of the snowpack was taken into account so as to compare numerical and experimental results, which were in good agreement, suggesting that the simulations can reproduce crack propagation in PSTs. Finally, an in-depth analysis of the
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Directory of Open Access Journals (Sweden)
Haitao Cao
2014-01-01
Full Text Available We propose a fully discrete method for the multiscale Richards’ equation of van Genuchten-Mualem model which describes the flow transport in unsaturated heterogenous porous media. Under the framework of heterogeneous multiscale method (HMM, a fully discrete scheme combined with a regularized procedure is proposed. Including the numerical integration, the discretization is given by C0 piecewise finite element in space and an implicit scheme in time. Error estimates between the numerical solution and the solution of homogenized problem are derived under the assumption that the permeability is periodic. Numerical experiments with periodic and random permeability are carried out for the van Genuchten-Mualem model of Richards’ equation to show the efficiency and accuracy of the proposed method.
Fish passage through hydropower turbines: Simulating blade strike using the discrete element method
Richmond, M. C.; Romero-Gomez, P.
2014-03-01
Among the hazardous hydraulic conditions affecting anadromous and resident fish during their passage though hydro-turbines two common physical processes can lead to injury and mortality: collisions/blade-strike and rapid decompression. Several methods are currently available to evaluate these stressors in installed turbines, e.g. using live fish or autonomous sensor devices, and in reduced-scale physical models, e.g. registering collisions from plastic beads. However, a priori estimates with computational modeling approaches applied early in the process of turbine design can facilitate the development of fish-friendly turbines. In the present study, we evaluated the frequency of blade strike and rapid pressure change by modeling potential fish trajectories with the Discrete Element Method (DEM) applied to fish-like composite particles. In the DEM approach, particles are subjected to realistic hydraulic conditions simulated with computational fluid dynamics (CFD), and particle-structure interactions-representing fish collisions with turbine components such as blades-are explicitly recorded and accounted for in the calculation of particle trajectories. We conducted transient CFD simulations by setting the runner in motion and allowing for unsteady turbulence using detached eddy simulation (DES), as compared to the conventional practice of simulating the system in steady state (which was also done here for comparison). While both schemes yielded comparable bulk hydraulic performance values, transient conditions exhibited an improvement in describing flow temporal and spatial variability. We released streamtraces (in the steady flow solution) and DEM particles (transient solution) at the same locations where sensor fish (SF) were released in previous field studies of the advanced turbine unit. The streamtrace- based results showed a better agreement with SF data than the DEM-based nadir pressures did because the former accounted for the turbulent dispersion at the
Mandal, Sandip; Khakhar, D. V.
2016-10-01
Granular materials handled in industries are typically non-spherical in shape and understanding the flow of such materials is important. The steady flow of mono-disperse, frictional, inelastic dumbbells in two-dimensions is studied by soft sphere, discrete element method simulations for chute flow and shear cell flow. The chute flow data are in the dense flow regime, while the shear cell data span a wide range of solid fractions. Results of a detailed parametric study for both systems are presented. In chute flow, increase in the aspect ratio of the dumbbells results in significant slowing of the flow at a fixed inclination and in the shear cell it results in increase in the shear stress and pressure for a fixed shear rate. The flow is well-described by the μ-I scaling for inertial numbers as high as I = 1, corresponding to solid fractions as low as ϕ = 0.3, where μ is the effective friction (the ratio of shear stress to pressure) and I is the inertial number (a dimensionless shear rate scaled with the time scale obtained from the local pressure). For a fixed inertial number, the effective friction increases by 60%-70% when aspect ratio is increased from 1.0 (sphere) to 1.9. At low values of the inertial number, there is little change in the solid fraction with aspect ratio of the dumbbells, whereas at high values of the inertial number, there is a significant increase in solid fraction with increase in aspect ratio. The dense flow data are well-described by the Jop-Forterre-Pouliquen model [P. Jop et al., Nature 441, 727-730 (2006)] with the model parameters dependent on the dumbbell aspect ratio. The variation of μ with I over the extended range shows a maximum in the range I ∈ (0.4, 0.5), while the solid fraction shows a faster than linear decrease with inertial number. A modified version of the JFP model for μ(I) and a power law model for ϕ(I) is shown to describe the combined data over the extended range of I.
Bedload Transport on Steep Slopes with Coupled Modeling Based on the Discrete Element Method
Chauchat, J.; Maurin, R.; Chareyre, B.; Frey, P.
2014-12-01
After more than a century of research, a clear understanding of the physical processes involved in sediment transport problems is still lacking. In particular, modeling of intergranular interactions and fluid-particle interactions in bedload transport need to be improved. In this contribution, we propose a simple numerical model coupling a Discrete Element Method (DEM) for the grain dynamics with a simple 1D vertical fluid phase model inspired from the two-phase approach [1] in order to contribute to this open question. The Reynolds stress is parameterized by a mixing length model which depends on the integral of the grain volume fraction. The coupling between the grains and the fluid phase is essentially achieved through buoyancy and drag forces. The open source DEM code Yade [2] is used with a linear spring-dashpot contact law that allows the description of the behavior of the particles from the quasi-static to the dynamical state. The model is compared with classical results [3] and with particle-scale experimental results obtained in the quasi-2D flume at IRSTEA, Grenoble [4]. We discuss the closures of the model and the sensitivity to the different physical and numerical parameters. [1] Revil-Baudard, T. and J. Chauchat. A two-phase model for sheet flow regime based on dense granular flow rheology. Journal of Geophysical Research: Oceans, 118(2):619-634, 2013. [2] Šmilauer V. , E. Catalano, B. Chareyre, S. Dorofeenko, J. Duriez, A. Gladky, J. Kozicki, C . Modenese, L. Scholtès, L. Sibille, J. Str.nský, and K. Thoeni. Yade Documentation (V. Šmilauer, ed.), The Yade Project, 1st ed., http://yade-dem.org/doc/., 2010. [3] Meyer-Peter, E. and R. Müller. Formulas for bed-load transport. In Proc. 2nd Meeting, pages 39-64. IAHR, 1948. [4] Frey, P. Particle velocity and concentration profiles in bedload experiments on a steep slope. Earth Surface Processes and Landforms, 39(5):646-655, 2014.
Modelling Gas Diffusion from Breaking Coal Samples with the Discrete Element Method
Directory of Open Access Journals (Sweden)
Dan-Ling Lin
2015-01-01
Full Text Available Particle scale diffusion is implemented in the discrete element code, Esys-Particle. We focus on the question of how to calibrate the particle scale diffusion coefficient. For the regular 2D packing, theoretical relation between micro- and macrodiffusion coefficients is derived. This relation is then verified in several numerical tests where the macroscopic diffusion coefficient is determined numerically based on the half-time of a desorption scheme. To further test the coupled model, we simulate the diffusion and desorption in the circular sample. The numerical results match the analytical solution very well. An example of gas diffusion and desorption during sample crushing and fragmenting is given at the last. The current approach is the first step towards a realistic and comprehensive modelling of coal and gas outbursts.
Kulchitsky, A. V.; Johnson, J.; Duvoy, P.; Wilkinson, A.; Creager, C. M.
2012-12-01
For in situ resource utilization on the Moon, asteroids, Mars, or other space body it is necessary to be able to simulate the interaction of mobile platforms and excavation machines with the regolith for engineering design, planning, and operations. For accurate simulations, tools designed to measure regolith properties will need to be deployed and interpreted. Two such tools are the penetrometer, used to measure a soil strength index as a function of depth, and the bevameter, used to characterize regolith surface properties of strength, friction and sinkage. The penetrometer interrogates regolith properties from the surface to a depth limited only by the capabilities of the instrument to penetrate the regolith while a bevameter interrogates only the upper few centimeters needed to describe a mobility platform's traction and sinkage. Interpretation of penetrometer and bevameter data can be difficult, especially on low gravity objects. We use the discrete element method (DEM) model to simulate the large regolith deformations and failures associated with the tests to determine regolith properties. The DEM simulates granular material behavior using large aggregates of distinct particles. Realistic physics of particle-particle interaction introduces many granular specific phenomena such as interlocking and force chain formation that cannot be represented using continuum methods. In this work, experiments using a cone penetrometer test (CPT) and bevameter on lunar simulants JSC-1A and GRC-1 were performed at NASA Glenn Research Center. These tests were used to validate the physics in the COUPi DEM model. COUPi is a general physical DEM code being developed to model machine/regolith interactions as part of a NASA Lunar Science Institute sponsored project on excavation and mobility modeling. The experimental results were used in this work to build an accurate model to simulate the lunar regolith. The CPT consists of driving an instrumented cone with opening angle of 60
Matuttis, Hans-Georg
2014-01-01
Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particlesProvides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulationHighlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiment
Yeom, Seungcheol; Sjoblom, Kurt
2016-12-01
The mechanical nature of crust formation as a result of raindrop impacts was simulated within a discrete element modeling environment. Simulations were conducted in two-dimensions (2D) using both linear and non-linear elastic contact models. The 2D approach was found to minimize the computational effort required and maximize the number of particles in the soil profile. For the non-linear model, the effect of the coefficient of restitution (COR) for soil-rain and soil-soil was investigated. Finally, the comparison between the linear and nonlinear elastic contact model was presented. The simulation indicated that the COR for rain-soil had negligible effect on the crust development but the computational time was exponentially increased with increasing coefficient value. In contrast, the COR for soil-soil had a dominant influence on the crust development. To validate the numerical results, a micro computerized tomography (microCT) technique was applied to characterize the changes in pore structure to a USCS SP soil after exposure under a rainfall simulator. Additionally, the effect of cyclic wetting and drying (without rainfall) on the changes in porosity was investigated. The experimental results showed that the rainfall simulator sufficiently densified the soil but the effect of cyclic wetting and drying was negligible. The numerical simulations showed similar changes in porosity along the depth of the soil profile as compared with the experimental results thus validating the DEM technique to simulate crust development.
Directory of Open Access Journals (Sweden)
Maitraye Sen
2017-04-01
Full Text Available A discrete element model (DEM has been developed for an industrial batch bin blender in which three different types of materials are mixed. The mixing dynamics have been evaluated from a model-based study with respect to the blend critical quality attributes (CQAs which are relative standard deviation (RSD and segregation intensity. In the actual industrial setup, a sensor mounted on the blender lid is used to determine the blend composition in this region. A model-based analysis has been used to understand the mixing efficiency in the other zones inside the blender and to determine if the data obtained near the blender-lid region are able to provide a good representation of the overall blend quality. Sub-optimal mixing zones have been identified and other potential sampling locations have been investigated in order to obtain a good approximation of the blend variability. The model has been used to study how the mixing efficiency can be improved by varying the key processing parameters, i.e., blender RPM/speed, fill level/volume and loading order. Both segregation intensity and RSD reduce at a lower fill level and higher blender RPM and are a function of the mixing time. This work demonstrates the use of a model-based approach to improve process knowledge regarding a pharmaceutical mixing process. The model can be used to acquire qualitative information about the influence of different critical process parameters and equipment geometry on the mixing dynamics.
Roux, A; Laporte, S; Lecompte, J; Gras, L-L; Iordanoff, I
2016-01-25
The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC׳s behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young׳s modulus values of the MTC׳s components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle׳s fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure׳s effects, added to the geometrical parameters, highlight the MTC׳s mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC׳s components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements. Copyright © 2015 Elsevier Ltd. All rights reserved.
Discrete element modeling of subglacial sediment deformation
DEFF Research Database (Denmark)
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.
2013-01-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the...
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 曾庆存; 谢正辉
2004-01-01
The mixed finite element (MFE) methods for a shallow water equation system consisting of water dynamics equations, silt transport equation, and the equation of bottom topography change were derived. A fully discrete MFE scheme for the discrete-time along characteristics is presented and error estimates are established. The existence and convergence of MFE solution of the discrete current velocity, elevation of the bottom topography, thickness of fluid column, and mass rate of sediment is demonstrated.
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J. Ochoa-Avendaño
2017-01-01
Full Text Available This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.
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Qingdong Zeng
2015-10-01
Full Text Available Fluid-solid coupling is ubiquitous in the process of fluid flow underground and has a significant influence on the development of oil and gas reservoirs. To investigate these phenomena, the coupled mathematical model of solid deformation and fluid flow in fractured porous media is established. In this study, the discrete fracture model (DFM is applied to capture fluid flow in the fractured porous media, which represents fractures explicitly and avoids calculating shape factor for cross flow. In addition, the extended finite element method (XFEM is applied to capture solid deformation due to the discontinuity caused by fractures. More importantly, this model captures the change of fractures aperture during the simulation, and then adjusts fluid flow in the fractures. The final linear equation set is derived and solved for a 2D plane strain problem. Results show that the combination of discrete fracture model and extended finite element method is suited for simulating coupled deformation and fluid flow in fractured porous media.
Gao, F. Q.; Kang, H. P.
2016-04-01
When rock failure is unavoidable, the designer of engineering structures must know and account for the residual strength of the rock mass. This is particularly relevant in underground coal mine openings. Pre-existing discontinuities play an important role in the mechanical behavior of rock masses and thus it is important to understand the effects of such pre-existing discontinuities on the residual strength. For this purpose, the present study demonstrates a numerical analysis using a discrete element method simulation. The numerical results indicate that fracture intensity has no significant influence on the residual strength of jointed rock masses, independent of confining conditions. As confining pressures increase, both peak and residual strengths increase, with residual strength increasing at a faster rate. The finding was further demonstrated by analyzing documented laboratory compressive test data from a variety of rocks along with field data from coal pillars. A comprehensive interpretation of the finding was conducted using a cohesion-weakening-friction-strengthening (CWFS) model. The effect of rock bolts on rock mass strength was also evaluated by using a discrete element method model which suggested that rock bolts can significantly increases residual strength but have limited effect on increasing the peak strength of rock masses.
Discrete element method based scale-up model for material synthesis using ball milling
Santhanam, Priya Radhi
Mechanical milling is a widely used technique for powder processing in various areas. In this work, a scale-up model for describing this ball milling process is developed. The thesis is a combination of experimental and modeling efforts. Initially, Discrete Element Model (DEM) is used to describe energy transfer from milling tools to the milled powder for shaker, planetary, and attritor mills. The rolling and static friction coefficients are determined experimentally. Computations predict a quasisteady rate of energy dissipation, E d, for each experimental configuration. It is proposed that the milling dose defined as a product of Ed and milling time, t, divided by the mass of milled powder, mp characterizes the milling progress independently of the milling device or milling conditions used. Once the milling dose is determined for one experimental configuration, it can be used to predict the milling time required to prepare the same material in any milling configuration, for which Ed is calculated. The concept is validated experimentally for DEM describing planetary and shaker mills. For attritor, the predicted Ed includes substantial contribution from milling tool interaction events with abnormally high forces (>103 N). The energy in such events is likely dissipated to heat or plastically deform milling tools rather than refine material. Indeed, DEM predictions for the attritor correlate with experiments when such events are ignored in the analysis. With an objective of obtaining real-time indicators of milling progress, power, torque, and rotation speed of the impeller of an attritor mill are measured during preparation of metal matrix composite powders in the subsequent portion of this thesis. Two material systems are selected and comparisons made between in-situ parameters and experimental milling progress indicators. It is established that real-time measurements can certainly be used to describe milling progress. However, they need to be interpreted carefully
Tian, Wenyi; Yuan, Xiaoming
2016-11-01
Linear inverse problems with total variation regularization can be reformulated as saddle-point problems; the primal and dual variables of such a saddle-point reformulation can be discretized in piecewise affine and constant finite element spaces, respectively. Thus, the well-developed primal-dual approach (a.k.a. the inexact Uzawa method) is conceptually applicable to such a regularized and discretized model. When the primal-dual approach is applied, the resulting subproblems may be highly nontrivial and it is necessary to discuss how to tackle them and thus make the primal-dual approach implementable. In this paper, we suggest linearizing the data-fidelity quadratic term of the hard subproblems so as to obtain easier ones. A linearized primal-dual method is thus proposed. Inspired by the fact that the linearized primal-dual method can be explained as an application of the proximal point algorithm, a relaxed version of the linearized primal-dual method, which can often accelerate the convergence numerically with the same order of computation, is also proposed. The global convergence and worst-case convergence rate measured by the iteration complexity are established for the new algorithms. Their efficiency is verified by some numerical results.
Virgo, Simon; Ankit, Kumar; Nestler, Britta; Urai, Janos L.
2016-04-01
Crack-seal veins form in a complex interplay of coupled thermal, hydraulic, mechanical and chemical processes. Their formation and cyclic growth involves brittle fracturing and dilatancy, phases of increased fluid flow and the growth of crystals that fill the voids and reestablish the mechanical strength. Existing numerical models of vein formation focus on selected aspects of the coupled process. Until today, no model exists that is able to use a realistic representation of the fracturing AND sealing processes, simultaneously. To address this challenge, we propose the bidirectional coupling of two numerical methods that have proven themselves as very powerful to model the fundamental processes acting in crack-seal systems: Phase-field and the Discrete Element Method (DEM). The phase-field Method was recently successfully extended to model the precipitation of quartz crystals from an aqueous solution and applied to model the sealing of a vein over multiple opening events (Ankit et al., 2013; Ankit et al., 2015a; Ankit et al., 2015b). The advantage over former, purely kinematic approaches is that in phase-field, the crystal growth is modeled based on thermodynamic and kinetic principles. Different driving forces for microstructure evolution, such as chemical bulk free energy, interfacial energy, elastic strain energy and different transport processes, such as mass diffusion and advection, can be coupled and the effect on the evolution process can be studied in 3D. The Discrete Element Method was already used in several studies to model the fracturing of rocks and the incremental growth of veins by repeated fracturing (Virgo et al., 2013; Virgo et al., 2014). Materials in DEM are represented by volumes of packed spherical particles and the response to the material to stress is modeled by interaction of the particles with their nearest neighbours. For rocks, in 3D, the method provides a realistic brittle failure behaviour. Exchange Routines are being developed that
Energy Technology Data Exchange (ETDEWEB)
Tao, Liang; McCurdy, C.W.; Rescigno, T.N.
2008-11-25
We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.
Directory of Open Access Journals (Sweden)
Jae-Hong Pyo
2013-01-01
Full Text Available The stabilized Gauge-Uzawa method (SGUM, which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations on the fully discrete finite element space via variational approach for the velocity, pressure, and temperature, the three physical unknowns. We conclude with numerical tests to check accuracy and physically relevant numerical simulations, the Bénard convection problem and the thermal driven cavity flow.
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Stang, Henrik
2016-01-01
modulus. Three different approaches have been used and compared for calibrating the Burger's contact model. Values of the dynamic modulus and phase angle of asphalt mixtures were predicted by conducting DE simulation under dynamic strain control loading. The excellent agreement between the predicted......In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional discrete element method. Combined with Burger's model, three contact models were used for the construction of constitutive asphalt mixture model with viscoelastic properties...... in the commercial software PFC3D, including the slip model, linear stiffness-contact model, and contact bond model. A macro-scale Burger's model was first established and the input parameters of Burger's contact model were calibrated by adjusting them so that the model fitted the experimental data for the complex...
A Study of Three Intrinsic Problems of the Classic Discrete Element Method Using Flat-Joint Model
Wu, Shunchuan; Xu, Xueliang
2016-05-01
Discrete element methods have been proven to offer a new avenue for obtaining the mechanics of geo-materials. The standard bonded-particle model (BPM), a classic discrete element method, has been applied to a wide range of problems related to rock and soil. However, three intrinsic problems are associated with using the standard BPM: (1) an unrealistically low unconfined compressive strength to tensile strength (UCS/TS) ratio, (2) an excessively low internal friction angle, and (3) a linear strength envelope, i.e., a low Hoek-Brown (HB) strength parameter m i . After summarizing the underlying reasons of these problems through analyzing previous researchers' work, flat-joint model (FJM) is used to calibrate Jinping marble and is found to closely match its macro-properties. A parametric study is carried out to systematically evaluate the micro-parameters' effect on these three macro-properties. The results indicate that (1) the UCS/TS ratio increases with the increasing average coordination number (CN) and bond cohesion to tensile strength ratio, but it first decreases and then increases with the increasing crack density (CD); (2) the HB strength parameter m i has positive relationships to the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle, but a negative relationship to the average coordination number (CN); (3) the internal friction angle increases as the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle increase; (4) the residual friction angle has little effect on these three macro-properties and mainly influences post-peak behavior. Finally, a new calibration procedure is developed, which not only addresses these three problems, but also considers the post-peak behavior.
Cil, Mehmet B.; Alshibli, Khalid A.
2015-02-01
The constitutive behavior and deformation characteristics of uncemented granular materials are to a large extent derived from the fabric or geometry of the particle structure and the interparticle friction resulting from normal forces acting on particles or groups of particles. Granular materials consist of discrete particles with a fabric (microstructure) that changes under loading. Synchrotron micro-computed tomography (SMT) has emerged as a powerful non-destructive 3D scanning technique to study geomaterials. In this paper, SMT was used to acquire in situ scans of the oedometry test of a column of three silica sand particles. The sand is known as ASTM 20-30 Ottawa sand, and has a grain size between US sieves #20 (0.841 mm) and #30 (0.595 mm). The characteristics and evolution of particle fracture in sand were examined using SMT images, and a 3D discrete element method (DEM) was used to model the fracture behavior of sand particles. It adopts the bonded particle model to generate a crushable agglomerate that consists of a large number of small spherical sub-particles. The agglomerate shape matches the 3D physical shape of the tested sand particles by mapping the particle morphology from the SMT images. The paper investigates and discusses the influence of agglomerate packing (i.e., the number and size distribution of spherical sub-particles that constitute the agglomerate) and agglomerate shape on the fracture behavior of crushable particles.
Discrete mathematics, discrete physics and numerical methods
Directory of Open Access Journals (Sweden)
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
The compaction of a random distribution of metal cylinders by the discrete element method
DEFF Research Database (Denmark)
Redanz, Pia; Fleck, N. A.
2001-01-01
-linear springs. The initial packing of the particles is generated by the ballistic deposition method. Salient micromechanical features of closed die and isostatic powder compaction are elucidated for both frictionless and sticking contacts. It is found that substantial rearrangement of frictionless particles...
Pestiaux, A.; Kärnä, T.; Melchior, S.; Lambrechts, J.; Remacle, J. F.; Deleersnijder, E.; Fichefet, T.
2012-04-01
The discretization of the Gent-McWilliams velocity and isopycnal diffusion with a discontinuous Galerkin finite element method is presented. Both processes are implemented in an ocean model thanks to a tensor related to the mesoscale eddies. The antisymmetric part of this tensor is computed from the Gent-McWilliams velocity and is subsequently included in the tracer advection equation. This velocity can be constructed to be divergence-free. The symmetric part that describes the diapycnal and isopycnal diffusions requires a special treatment. A stable and physically sound isopycnal tracer diffusion scheme is needed. Here, an interior penalty method is chosen that enables to build stable diffusion terms. However, due to the strong anisotropy of the diffusion, the common-usual penalty factor by Ern et al. (2008) is not sufficient. A novel method for computing the penalty term of Ern is then proposed for diffusion equations when both the diffusivity and the mesh are strongly anisotropic. Two test cases are resorted to validate the methodology and two more realistic applications illustrate the diapycnal and isopycnal diffusions, as well as the Gent-McWilliams velocity.
Marson, Ryan; Spellings, Matthew; Anderson, Joshua; Glotzer, Sharon
2014-03-01
Faceted shapes, such as polyhedra, are commonly created in experimental systems of nanoscale, colloidal, and granular particles. Many interesting physical phenomena, like crystalline nucleation and growth, vacancy motion, and glassy dynamics, are challenging to model in these systems because they require detailed dynamical information at the individual particle level. Within the granular materials community the Discrete Element Method has been used extensively to model systems of anisotropic particles under gravity, with friction. We report the first implementation of DEM MD intended for thermodynamic nanoscale simulation. Our method is implemented in parallel on the GPU within the HOOMD-Blue framework. By decomposing the force calculation into its components, this implementation can take advantage of massive data parallelism, enabling optimal use of the GPU for even relatively small systems while achieving a speedup of 60 times over a single CPU core. This method is a natural extension of classical molecular dynamics into the realm of faceted particles, and allows simulation of disparate size scales ranging from the nanoscale to granular particulates, all within the same framework.
Luding, Stefan
2008-01-01
One challenge of today's research is the realistic simulation of granular materials, like sand or powders, consisting of millions of particles. In this article, the discrete element method (DEM), as based on molecular dynamics methods, is introduced. Contact models are at the physical basis of DEM.
Discrete elements for 3D microfluidics.
Bhargava, Krisna C; Thompson, Bryant; Malmstadt, Noah
2014-10-21
Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry.
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Guodong Liu
2013-01-01
Full Text Available Modular pebble-bed nuclear reactor (MPBNR technology is promising due to its attractive features such as high fuel performance and inherent safety. Particle motion of fuel and graphite pebbles is highly associated with the performance of pebbled-bed modular nuclear reactor. To understand the mechanism of pebble’s motion in the reactor, we numerically studied the influence of number ratio of fuel and graphite pebbles, funnel angle of the reactor, height of guide ring on the distribution of pebble position, and velocity by means of discrete element method (DEM in a two-dimensional MPBNR. Velocity distributions at different areas of the reactor as well as mixing characteristics of fuel and graphite pebbles were investigated. Both fuel and graphite pebbles moved downward, and a uniform motion was formed in the column zone, while pebbles motion in the cone zone was accelerated due to the decrease of the cross sectional flow area. The number ratio of fuel and graphite pebbles and the height of guide ring had a minor influence on the velocity distribution of pebbles, while the variation of funnel angle had an obvious impact on the velocity distribution. Simulated results agreed well with the work in the literature.
Tran, Quoc Anh; Chevalier, Bastien; Benz, Miguel; Breul, Pierre; Gourvès, Roland
2017-06-01
The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load-penetration curve σp - sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load-penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip's load-penetration curve. The load-penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.
2017-01-01
We report a computational fluid dynamics–discrete element method (CFD-DEM) simulation study on the interplay between mass transfer and a heterogeneous catalyzed chemical reaction in cocurrent gas-particle flows as encountered in risers. Slip velocity, axial gas dispersion, gas bypassing, and particle mixing phenomena have been evaluated under riser flow conditions to study the complex system behavior in detail. The most important factors are found to be directly related to particle cluster formation. Low air-to-solids flux ratios lead to more heterogeneous systems, where the cluster formation is more pronounced and mass transfer more influenced. Falling clusters can be partially circumvented by the gas phase, which therefore does not fully interact with the cluster particles, leading to poor gas–solid contact efficiencies. Cluster gas–solid contact efficiencies are quantified at several gas superficial velocities, reaction rates, and dilution factors in order to gain more insight regarding the influence of clustering phenomena on the performance of riser reactors. PMID:28553011
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Goh Wei Pin
2017-01-01
Full Text Available The size distribution, shape and aspect ratio of particles are the common factors that affect their packing in a particle bed. Agitated powder beds are commonly used in the process industry for various applications. The stresses arising as a result of shearing the bed could result in undesirable particle breakage with adverse impact on manufacturability. We report on our work on analysing the stress distribution within an agitated particle bed with several particle aspect ratios by the Discrete Element Method (DEM. Rounded cylinders with different aspect ratios are generated and incorporated into the DEM simulation. The void fraction of the packing of the static and agitated beds with different particle aspect ratios is analysed. Principal and deviatoric stresses are quantified in the regions of interest along the agitating impeller blade for different cases of particle aspect ratios. The relationship between the particle aspect ratio and the stress distribution of the bed over the regions of interest is then established and will be presented.
Discrete Element Analysis of Huangtupo Landslide
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
On the basis of the deep geology and the geological structure of Huangtupo landslide, an ancient landslide in the reservoir of the Three Gorges, the geo-environmental model of the landslide is established to analyze quantitatively the sliding mechanism by using the discrete element method. It is concluded that interbedding structure of soft and hard formation consists of the main geological background,which induced the arching of the formation under gravity. Stability analysis of different loadings shows that the ground building weight on the middle slope may restrain the extension of shear sliding zone below, but may activate the foot area which will reduce the safety factor of the front.
New discrete element models for elastoplastic problems
Institute of Scientific and Technical Information of China (English)
Ming Cheng; Weifu Liu; Kaixin Liu
2009-01-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application, The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
New discrete element models for elastoplastic problems
Cheng, Ming; Liu, Weifu; Liu, Kaixin
2009-10-01
The discrete element method (DEM) has attractive features for problems with severe damages, but lack of theoretical basis for continua behavior especially for nonlinear behavior has seriously restricted its application. The present study proposes a new approach to developing the DEM as a general and robust technique for modeling the elastoplastic behavior of solid materials. New types of connective links between elements are proposed, the inter-element parameters are theoretically determined based on the principle of energy equivalence and a yield criterion and a flow rule for DEM are given for describing nonlinear behavior of materials. Moreover, a numerical scheme, which can be applied to modeling the behavior of a continuum as well as the transformation from a continuum to a discontinuum, is obtained by introducing a fracture criterion and a contact model into the DEM. The elastoplastic stress wave propagations and the tensile failure process of a steel plate are simulated, and the numerical results agree well with those obtained from the finite element method (FEM) and corresponding experiment, and thus the accuracy and efficiency of the DEM scheme are demonstrated.
Zeeb, Conny; Frühwirt, Thomas; Konietzky, Heinz
2015-04-01
Key to a successful exploitation of deep geothermal reservoirs in a petrothermal environment is the hydraulic stimulation of the host rock to increase permeability. The presented research investigates the fracture propagation and interaction during hydraulic stimulation of multiple fractures in a highly anisotropic stress field. The presented work was conducted within the framework of the OPTIRISS project, which is a cooperation of industry partners and universities in Thuringia and Saxony (Federal States of Germany) and was funded by the European Fond for Regional Development. One objective was the design optimization of the subsurface geothermal heat exchanger (SGHE) by means of numerical simulations. The presented simulations were conducted applying 3DEC (Itasca™), a software tool based on the discrete element method. The simulation results indicate that the main direction of fracture propagation is towards lower stresses and thus towards the biosphere. Therefore, barriers might be necessary to limit fracture propagation to the designated geological formation. Moreover, the hydraulic stimulation significantly alters the stresses in the vicinity of newly created fractures. Especially the change of the minimum stress component affects the hydraulic stimulation of subsequent fractures, which are deflected away from the previously stimulated fractures. This fracture deflection can render it impossible to connect all fractures with a second borehole for the later production. The results of continuative simulations indicate that a fracture deflection cannot be avoided completely. Therefore, the stage alignment was modified to minimize fracture deflection by varying (1) the pauses between stages, (2) the spacing's between adjacent stages, and (3) the angle between stimulation borehole and minimum stress component. An optimum SGHE design, which implies that all stimulated fractures are connected to the production borehole, can be achieved by aligning the stimulation
Institute of Scientific and Technical Information of China (English)
Yin-nianHe
2004-01-01
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a H1-optimal velocity approximation and a L2-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small,nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, one linear Stokes problem on the fine mesh with mesh size h <
Discretized Volumes in Numerical Methods
Antal, Miklós
2007-01-01
We present two techniques novel in numerical methods. The first technique compiles the domain of the numerical methods as a discretized volume. Congruent elements are glued together to compile the domain over which the solution of a boundary value problem is sought. We associate a group and a graph to that volume. When the group is symmetry of the boundary value problem under investigation, one can specify the structure of the solution, and find out if there are equispectral volumes of a given type. The second technique uses a complex mapping to transplant the solution from volume to volume and a correction function. Equation for the correction function is given. A simple example demonstrates the feasibility of the suggested method.
Directory of Open Access Journals (Sweden)
Akimov Pavel
2016-01-01
Full Text Available The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM. This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction, also decrease the size of the problem to one-dimensional common finite element analysis. Two numerical examples of structural analysis with the use of DCFEM are considered, conventional finite element method (FEM is used for verification purposes. The presented examples show some of the advantages of the suggested approach to semianalytical analysis of the shear wall. Future development of DCFEM, particularly associated with multigrid approach, is under consideration as well.
Directory of Open Access Journals (Sweden)
L. Jones Tarcius Doss
2012-01-01
Full Text Available A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Sheikh, Bahman; Pak, Ali
2015-05-01
Permeability of porous materials is an important characteristic which is extensively used in various engineering disciplines. There are a number of issues that influence the permeability coefficient among which the porosity, size of particles, pore shape, tortuosity, and particle size distribution are of great importance. In this paper a C++ GPU code based on three-dimensional lattice Boltzmann method (LBM) has been developed and used for investigating the effects of the above mentioned factors on the permeability coefficient of granular materials. Multirelaxation time collision scheme of the LBM equations is used in the simulator, which is capable of modeling the exact position of the fluid-solid interface leading to viscosity-independent permeabilities and better computational stability due to separation of the relaxations of various kinetic models. GPU-CPU parallel processing has been employed to reduce the computational time associated with three-dimensional simulations. Soil samples have been prepared using the discrete element method. The obtained results have demonstrated the importance of employing the concept of effective porosity instead of total porosity in permeability relationships. The results also show that a threshold porosity exists below which the connectivity of the pores vanishes and the permeability of the soils reduces drastically.
Discrete element simulation of crushable rockfill materials
Institute of Scientific and Technical Information of China (English)
Lei SHAO; Shi-chun CHI; Liang-jing ZHOU; Yu-zan WANG
2013-01-01
A discrete element method was used to study the evolution of particle crushing in a rockfill sample subjected to triaxial shear. A simple procedure was developed to generate clusters with arbitrary shapes, which resembled real rockfill particles. A theoretical method was developed to define the failure criterion for an individual particle subjected to an arbitrary set of contact forces. Then, a series of numerical tests of large-scale drained triaxial tests were conducted to simulate the behaviors of the rockfill sample. Finally, we examined the development of micro-characteristics such as particle crushing, contact characteristics, porosity, deformation, movement, and energy dissipation. The simulation results were partially compared with the laboratory experiments, and good agreement was achieved, demonstrating that the particle crushing model proposed can be used to simulate the drained triaxial test of rockfill materials. Based on a comparison of macro behaviors of the rockfill sample and micro structures of the particles, the microscopic mechanism of the rockfill materials subjected to triaxial shear was determined qualitatively. It is shown that the crushing rate, rather than the number of crushed particles, can be used to reflect the relationship between macro- and micro-mechanical characteristics of rockfill materials. These research results further develop our understanding of the deformation mechanism of rockfill materials.
Discrete element simulation of crushable rockfill materials
Directory of Open Access Journals (Sweden)
Lei SHAO
2013-04-01
Full Text Available A discrete element method was used to study the evolution of particle crushing in a rockfill sample subjected to triaxial shear. A simple procedure was developed to generate clusters with arbitrary shapes, which resembled real rockfill particles. A theoretical method was developed to define the failure criterion for an individual particle subjected to an arbitrary set of contact forces. Then, a series of numerical tests of large-scale drained triaxial tests were conducted to simulate the behaviors of the rockfill sample. Finally, we examined the development of micro-characteristics such as particle crushing, contact characteristics, porosity, deformation, movement, and energy dissipation. The simulation results were partially compared with the laboratory experiments, and good agreement was achieved, demonstrating that the particle crushing model proposed can be used to simulate the drained triaxial test of rockfill materials. Based on a comparison of macro behaviors of the rockfill sample and micro structures of the particles, the microscopic mechanism of the rockfill materials subjected to triaxial shear was determined qualitatively. It is shown that the crushing rate, rather than the number of crushed particles, can be used to reflect the relationship between macro- and micro-mechanical characteristics of rockfill materials. These research results further develop our understanding of the deformation mechanism of rockfill materials.
大西, 泰史
2017-01-01
The purpose of this study is to perform to earth pressure coefficient calculation simulation using the Distinct Element Method (DEM). Earth pressure theory has been established since long ago and is still in use. Therefore, simulation based on Coulomb and Rankine's theory of earth pressure is carried out to confirm usability of DEM. As a result of the static earth pressure coefficient calculation simulation, good results were obtained. However, in the passive earth pressure coefficient calcul...
Discrete Element Modeling for Mobility and Excavation
Knuth, M. A.; Hopkins, M. A.
2011-12-01
The planning and completion of mobility and excavation efforts on the moon requires a thorough understanding of the planetary regolith. In this work, a discrete element method (DEM) model is created to replicate those activities in the laboratory and for planning mission activities in the future. The crux of this work is developing a particle bed that best replicates the regolith tool/wheel interaction seen in the laboratory. To do this, a DEM geotechnical triaxial strength cell was created allowing for comparison of laboratory JSC-1a triaxial tests to DEM simulated soils. This model relies on a triangular lattice membrane covered triaxial cell for determining the macroscopic properties of the modeled granular material as well as a fast and efficient contact detection algorithm for a variety of grain shapes. Multiple grain shapes with increasing complexity (ellipsoid, poly-ellipsoid and polyhedra) have been developed and tested. This comparison gives us a basis to begin scaling DEM grain size and shape to practical values for mobility and excavation modeling. Next steps include development of a DEM scoop for percussive excavation testing as well as continued analysis of rover wheel interactions using a wide assortment of grain shape and size distributions.
Discrete element modeling of subglacial sediment deformation
Damsgaard, Anders; Egholm, David L.; Piotrowski, Jan A.; Tulaczyk, Slawek; Larsen, Nicolaj K.; Tylmann, Karol
2013-12-01
The Discrete Element Method (DEM) is used in this study to explore the highly nonlinear dynamics of a granular bed when exposed to stress conditions comparable to those at the bed of warm-based glaciers. Complementary to analog experiments, the numerical approach allows a detailed analysis of the material dynamics and the shear zone development during progressive shear strain. The geometry of the heterogeneous stress network is visible in the form of force-carrying grain bridges and adjacent, volumetrically dominant, inactive zones. We demonstrate how the shear zone thickness and dilation depend on the level of normal (overburden) stress, and we show how high normal stress can mobilize material to great depths. The particle rotational axes tend to align with progressive shear strain, with rotations both along and reverse to the shear direction. The results from successive laboratory ring-shear experiments on simple granular materials are compared to results from similar numerical experiments. The simulated DEM material and all tested laboratory materials deform by an elastoplastic rheology under the applied effective normal stress. These results demonstrate that the DEM is a viable alternative to continuum models for small-scale analysis of sediment deformation. It can be used to simulate the macromechanical behavior of simple granular sediments, and it provides an opportunity to study how microstructures in subglacial sediments are formed during progressive shear strain.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
A discrete element model for simulating saturated granular soil
Institute of Scientific and Technical Information of China (English)
Mahan Lamei; Ali Asghar Mirghasemi
2011-01-01
A numerical model is developed to simulate saturated granular soil,based on the discrete element method.Soil particles are represented by Lagrangian discrete elements,and pore fluid,by appropriate discrete elements which represent alternately Lagrangian mass of water and Eulerian volume of space.Macroscale behavior of the model is verified by simulating undrained biaxial compression tests.Micro-scale behavior is compared to previous literature through pore pressure pattern visualization during shear tests,it is demonstrated that dynamic pore pressure patterns are generated by superposed stress waves.These pore-pressure patterns travel much faster than average drainage rate of the pore fluid and may initiate soil fabric change,ultimately leading to liquefaction in loose sands.Thus,this work demonstrates a tool to roughly link dynamic stress wave patterns to initiation of liquefaction phenomena.
Zampini, Stefano
2016-06-02
Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of
Stühler, Sven; Fleissner, Florian; Eberhard, Peter
2016-11-01
We present an extended particle model for the discrete element method that on the one hand is tetrahedral in shape and on the other hand is capable to describe deformations. The deformations of the tetrahedral particles require a framework to interrelate the particle strains and resulting stresses. Hence, adaptations from the finite element method were used. This allows to link the two methods and to adequately describe material and simulation parameters separately in each scope. Due to the complexity arising of the non-spherical tetrahedral geometry, all possible contact combinations of vertices, edges, and surfaces must be considered by the used contact detection algorithm. The deformations of the particles make the contact evaluation even more challenging. Therefore, a robust contact detection algorithm based on an optimization approach that exploits temporal coherence is presented. This algorithm is suitable for general {R}^{{n}} simplices. An evaluation of the robustness of this algorithm is performed using a numerical example. In order to create complex geometries, bonds between these deformable particles are introduced. This coupling via the tetrahedra faces allows the simulation bonding of deformable bodies composed of several particles. Numerical examples are presented and validated with results that are obtained by the same simulation setup modeled with the finite element method. The intention of using these bonds is to be able to model fracture and material failure. Therefore, the bonds between the particles are not lasting and feature a release mechanism based on a predefined criterion.
Binary discrete method of topology optimization
Institute of Scientific and Technical Information of China (English)
MEI Yu-lin; WANG Xiao-ming; CHENG Geng-dong
2007-01-01
The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate,even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements,meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.
Discrete Element Modeling of Complex Granular Flows
Movshovitz, N.; Asphaug, E. I.
2010-12-01
Granular materials occur almost everywhere in nature, and are actively studied in many fields of research, from food industry to planetary science. One approach to the study of granular media, the continuum approach, attempts to find a constitutive law that determines the material's flow, or strain, under applied stress. The main difficulty with this approach is that granular systems exhibit different behavior under different conditions, behaving at times as an elastic solid (e.g. pile of sand), at times as a viscous fluid (e.g. when poured), or even as a gas (e.g. when shaken). Even if all these physics are accounted for, numerical implementation is made difficult by the wide and often discontinuous ranges in continuum density and sound speed. A different approach is Discrete Element Modeling (DEM). Here the goal is to directly model every grain in the system as a rigid body subject to various body and surface forces. The advantage of this method is that it treats all of the above regimes in the same way, and can easily deal with a system moving back and forth between regimes. But as a granular system typically contains a multitude of individual grains, the direct integration of the system can be very computationally expensive. For this reason most DEM codes are limited to spherical grains of uniform size. However, spherical grains often cannot replicate the behavior of real world granular systems. A simple pile of spherical grains, for example, relies on static friction alone to keep its shape, while in reality a pile of irregular grains can maintain a much steeper angle by interlocking force chains. In the present study we employ a commercial DEM, nVidia's PhysX Engine, originally designed for the game and animation industry, to simulate complex granular flows with irregular, non-spherical grains. This engine runs as a multi threaded process and can be GPU accelerated. We demonstrate the code's ability to physically model granular materials in the three regimes
International Conference eXtended Discretization MethodS
Benvenuti, Elena
2016-01-01
This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.
Discrete Element Modelling of Floating Debris
Mahaffey, Samantha; Liang, Qiuhua; Parkin, Geoff; Large, Andy; Rouainia, Mohamed
2016-04-01
Flash flooding is characterised by high velocity flows which impact vulnerable catchments with little warning time and as such, result in complex flow dynamics which are difficult to replicate through modelling. The impacts of flash flooding can be made yet more severe by the transport of both natural and anthropogenic debris, ranging from tree trunks to vehicles, wheelie bins and even storage containers, the effects of which have been clearly evident during recent UK flooding. This cargo of debris can have wide reaching effects and result in actual flood impacts which diverge from those predicted. A build-up of debris may lead to partial channel blockage and potential flow rerouting through urban centres. Build-up at bridges and river structures also leads to increased hydraulic loading which may result in damage and possible structural failure. Predicting the impacts of debris transport; however, is difficult as conventional hydrodynamic modelling schemes do not intrinsically include floating debris within their calculations. Subsequently a new tool has been developed using an emerging approach, which incorporates debris transport through the coupling of two existing modelling techniques. A 1D hydrodynamic modelling scheme has here been coupled with a 2D discrete element scheme to form a new modelling tool which predicts the motion and flow-interaction of floating debris. Hydraulic forces arising from flow around the object are applied to instigate its motion. Likewise, an equivalent opposing force is applied to fluid cells, enabling backwater effects to be simulated. Shock capturing capabilities make the tool applicable to predicting the complex flow dynamics associated with flash flooding. The modelling scheme has been applied to experimental case studies where cylindrical wooden dowels are transported by a dam-break wave. These case studies enable validation of the tool's shock capturing capabilities and the coupling technique applied between the two numerical
New Discrete Element Models for Three-Dimensional Impact Problems
Institute of Scientific and Technical Information of China (English)
SHAN Li; CHENG Ming; LIU Kai-xin; LIU Wei-Fu; CHEN Shi-Yang
2009-01-01
Two 3-D numerical models of the discrete element method(DEM)for impact problems are proposed.The models can calculate not only the impact problems of continuum and non-continuum,but also the transient process from continuum to non-continuum.The stress wave propagation in a concrete block and a dynamic splitting process of a marble disc under impact loading are numerically simulated with the proposed models.By comparing the numerical results with the corresponding results obtained by the finite element method(FEM)and the experiments,it is proved that the models are reliable for three-dimensional impact problems.
Gui, Y. L.; Zhao, Z. Y.; Zhou, H. Y.; Wu, W.
2016-10-01
In this paper, a cohesive fracture model is applied to model P-wave propagation through fractured rock mass using hybrid continuum-discrete element method, i.e. Universal Distinct Element Code (UDEC). First, a cohesive fracture model together with the background of UDEC is presented. The cohesive fracture model considers progressive failure of rock fracture rather than an abrupt damage through simultaneously taking into account the elastic, plastic and damage mechanisms as well as a modified failure function. Then, a series of laboratory tests from the literature on P-wave propagation through rock mass containing single fracture and two parallel fractures are introduced and the numerical models used to simulate these laboratory tests are described. After that, all the laboratory tests are simulated and presented. The results show that the proposed model, particularly the cohesive fracture model, can capture very well the wave propagation characteristics in rock mass with non-welded and welded fractures with and without filling materials. In the meantime, in order to identify the significance of fracture on wave propagation, filling materials with different particle sizes and the fracture thickness are discussed. Both factors are found to be crucial for wave attenuation. The simulations also show that the frequency of transmission wave is lowered after propagating through fractures. In addition, the developed numerical scheme is applied to two-dimensional wave propagation in the rock mass.
Institute of Scientific and Technical Information of China (English)
Pooya Hamdi; Doug Stead; Davide Elmo
2015-01-01
abstract Heterogeneity is an inherent component of rock and may be present in different forms including mineral heterogeneity, geometrical heterogeneity, weak grain boundaries and micro-defects. Microcracks are usually observed in crystalline rocks in two forms: natural and stress-induced; the amount of stress-induced microcracking increases with depth and in-situ stress. Laboratory results indicate that the physical properties of rocks such as strength, deformability, P-wave velocity and permeability are influenced by increase in microcrack intensity. In this study, the finite-discrete element method (FDEM) is used to model microcrack heterogeneity by introducing into a model sample sets of microcracks using the proposed micro discrete fracture network (mDFN) approach. The characteristics of the microcracks required to create mDFN models are obtained through image analyses of thin sections of Lac du Bonnet granite adopted from published literature. A suite of two-dimensional laboratory tests including uniaxial, triaxial compression and Brazilian tests is simulated and the results are compared with laboratory data. The FDEM-mDFN models indicate that micro-heterogeneity has a profound influence on both the me-chanical behavior and resultant fracture pattern. An increase in the microcrack intensity leads to a reduction in the strength of the sample and changes the character of the rock strength envelope. Spalling and axial splitting dominate the failure mode at low confinement while shear failure is the dominant failure mode at high confinement. Numerical results from simulated compression tests show that microcracking reduces the cohesive component of strength alone, and the frictional strength component remains unaffected. Results from simulated Brazilian tests show that the tensile strength is influenced by the presence of microcracks, with a reduction in tensile strength as microcrack intensity increases. The importance of microcrack heterogeneity in reproducing
Directory of Open Access Journals (Sweden)
Tran Quoc Anh
2017-01-01
Full Text Available The recent technological developments made on the light dynamic penetration test Panda 3 ® provide a dynamic load–penetration curve σp – sp for each impact. This curve is influenced by the mechanical and physical properties of the investigated granular media. In order to analyze and exploit the load-penetration curve, a numerical model of penetration test using 3D Discrete Element Method is proposed for reproducing tests in dynamic conditions in granular media. All parameters of impact used in this model have at first been calibrated by respecting mechanical and geometrical properties of the hammer and the rod. There is a good agreement between experimental results and the ones obtained from simulations in 2D or 3D. After creating a sample, we will simulate the Panda 3 ®. It is possible to measure directly the dynamic load–penetration curve occurring at the tip for each impact. Using the force and acceleration measured in the top part of the rod, it is possible to separate the incident and reflected waves and then calculate the tip’s load-penetration curve. The load–penetration curve obtained is qualitatively similar with that obtained by experimental tests. In addition, the frequency analysis of the measured signals present also a good compliance with that measured in reality when the tip resistance is qualitatively similar.
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette
2010-02-23
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.
Discrete Event Simulation Modeling of Radiation Medicine Delivery Methods
Energy Technology Data Exchange (ETDEWEB)
Paul M. Lewis; Dennis I. Serig; Rick Archer
1998-12-31
The primary objective of this work was to evaluate the feasibility of using discrete event simulation (DES) modeling to estimate the effects on system performance of changes in the human, hardware, and software elements of radiation medicine delivery methods.
From discrete elements to continuum fields: Extension to bidisperse systems
Tunuguntla, Deepak R.; Thornton, Anthony R.; Weinhart, Thomas
2016-07-01
Micro-macro transition methods can be used to, both, calibrate and validate continuum models from discrete data obtained via experiments or simulations. These methods generate continuum fields such as density, momentum, stress, etc., from discrete data, i.e. positions, velocity, orientations and forces of individual elements. Performing this micro-macro transition step is especially challenging for non-uniform or dynamic situations. Here, we present a general method of performing this transition, but for simplicity we will restrict our attention to two-component scenarios. The mapping technique, presented here, is an extension to the micro-macro transition method, called coarse-graining, for unsteady two-component flows and can be easily extended to multi-component systems without any loss of generality. This novel method is advantageous; because, by construction the obtained macroscopic fields are consistent with the continuum equations of mass, momentum and energy balance. Additionally, boundary interaction forces can be taken into account in a self-consistent way and thus allow for the construction of continuous stress fields even within one element radius of the boundaries. Similarly, stress and drag forces can also be determined for individual constituents of a multi-component mixture, which is critical for several continuum applications, e.g. mixture theory-based segregation models. Moreover, the method does not require ensemble-averaging and thus can be efficiently exploited to investigate static, steady and time-dependent flows. The method presented in this paper is valid for any discrete data, e.g. particle simulations, molecular dynamics, experimental data, etc.; however, for the purpose of illustration we consider data generated from discrete particle simulations of bidisperse granular mixtures flowing over rough inclined channels. We show how to practically use our coarse-graining extension for both steady and unsteady flows using our open-source coarse
Directory of Open Access Journals (Sweden)
Xiaolin Huang
2016-12-01
Full Text Available This paper numerically investigates the seismic response of the filled joint under high amplitude stress waves using the combined finite-discrete element method (FDEM. A thin layer of independent polygonal particles are used to simulate the joint fillings. Each particle is meshed using the Delaunay triangulation scheme and can be crushed when the load exceeds its strength. The propagation of the 1D longitude wave through a single filled joint is studied, considering the influences of the joint thickness and the characteristics of the incident wave, such as the amplitude and frequency. The results show that the filled particles under high amplitude stress waves mainly experience three deformation stages: (i initial compaction stage; (ii crushing stage; and (iii crushing and compaction stage. In the initial compaction stage and crushing and compaction stage, compaction dominates the mechanical behavior of the joint, and the particle area distribution curve varies little. In these stages, the transmission coefficient increases with the increase of the amplitude, i.e., peak particle velocity (PPV, of the incident wave. On the other hand, in the crushing stage, particle crushing plays the dominant role. The particle size distribution curve changes abruptly with the PPV due to the fragments created by the crushing process. This process consumes part of wave energy and reduces the stiffness of the filled joint. The transmission coefficient decreases with increasing PPV in this stage because of the increased amount of energy consumed by crushing. Moreover, with the increase of the frequency of the incident wave, the transmission coefficient decreases and fewer particles can be crushed. Under the same incident wave, the transmission coefficient decreases when the filled thickness increases and the filled particles become more difficult to be crushed.
A distortional semi-discretized thin-walled beam element
DEFF Research Database (Denmark)
Andreassen, Michael Joachim; Jönsson, Jeppe
2013-01-01
Due to the increased consumption of thin-walled structural elements there has been increasing focus and need for more detailed calculations as well as development of new approaches. In this paper a thin-walled beam element including distortion of the cross section is formulated. The formulation...... is based on a generalized beam theory (GBT), in which the classic Vlasov beam theory for analysis of open and closed thin-walled cross sections is generalized by including distortional displacements. The beam element formulation utilizes a semi-discretization approach in which the cross section...... is discretized into wall elements and the analytical solutions of the related GBT beam equations are used as displacement functions in the axial direction. Thus the beam element contains the semi-analytical solutions. In three related papers the authors have recently presented the semi-discretization approach...
基于颗粒尺度的离散颗粒传热模型%Heat transfer model for particles with discrete element method
Institute of Scientific and Technical Information of China (English)
卜昌盛; 陈晓平; 刘道银; 段钰锋
2012-01-01
颗粒间传热在诸多工业过程中有着十分重要的作用.详细考虑颗粒间传热机理,对颗粒间各传热途径建模,包括颗粒内部导热、颗粒粗糙表面传热、颗粒表面气膜及接触颗粒间隙气膜传热,并与离散颗粒模型(DEM)耦合,建立颗粒尺度下离散颗粒传热模型.以固定床为对象,考察颗粒粒径、颗粒比热容、颗粒热导率及压缩负载对固定床有效传热系数的影响,并将本文计算值和文献的实验值及模型预测值对比,结果表明,该模型可定量预测固定床有效传热系数.本文建立的离散颗粒传热模型为合理预测颗粒体系内的传热提供了一种有效方法.%Heat conduction in granular assemblies plays an important role in industrial applications. In this paper, the details of heat transfer mechanism are considered in particle scale. The conduction resistances of solid interior, rough surface, gas film between solids, and gas-gap between contacted surfaces are modeled and coupled with discrete element method to deduce a heat transfer model. Numerical simulations are performed to investigate the effects of particle diameter, specific thermal capacity, thermal conductivity of particles and compressive load on effective thermal conductivity (ETC) in fixed beds. The predicted ETC is compared with experimental and simulated data in literature, indicating that the presented model can predict ETC satisfactorily, which provides a useful tool for studying heat transfer in particle assemblies.
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin
2015-01-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined used for deriving and conditions for when and where to apply model reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5 - 50 times for model reduction level between 70 - 95 %.
Adaptive model reduction for nonsmooth discrete element simulation
Servin, Martin; Wang, Da
2016-03-01
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies of the corresponding shape and mass distribution. The method also support particles merging with articulated multibody systems. A model approximation error is defined and used to derive conditions for when and where to apply reduction and refinement back into particles and smaller rigid bodies. Three methods for refinement are proposed and tested: prediction from contact events, trial solutions computed in the background and using split sensors. The computational performance can be increased by 5-50 times for model reduction level between 70-95 %.
The Numerical Integration of Discrete Functions on a Triangular Element
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
With the application of Hammer integral formulas of a continuousfunction on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
Discrete element modelling of sediment falling in water.
Wang, Dong; Ho-Minh, Dao; Tan, Danielle S
2016-11-01
The Discrete Element Method (DEM) is a discrete, particle-based method commonly used in studies involving granular media, e.g. sediment transport, and geomechanics. It is heavily dependent on particle properties, and one important component is the force model, which relates the relative positions and velocities of the simulated particles to the forces they experience. In this paper we model a collection of lightly compacted granular material, released at a short distance above a flat base in a quiescent fluid --similar to the process whereby sediment tailings are released back into the sea during nodule harvesting. We employ different typical force models, and consider how their varying components affect the simulated outcome. The results are compared with a physical experiment of similar dimensions. We find that a realistic simulation is achieved when the force model considers the local solid fraction in the drag force, and incorporates the hydrodynamic effect of neighbouring particles. The added mass effect increases the accuracy of the outcome, but does not contribute significantly in a qualitative sense.
Discrete mathematics: methods and challenges
Alon, Noga
2002-01-01
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight connection between Discrete Mathematics and Theoretical Computer Science, and the rapid development of the latter. While in the past many of the basic combinatorial results were obtained mainly by ingenuity and detailed reasoning, the modern theory has grown ...
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discretization vs. Rounding Error in Euler's Method
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Discrete Element Simulation of Asphalt Mastics Based on Burgers Model
Institute of Scientific and Technical Information of China (English)
LIU Yu; FENG Shi-rong; HU Xia-guang
2007-01-01
In order to investigate the viscoelastic performance of asphalt mastics, a micro-mechanical model for asphalt mastics was built by applying Burgers model to discrete element simulation and constructing Burgers contact model. Then the numerical simulation of creep tests was conducted, and results from the simulation were compared with the analytical solution for Burgers model. The comparision snowed that the two results agreed well with each other, suggesting that discrete element model based on Burgers model could be employed in the numerical simulation for asphalt mastics.
Virgo, Simon; Abe, Steffen; Urai, Janos L.
2016-03-01
We present the results of a comparative study of loading conditions on the interactions between extension fractures and veins. We model the fracture behavior of brittle discrete element materials each containing a tabular vein body of variable orientation and strength in two different loading conditions. The first is uniaxial tension, applied with servo-controlled sidewalls. The second is a boudinage boundary condition in which a tensile triaxial stress state is induced in the brittle model volume by quasi-viscous extensional deformation in the adjacent layers. Most of the fracture- vein interactions observed in uniaxial tension also exists in boudinage boundary conditions. However, the importance of each interaction mechanism for a given configuration of relative strength and misorientation of the vein may differ according to the loading mechanism. Nucleation and internal deflection is under both boundary conditions the dominating fracture-vein interaction style in weak veins. In uniaxial tension models, strong veins tend to alter the fracture path by external deflection, while under boudinage loading these veins are more likely overcome by the fracture step over mechanism. Dynamic bifurcation of fractures was observed in uniaxial tension models but never for boudinage boundary conditions. This is because the acceleration of fracture tips in these conditions is suppressed by interaction with distributed fractures as well as viscous damping by the neighboring layers.
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2003-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid¿solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Microsca
Discrete element modelling of fluidised bed spray granulation
Goldschmidt, M.J.V.; Weijers, G.G.C.; Boerefijn, R.; Kuipers, J.A.M.
2002-01-01
A novel discrete element spray granulation model capturing the key features of fluidised bed hydrodynamics, liquid-solid contacting and agglomeration is presented. The model computes the motion of every individual particle and droplet in the system, considering the gas phase as a continuum. Micro sc
Discrete element modelling of pebble packing in pebble bed reactors
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Suikkanen, Heikki, E-mail: heikki.suikkanen@lut.fi; Ritvanen, Jouni, E-mail: jouni.ritvanen@lut.fi; Jalali, Payman, E-mail: payman.jalali@lut.fi; Kyrki-Rajamäki, Riitta, E-mail: riitta.kyrki-rajamaki@lut.fi
2014-07-01
Highlights: • A discrete element method code is developed for pebble bed reactor analyses. • Methods are established to extract packing information at various spatial scales. • Packing simulations inside annular core geometry are done varying input parameters. • The restitution coefficient has the strongest effect on the resulting packing density. • Detailed analyses reveal local densification especially near the walls. - Abstract: It is important to understand the packing characteristics and behaviour of the randomly packed pebble bed to further analyse the reactor physical and thermal-hydraulic behaviour and to design a safe and economically feasible pebble bed reactor. The objective of this work was to establish methods to model and analyse the pebble packing in detail to provide useful tools and data for further analyses. Discrete element method (DEM) is a well acknowledged method for analysing granular materials, such as the fuel pebbles in a pebble bed reactor. In this work, a DEM computer code was written specifically for pebble bed analyses. Analysis methods were established to extract data at various spatial scales from the pebble beds resulting from the DEM simulations. A comparison with available experimental data was performed to validate the DEM implementation. To test the code implementation in full-scale reactor calculations, DEM packing simulations were done in annular geometry with 450,000 pebbles. Effects of the initial packing configuration, friction and restitution coefficients and pebble size distribution to the resulting pebble bed were investigated. The packing simulations revealed that from the investigated parameters the restitution coefficient had the largest effect on the resulting average packing density while other parameters had smaller effects. Detailed local packing density analysis of pebble beds with different average densities revealed local variations especially strong in the regions near the walls. The implemented DEM
Uniform Deterministic Discrete Method for Three Dimensional Systems
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
For radiative direct exchange areas in three dimensional system,the Uniform Deterministic Discrete Method(UDDM) was adopted.The spherical surface dividing method for sending area element and the regular icosahedron for sending volume element can meet with the direct exchange area computation of any kind of zone pairs.The numerical examples of direct exchange area in three dimensional system with nonhomogeneous attenuation coefficients indicated that the UDDM can give very high numercal accuracy.
Institute of Scientific and Technical Information of China (English)
李林涛; 谭援强; 姜胜强
2012-01-01
采用离散元法(DEM),用BPM(Bonded-particle model)模型分别建立并校准SiC陶瓷基体和碳纤维离散元模型,采用位移软化接触模型表征层间和纤维/基体之间的界面元损伤双线性本构关系.通过DCB试验(Double cantilever beam virtual test)和微滴脱黏试验分别对其界面强度进行收敛试验,动态地观察了塑性变形、裂纹扩展及界面脱黏过程.结果表明,位移软化接触模型可以很好地表征界面损伤过程,采用离散元法可以很好地动态模拟较复杂复合材料的损坏过程.%With the aid of BPM (Bonded-particle model), the discrete element models of SiC ceramics matrix and carbon fiber were set up and calibrated separately by the discrete element method(DEM). The bilinear cohesive law of interface element damage in interlayer and on matrix/fiber interface was characterized using displacement-softening contact models, and then calibrated by DCB test (Double cantilever beam virtual test) and microbond test, respectively. Plastic deformation, crac-king growth situation and dynamic processes of interface debonding were observed in these simulation tests. The results show that the displacement-softening contact model could characterize in-terfacial damage process nicely, and discrete element method could simulate dynamic damage process for more complex composite materials admirably.
Tseng, C. H.; Chan, Y. C.; Jeng, C. J.; Hsieh, Y. C.
2015-12-01
Slope failure is a widely observed phenomenon in hill and mountainous areas in Taiwan, which is characterized by high erosion rates (up to 60 mm/yr) due to its climatic and geographical conditions. Slope failure events easily occur after intense rainfall, especially resulting from typhoons and accordingly cause a great loss of human lives and property. At the northern end of the Western Foothill belt in northern Taiwan, Huafan University campus (121.692448˚ E, 24.980724˚ N ) is founded on a dip slope, ~20˚ toward southwest, being composed of early Miocene alternations of sandstone and shale. Data from continuous monitoring over the years by means of inclinometers and groundwater gauges reveal that creep of 6-10 mm of the slope occurred when precipitation exceeded 300 mm during typhoons' striking. In addition, extension cracks on the ground are also found within and on the edge of the campus. Furthermore, potential slip surfaces are detected shown by rock cores to exist 10 and 30 m in depth as well. To understand the kinematic behaviors of the rock slope failure beneath the university campus, a 3D discrete element mothed is applied in this study. Results of the modeling indicate that creeping is the primary behavior pattern when the friction coefficient reduces owing to rise of groundwater during rainstorms. However, rapid slip may take place under influences of earthquake with large magnitude. Suggestions for preventing the slope creep are to construct catchpits to drainage runoff and lower the groundwater table and ground anchors through the slip surfaces to stabilize the slide blocks.
Discrete Methods and their Applications
1993-02-03
paper [32]. Special classes of matrices are often of interest in combinatorics. Let A be an nxn matrix of real numbers. A is called a Z- matriz if all...34Reliable Networks from Non-reliable Elements," invited seminar talk, Boston University, Boston , MA, March 1992. "Non-Hamiltonian Graphs and Barnette’s...MA, May 1992. "Coding of Spanning Trees of the Extended Graphs," invited seminar talk, ortheastern University, Boston , MA, May 1992. "Universal
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Jia, Pin; Cheng, Linsong; Huang, Shijun; Xu, Zhongyi; Xue, Yongchao; Cao, Renyi; Ding, Guanyang
2017-08-01
This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the
Institute of Scientific and Technical Information of China (English)
张红梅; 肖映雄; 欧阳媛
2012-01-01
Higher-order conforming finite elements can effectively overcome the poisson-Locking in linear elasticity,which is call and Locking-free finite elements. But when compared with the linear element,it often requires more computer storage and has a higher computational complexity. For the Locking-free (quartic) finite element discretization in linear elasticity,a general two-level method is proposed by analyzing the relationship between the quadratic finite element space and the quartic finite element space and by taking advantage of the special nature of the finite element's basi functions,such as compactly supported. First,the quadratic element is chosen as the coarse level space. Secon'd,by combining the selective reduced integration and some efficient smoothers,then,obtain the two-level method is obtained in which the element is chosen as the coarse level space for the Locking-free finite element discretization with better robustness and high efficiency. The numerical results show the efficiency of the resulting method.%高次协调元能有效克服弹性力学问题的闭锁( Locking)现象,称这种单元为无闭锁(Locking—free)有限元,但它与线性元相比,往往需要更多的计算机存储单元,具有更高的计算复杂性.针对弹性力学问题Locking—free(四次)有限元离散系统的求解,本文通过分析四次有限元与二次有限元空间之间的关系,并利用有限元基函数的特殊性质,如紧支集性,建立一种以二次有限元(P2)为粗水平空间的两水平方法;然后,利用减缩积分方案,以P2／P0元作为四次元空间的粗水平空间,并结合有效的磨光算子,为Locking—free有限元离散系统设计具有更好计算效率和鲁棒性的求解方法.数值实验结果验证了算法的有效性.
Energy Technology Data Exchange (ETDEWEB)
Rousseau, J.
2009-07-15
That study focuses on concrete structures submitted to impact loading and is aimed at predicting local damage in the vicinity of an impact zone as well as the global response of the structure. The Discrete Element Method (DEM) seems particularly well suited in this context for modeling fractures. An identification process of DEM material parameters from macroscopic data (Young's modulus, compressive and tensile strength, fracture energy, etc.) will first be presented for the purpose of enhancing reproducibility and reliability of the simulation results with DE samples of various sizes. Then, a particular interaction, between concrete and steel elements, was developed for the simulation of reinforced concrete. The discrete elements method was validated on quasi-static and dynamic tests carried out on small samples of concrete and reinforced concrete. Finally, discrete elements were used to simulate impacts on reinforced concrete slabs in order to confront the results with experimental tests. The modeling of a large structure by means of DEM may lead to prohibitive computation times. A refined discretization becomes required in the vicinity of the impact, while the structure may be modeled using a coarse FE mesh further from the impact area, where the material behaves elastically. A coupled discrete-finite element approach is thus proposed: the impact zone is modeled by means of DE and elastic FE are used on the rest of the structure. An existing method for 3D finite elements was extended to shells. This new method was then validated on many quasi-static and dynamic tests. The proposed approach is then applied to an impact on a concrete structure in order to validate the coupled method and compare computation times. (author)
Institute of Scientific and Technical Information of China (English)
潘成杰
2016-01-01
At present in structural strength analysis of underground dump truck, the pre-estimate of applied stress usually depends on experience and simple calculation, leading to large deviation. In the paper, the discrete element method is introduced to the finite element strength check. The coal material's discrete element model is established to simulate the material loaded process, and acquire the applied force of the truck body from coal material discrete element. Then the finite element software is used to conduct coupling and strength checking with the obtained data. The method can accurately apply the force of coal material to the finite element model, get the stress and strain of the vehicle body, and obtain the credible force of the hopper according to the calculation scale factor.%针对目前运矿车结构强度分析，施加载荷环节往往依靠经验或简单计算进行预估，分析结果不能完全真实地反映车体实际受力情况。将离散元方法引入到设备有限元强度校核中，建立煤料离散元模型，通过模拟装载过程，获取煤料离散单元对车体的作用力，然后将数据导入到有限元软件中进行耦合，进行强度校核。该方法真实地将煤料对车体的作用力准确地施加到有限元模型中，可得到车体应力应变，以及根据计算比例因子，得到料斗所受可信作用力。该研究将为改进运矿车的设计和使用性能，提高产品生产效率，提供强大依据。
HEURISTIC DISCRETIZATION METHOD FOR BAYESIAN NETWORKS
Directory of Open Access Journals (Sweden)
Mariana D.C. Lima
2014-01-01
Full Text Available Bayesian Network (BN is a classification technique widely used in Artificial Intelligence. Its structure is a Direct Acyclic Graph (DAG used to model the association of categorical variables. However, in cases where the variables are numerical, a previous discretization is necessary. Discretization methods are usually based on a statistical approach using the data distribution, such as division by quartiles. In this article we present a discretization using a heuristic that identifies events called peak and valley. Genetic Algorithm was used to identify these events having the minimization of the error between the estimated average for BN and the actual value of the numeric variable output as the objective function. The BN has been modeled from a database of Bit’s Rate of Penetration of the Brazilian pre-salt layer with 5 numerical variables and one categorical variable, using the proposed discretization and the division of the data by the quartiles. The results show that the proposed heuristic discretization has higher accuracy than the quartiles discretization.
Wang, Dafang; Kirby, Robert M; Johnson, Chris R
2011-06-01
We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite-element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of hybrid finite elements composed of tetrahedra and prism elements. Also, in order to maintain consistent numerical quality when the inverse problem is discretized into different scales, we propose a new family of regularizers using the variational principle underlying finite-element methods. These variational-formed regularizers serve as an alternative to the traditional Tikhonov regularizers, but preserves the L(2) norm and thereby achieves consistent regularization in multiscale simulations. The variational formulation also enables a simple construction of the discrete gradient operator over irregular meshes, which is difficult to define in traditional discretization schemes. We validated our hybrid element technique and the variational regularizers by simulations on a realistic 3-D torso/heart model with empirical heart data. Results show that discretization based on our proposed strategies mitigates the ill-conditioning and improves the inverse solution, and that the variational formulation may benefit a broader range of potential-based bioelectric problems.
Institute of Scientific and Technical Information of China (English)
邱流潮; 张之豪; 袁林娟
2015-01-01
A discrete element method-based simulation platform for dry and wet particulate systems, DEMSIM,is introduced in this paper.In the case of dry particulate systems,DEMSIM has the ability to model the elastic and plastic contact of granular systems in two and three dimensions.For particulate system with few liquid,a liquid bridge model is applied in this simulation platform.In addition,a numerical method coupling discrete element method (DEM)with computational fluid dynamics (CFD)is developed to simulate particle-liquid flow in DEMSIM.The liquid motion was considered as a weakly compressible flow solved using CFD solvers while the discrete particle motion is solved using DEM in which the particle-particle interaction are based on theoretical contact mechanics thereby enabling particles to be directly specified using realistic material properties such as friction and elasticity.Several numerical examples are presented to verify the simulation platform by comparing the numerical results with theoretic solution and experimental data in the literature.The results demonstrate the ability to simulate the dynamics of the dry and wet particulate systems.%介绍了基于离散元法的干湿颗粒系统仿真软件 DEMSIM。对于干颗粒系统,DEMSIM 可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程；对于湿颗粒系统,DEMSIM 采用传统的液桥模型；对于颗粒-流体系统,DEMSIM 采用 CFD-DEM 细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM 的精度和有效性。
Institute of Scientific and Technical Information of China (English)
鲍鹏; 李丽; 赵捷
2008-01-01
Based on the principle of deformation dynamics, a new discrete element model for deformable bodies is established in this paper. From the side-side contact relation and the dynamic relaxation method, theoretical formulas are derived and the corresponding calculation program is worked out according to the discrete element method (DEM). From the astringency of the calculation results in the static problem, the validity of the calculation program and the selected parameters is verified, and the motive reaction of the underground structure under artificial seismic wave is solved.%基于变形体动力学原理,建立了新的可变形块体单元模型.根据离散元法原理,采用边-边接触关系及动态松弛法,推导出其理论公式并编制了计算程序;由静力问题计算结果的收敛性,验证了计算程序和计算参数选取的正确性,求出了地下结构在人工地震波作用下的动力反应.
Discrete Element Crowd Model for Pedestrian Evacuation Through an Exit
Lin, Peng; Lo, Siuming
2016-01-01
A series of accidents caused by crowd within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on discrete element method, a granular dynamic model, in which human body is simplified as self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of human body is simulated by applying the second Newton's law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, clogging phenomenon occurs more easily when the velocity of desired is high and the exit may as a result be totally blocked at a desired velocity of 1.6m/s or above, leading to fas...
Discrete element crowd model for pedestrian evacuation through an exit
Peng, Lin; Jian, Ma; Siuming, Lo
2016-03-01
A series of accidents caused by crowds within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on the discrete element method, a granular dynamic model, in which the human body is simplified as a self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of the human body is simulated by applying the second Newton’s law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, the clogging phenomenon occurs more easily when the desired velocity is high and the exit may as a result be totally blocked at a desired velocity of 1.6 m/s or above, leading to faster-to-frozen effect. Project supported by the National Natural Science Foundation of China (Grant Nos. 71473207, 51178445, and 71103148), the Research Grant Council, Government of Hong Kong, China (Grant No. CityU119011), and the Fundamental Research Funds for the Central Universities, China (Grant Nos. 2682014CX103 and 2682014RC05).
Generalized Rayleigh quotient and finite element two-grid discretization schemes
Institute of Scientific and Technical Information of China (English)
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Generalized Rayleigh quotient and finite element two-grid discretization schemes
Institute of Scientific and Technical Information of China (English)
YANG YiDu; FAN XinYue
2009-01-01
This study discusses generalized Rayleigh quotient and high efficiency finite element dis-cretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of finite element approximate eigenvalue. 3) Based on the work of Xu Jinchao and Zhou Aihui, finite element two-grid discretization schemes are established to solve nonselfadjoint elliptic differential operator eigenvalue problems and these schemes are used in both conforming finite element and non-conforming finite element. Besides, the efficiency of the schemes is proved by both theoretical analysis and numerical experiments. 4) Iterated Galerkin method, interpolated correction method and gradient recovery for selfadjoint elliptic differential operator eigenvalue problems are extended to nonselfadjoint elliptic differential operator eigenvalue problems.
Directory of Open Access Journals (Sweden)
M. P. Menguc
2011-09-01
Full Text Available We embark on this preliminary study of the suitability of the discrete dipole approximation with surface interaction (DDA-SI method to model electric field scattering from noble metal nano-structures on dielectric substrates. The refractive index of noble metals, particularly due to their high imaginary components, require smaller lattice spacings and are especially sensitive to the shape integrity and the volume of the dipole model. The results of DDA-SI method are validated against those of the well-established finite element method (FEM and the finite difference time domain (FDTD method.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Institute of Scientific and Technical Information of China (English)
鲍春永; 赵啦啦; 刘万英; 杨康康
2016-01-01
Particle discrete element method is a kind of numerical simulation method widely used in the research of granular material mechanics behaviour.Computation efficiency is one of the main factors that restricts its development and application.In this paper,we build a hopper model by using Pro/E software,and use Stream DEM software to study the stimulations of discrete element method in regard to hopper’s particles filling process.We also compare the operation processes and results of CPU-based and GPU-based acceleration algorithms. Results show that the GPU-based computer graphics acceleration algorithm can dramatically improve the computation efficiency of the simulation process of particle discrete element method.When the number of particles to be filled reaches 130 000,its computational efficiency improves over 10 times than that of the CPU-based acceleration algorithm.%颗粒离散元法是一种广泛应用于研究颗粒物料力学行为的数值模拟方法，而计算效率是制约其发展和应用的主要因素之一。通过Pro／E软件建立了料斗模型，利用Stream DEM软件对料斗的颗粒充填过程进行离散元法模拟研究，并对基于CPU 和GPU加速算法的运算过程和结果进行对比。结果表明，基于GPU的计算机图形学加速算法可大幅提高颗粒离散元法模拟过程的运算效率。当填充颗粒数量达到13万时，其运算效率比基于CPU的运算效率提高了10倍以上。
Teaching Formal Methods and Discrete Mathematics
Directory of Open Access Journals (Sweden)
Mathieu Jaume
2014-04-01
Full Text Available Despite significant advancements in the conception of (formal integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help during the development cycle is essential but we think that education of computer scientists and software engineers is also an important challenge to take up. Indeed, we believe that formal methods courses do not appear sufficiently early in compter science curricula and thus are not widely used and perceived as a valid professional skill. In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop- ment within FoCaLiZe. We also believe that this could considerably benefit the learning of discrete mathematics.
Study of the Internal Mechanical response of an asphalt mixture by 3-D Discrete Element Modeling
DEFF Research Database (Denmark)
Feng, Huan; Pettinari, Matteo; Hofko, Bernhard
2015-01-01
In this paper the viscoelastic behavior of asphalt mixture was investigated by employing a three-dimensional Discrete Element Method (DEM). The cylinder model was filled with cubic array of spheres with a specified radius, and was considered as a whole mixture with uniform contact properties for ...
CSIR Research Space (South Africa)
Govender, Nicolin
2013-01-01
Full Text Available in nature and cannot be described by a closed form solution for more than a few particles. A popular and successful approach in simulating the underlying dynamics of GM is by using the Discrete Element Method (DEM). Computational viable simulations...
Discrete element simulation of mill charge in 3D using the BLAZE-DEM GPU framework
CSIR Research Space (South Africa)
Govender, Nicolin
2015-08-01
Full Text Available The Discrete Element Method (DEM) simulation of charge motion in ball, semi autogenous (SAG) and autogenous mills has advanced to a stage where the effects of lifter design, power draft and product size can be evaluated with sufficient accuracy...
Discrete equations and the singular manifold method
Estévez, P G
1999-01-01
The Painleve expansion for the second Painleve equation (PII) and fourth Painleve equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painleve type equations for which auto-Backlund transformations are obtained. These auto-Backlund transformations can be used to obtain discrete equations.
Discrete element modelling of screw conveyor-mixers
Directory of Open Access Journals (Sweden)
Jovanović Aca
2015-01-01
Full Text Available Screw conveyors are used extensively in food, plastics, mineral processing, agriculture and processing industries for elevating and/or transporting bulk materials over short to medium distances. Despite their apparent simplicity in design, the transportation action is very complex for design and constructors have tended to rely heavily on empirical performance data. Screw conveyor performance is affected by its operating conditions (such as: the rotational speed of the screw, the inclination of the screw conveyor, and its volumetric fill level. In this paper, horizontal, several single-pitch screw conveyors with some geometry variations in screw blade was investigated for mixing action during transport, using Discrete Element Method (DEM. The influence of geometry modifications on the performance of screw conveyor was examined, different screw designs were compared, and the effects of geometrical variations on mixing performances during transport were explored. During the transport, the particle tumbles down from the top of the helix to the next free surface and that segment of the path was used for auxiliary mixing action. The particle path is dramatically increased with the addition of three complementary helices oriented in the same direction as screw blades (1458.2 mm compared to 397.6 mm in case of single flight screw conveyor Transport route enlarges to 1764.4 mm, when installing helices oriented in the opposite direction from screw blades. By addition of straight line blade to single flight screw conveyor, the longest particle path is being reached: 2061.6 mm [Projekat Ministarstva nauke Republike Srbije, br. TR-31055
New treatment of breakup continuum in the method of continuum discretized coupled channels
Matsumoto, T; Ogata, K; Iseri, Y; Hiyama, E; Kamimura, M; Yahiro, M
2003-01-01
In the method of continuum discretized coupled channels (CDCC) for treating three-body processes in projectile breakup reactions, the discretization of continuous breakup channels is essential. We propose a practical method of the discretization. The validity of the method is numerically tested and confirmed for two realistic examples, $d+^{58}$Ni scattering at 80 MeV and $^{6}Li+^{40}$Ca scattering at 156 MeV. Calculated elastic and breakup S-matrix elements based on the new method converge as the number of discretized breakup channels is increased. The converged S-matrix element agrees with the exact one which is derived with average (Av) discretization established as an accurate method. The new discretization requires a smaller number of breakup channels than the Av method. The feasibility of the new method for more complicated reactions is also discussed.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Dispersion Analysis of Gravity Waves in Fluid Media Discretized by Energy-Orthogonal Finite Elements
José Brito Castro, Francisco
2014-11-01
This article studies the dispersion of gravity waves in fluid media discretized by the finite element method. The element stiffness matrix is split into basic and higher-order components which are respectively related to the mean and deviatoric components of the gradient of displacement potential. This decomposition is applied to the kinetic energy. The dispersion analysis yields a correlation between the higher-order kinetic energy and the kinetic energy error. The use of this correlation as a reference to apply the higher-order energy as an error indicator for the sloshing modes computed by the finite element method is explored.
Investigation into discretization methods of the six-parameter Iwan model
Li, Yikun; Hao, Zhiming; Feng, Jiaquan; Zhang, Dingguo
2017-02-01
Iwan model is widely applied for the purpose of describing nonlinear mechanisms of jointed structures. In this paper, parameter identification procedures of the six-parameter Iwan model based on joint experiments with different preload techniques are performed. Four kinds of discretization methods deduced from stiffness equation of the six-parameter Iwan model are provided, which can be used to discretize the integral-form Iwan model into a sum of finite Jenkins elements. In finite element simulation, the influences of discretization methods and numbers of Jenkins elements on computing accuracy are discussed. Simulation results indicate that a higher accuracy can be obtained with larger numbers of Jenkins elements. It is also shown that compared with other three kinds of discretization methods, the geometric series discretization based on stiffness provides the highest computing accuracy.
Dimension Reduction and Discretization in Stochastic Problems by Regression Method
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager
1996-01-01
The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation, ......, Slepian models, Stochastic finite elements.......The chapter mainly deals with dimension reduction and field discretizations based directly on the concept of linear regression. Several examples of interesting applications in stochastic mechanics are also given.Keywords: Random fields discretization, Linear regression, Stochastic interpolation...
An element by element spectral element method for elastic wave modeling
Institute of Scientific and Technical Information of China (English)
LIN Weijun; WANG Xiuming; ZHANG Hailan
2006-01-01
The spectral element method which combines the advantages of spectral method with those of finite element method,provides an efficient tool in simulating elastic wave equation in complex medium. Based on weak form of elastodynamic equations, mathematical formulations for Legendre spectral element method are presented. The wave field on an element is discretized using high-order Lagrange interpolation, and integration over the element is accomplished based upon the Gauss-Lobatto-Legendre integration rule. This results in a diagonal mass matrix which leads to a greatly simplified algorithm. In addition, the element by element technique is introduced in our method to reduce the memory sizes and improve the computation efficiency. Finally, some numerical examples are presented to demonstrate the spectral accuracy and the efficiency. Because of combinations of the finite element scheme and spectral algorithms, this method can be used for complex models, including free surface boundaries and strong heterogeneity.
Energy Technology Data Exchange (ETDEWEB)
Smith, Jovanca J.; Bishop, Joseph E.
2013-11-01
This report summarizes the work performed by the graduate student Jovanca Smith during a summer internship in the summer of 2012 with the aid of mentor Joe Bishop. The projects were a two-part endeavor that focused on the use of the numerical model called the Lattice Discrete Particle Model (LDPM). The LDPM is a discrete meso-scale model currently used at Northwestern University and the ERDC to model the heterogeneous quasi-brittle material, concrete. In the first part of the project, LDPM was compared to the Karagozian and Case Concrete Model (K&C) used in Presto, an explicit dynamics finite-element code, developed at Sandia National Laboratories. In order to make this comparison, a series of quasi-static numerical experiments were performed, namely unconfined uniaxial compression tests on four varied cube specimen sizes, three-point bending notched experiments on three proportional specimen sizes, and six triaxial compression tests on a cylindrical specimen. The second part of this project focused on the application of LDPM to simulate projectile perforation on an ultra high performance concrete called CORTUF. This application illustrates the strengths of LDPM over traditional continuum models.
Lu, An; Hsieh, Pei-Chen; Wu, Liang-Chun; Lin, Ming-Lang
2017-04-01
Earthquake and rainfall weakening potential sliding surface are common causes of dip slope failure. But in recent years, certain dip slopes failure, for example dip slope sliding without rain on the roadside of Formosa Freeway in northern Taiwan, are caused by uplift groundwater in vertical joints eventually weakening the potential sliding surface. The mechanism of sliding failure should be analyzed in more detail. Furthermore, prestress dissipating in anchors causing dip slope failure is also considered in this study. In this study, conceptual model is simplified from the case of Formosa Freeway in northern Taiwan and the main control factors including angle of slope, stratum, attitude of joints. In addition, drilling data, such as hydraulic conductivity, strength, friction angle and cohesion, are utilized to discuss mechanism and dominant factors of dip slope failure caused by uplift groundwater in vertical joints. UDEC(Universal Distinct Element Code) which is particularly well suited to problems involving jointed media and has been used extensively in stability analysis of jointed rock slopes is utilized in this study. The influence of external factors such as groundwater pressure on block sliding and deformation can also be simulated in UDEC. When the results from numerical simulation fit the condition of slope failure on the roadside of Formosa Freeway, the influence of prestress dissipating in anchors on slope stability is considered subsequently. Finally, simulation results by UDEC are compared with previous research results by FLAC, and discuss the difference between each other.
Institute of Scientific and Technical Information of China (English)
赵艳敏; 石东洋
2011-01-01
The infinite dimensional Hamiltonian system of three-dimensional vector wave equation is given and a new numerical approximate scheme is proposed in this paper. Based on the Gauss-Lobatto-Legendre polynomial, the spatial discretization scheme for the proposed infinite dimensional system is established by virtue of the vector spectral element method, and then a finite dimensional Hamiltonian system is attained. Moreover, in order to preserve the structure and energy of the system, the full discretization scheme of the finite dimensional system is derived by utilizing the symplectic difference method. Finally, the stiff matrix and mass matrix are disposed by the diagonal techniques. High accuracy approximation scheme is thus obtained, and simultaneously the computing cost and storage capacity are reduced significantly.%本文给出了三维矢量波动方程的无穷维Hamilton系统形式并提出了一个新的数值逼近格式.基于Gauss-Lobatto-Legendre多项式,建立了该无穷维系统的矢量谱元方法空间离散格式,并得到一个有限维Hamilton系统.进而,利用辛差分方法对该有限维系统进行全离散,以期保持系统的结构和能量.最后,借助于对角化技巧处理刚度矩阵和质量矩阵,在得到高精度逼近格式的同时,大幅降低了计算量和存储量.
Efficient discretization in finite difference method
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
Energy Technology Data Exchange (ETDEWEB)
Mugica R, A.; Valle G, E. del [IPN, ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: mugica@esfm.ipn.mx
2003-07-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Abushaikha, Ahmad S.; Voskov, Denis V.; Tchelepi, Hamdi A.
2017-10-01
We present a new fully-implicit, mixed-hybrid, finite-element (MHFE) discretization scheme for general-purpose compositional reservoir simulation. The locally conservative scheme solves the coupled momentum and mass balance equations simultaneously, and the fluid system is modeled using a cubic equation-of-state. We introduce a new conservative flux approach for the mass balance equations for this fully-implicit approach. We discuss the nonlinear solution procedure for the proposed approach, and we present extensive numerical tests to demonstrate the convergence and accuracy of the MHFE method using tetrahedral elements. We also compare the method to other advanced discretization schemes for unstructured meshes and tensor permeability. Finally, we illustrate the applicability and robustness of the method for highly heterogeneous reservoirs with unstructured grids.
Application of an efficient Bayesian discretization method to biomedical data
Directory of Open Access Journals (Sweden)
Gopalakrishnan Vanathi
2011-07-01
Full Text Available Abstract Background Several data mining methods require data that are discrete, and other methods often perform better with discrete data. We introduce an efficient Bayesian discretization (EBD method for optimal discretization of variables that runs efficiently on high-dimensional biomedical datasets. The EBD method consists of two components, namely, a Bayesian score to evaluate discretizations and a dynamic programming search procedure to efficiently search the space of possible discretizations. We compared the performance of EBD to Fayyad and Irani's (FI discretization method, which is commonly used for discretization. Results On 24 biomedical datasets obtained from high-throughput transcriptomic and proteomic studies, the classification performances of the C4.5 classifier and the naïve Bayes classifier were statistically significantly better when the predictor variables were discretized using EBD over FI. EBD was statistically significantly more stable to the variability of the datasets than FI. However, EBD was less robust, though not statistically significantly so, than FI and produced slightly more complex discretizations than FI. Conclusions On a range of biomedical datasets, a Bayesian discretization method (EBD yielded better classification performance and stability but was less robust than the widely used FI discretization method. The EBD discretization method is easy to implement, permits the incorporation of prior knowledge and belief, and is sufficiently fast for application to high-dimensional data.
Institute of Scientific and Technical Information of China (English)
谭援强; 张浩; 李明军
2011-01-01
According to coupling computational fluid dynamics and computational granular media mechanics method, the motion of abrasive flow in CMP with composite particles was simulated using discrete element method. With PFC3D software, a two-phase flow model that predicted the kinematics and trajectory of the abrasive particles was built herein,two verification simulations were conducted to demonstrate the capability of the current method to solve nano-size two-phase flow problems. Finally, the CMP geometry simulations were conducted, some phenomenon observed in the experiments were explained.%基于耦合计算流体力学和计算散体力学的方法,利用PFC3D软件模拟了复合磨粒抛光液化学机械抛光(CMP)中抛光液固液两相流的流动行为.通过2个数值实验并将其与他人实验数据进行对比,验证了利用PFC3D软件模拟纳米两相流问题的可行性.对CMP过程进行了数值模拟,解释了一些实验中观测到的现象.
A modified discrete element model for sea ice dynamics
Institute of Scientific and Technical Information of China (English)
LI Baohui; LI Hai; LIU Yu; WANG Anliang; JI Shunying
2014-01-01
Considering the discontinuous characteristics of sea ice on various scales, a modified discrete element mod-el (DEM) for sea ice dynamics is developed based on the granular material rheology. In this modified DEM, a soft sea ice particle element is introduced as a self-adjustive particle size function. Each ice particle can be treated as an assembly of ice floes, with its concentration and thickness changing to variable sizes un-der the conservation of mass. In this model, the contact forces among ice particles are calculated using a viscous-elastic-plastic model, while the maximum shear forces are described with the Mohr-Coulomb fric-tion law. With this modified DEM, the ice flow dynamics is simulated under the drags of wind and current in a channel of various widths. The thicknesses, concentrations and velocities of ice particles are obtained, and then reasonable dynamic process is analyzed. The sea ice dynamic process is also simulated in a vortex wind field. Taking the influence of thermodynamics into account, this modified DEM will be improved in the future work.
A minimal coupled fluid-discrete element model for bedload transport
Maurin, Raphael; Chareyre, Bruno; Frey, Philippe
2016-01-01
A minimal Lagragian two-phase model to study turbulent bedload transport focusing on the granular phase is presented, and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results s...
Discrete element simulation of powder compaction in cold uniaxial pressing with low pressure
Rojek, Jerzy; Nosewicz, Szymon; Jurczak, Kamila; Chmielewski, Marcin; Bochenek, Kamil; Pietrzak, Katarzyna
2016-11-01
This paper presents numerical studies of powder compaction in cold uniaxial pressing. The powder compaction in this work is considered as an initial stage of a hot pressing process so it is realized with relatively low pressure (up to 50 MPa). Hence the attention has been focused on the densification mechanisms at this range of pressure and models suitable for these conditions. The discrete element method employing spherical particles has been used in the numerical studies. Numerical simulations have been performed for two different contact models—the elastic Hertz-Mindlin-Deresiewicz model and the plastic Storåkers model. Numerical results have been compared with the results of laboratory tests of the die compaction of the NiAl powder. Comparisons have shown that the discrete element method is capable to represent properly the densification mechanisms by the particle rearrangement and particle deformation.
Finite-Element-Based Discretization and Regularization Strategies for 3D Inverse Electrocardiography
Wang, Dafang; Kirby, Robert M.; Johnson, Chris R.
2011-01-01
We consider the inverse electrocardiographic problem of computing epicardial potentials from a body-surface potential map. We study how to improve numerical approximation of the inverse problem when the finite element method is used. Being ill-posed, the inverse problem requires different discretization strategies from its corresponding forward problem. We propose refinement guidelines that specifically address the ill-posedness of the problem. The resulting guidelines necessitate the use of ...
Partition of the contact force network obtained in discrete element simulations of element tests
Huang, Xin; O'Sullivan, Catherine; Hanley, Kevin J.; Kwok, Chung-Yee
2017-04-01
The transmission of stress within a granular material composed of rigid spheres is explored using the discrete element method. The contribution of contacts to both deviatoric stress and structural anisotropy is investigated. The influences of five factors are considered: inter-particle friction coefficient, loading regime, packing density, contact model, and boundary conditions. The data generated indicate that using the above-average normal contact force criterion to decompose the contact force network into two subsets with distinct contributions to stress transmission and structural anisotropy is not robust. The characteristic normal contact forces marking the transition from negative to positive contribution to the overall deviatoric stress and structural anisotropy are not unique values but vary during shearing. Once the critical state is attained (i.e., once shearing continues at a constant deviator stress and solid fraction), the characteristic normal contact force remains approximately constant and this critical state characteristic normal force is observed to decrease with increasing inter-particle friction. The characteristic normal contact force considering the contribution to deviatoric stress has a power-law relationship with the mean effective stress at the critical state.
Partition of the contact force network obtained in discrete element simulations of element tests
Huang, Xin; O'Sullivan, Catherine; Hanley, Kevin J.; Kwok, Chung-Yee
2016-01-01
The transmission of stress within a granular material composed of rigid spheres is explored using the discrete element method. The contribution of contacts to both deviatoric stress and structural anisotropy is investigated. The influences of five factors are considered: inter-particle friction coefficient, loading regime, packing density, contact model, and boundary conditions. The data generated indicate that using the above-average normal contact force criterion to decompose the contact force network into two subsets with distinct contributions to stress transmission and structural anisotropy is not robust. The characteristic normal contact forces marking the transition from negative to positive contribution to the overall deviatoric stress and structural anisotropy are not unique values but vary during shearing. Once the critical state is attained (i.e., once shearing continues at a constant deviator stress and solid fraction), the characteristic normal contact force remains approximately constant and this critical state characteristic normal force is observed to decrease with increasing inter-particle friction. The characteristic normal contact force considering the contribution to deviatoric stress has a power-law relationship with the mean effective stress at the critical state.
Discrete Element Method for Modeling Penetration
2006-07-01
toughness K,, increases as the rate of applied load is increased. Mindess et al. (1987) conducted experiments on single-edge 24 notched concrete beams loaded...547. Mindess , S., Banthia, N., and Yan, C., "The Fracture Toughness of Concrete under Impact Loading," Cement and Concrete Research, Vol. 17, 1987
Cleary, Paul W; Prakash, Mahesh
2004-09-15
Particle-based simulation methods, such as the discrete-element method and smoothed particle hydrodynamics, have specific advantages in modelling complex three-dimensional (3D) environmental fluid and particulate flows. The theory of both these methods and their relative advantages compared with traditional methods will be discussed. Examples of 3D flows on realistic topography illustrate the environmental application of these methods. These include the flooding of a river valley as a result of a dam collapse, coastal inundation by a tsunami, volcanic lava flow and landslides. Issues related to validation and quality data availability are also discussed.
Institute of Scientific and Technical Information of China (English)
于瑞江; 汤晓华; 张玉玲
2015-01-01
Based on the discrete element method, using Inventor to establish a three dimensional model of horizontal screw conveyer, to import the model into EDEM software simulation. It was gained by analyzing that when the rotational speed of the screw conveyer and the volumetric fill level was 200 rpm and 20% respectively, transporting a certain mass material consumed power was to minimize; Through simulation obtain the average speed change rule of rice grain and the force situation of screw conveyor, when the volumetric fill level is 20%, 50%, 70%.%基于离散元法，应用Inventor软件建立水平螺旋输送机三维实体模型，将该模型导入EDEM软件进行仿真模拟。分析验证了水平螺旋输送机转速和填充率分别为200r/min和20%时，螺旋输送机输送一定质量物料消耗的功率最小；通过仿真模拟得出填充率为20%、50%、70%时大米颗粒平均速度变化规律以及螺旋输送机受力情况。
Rahmouni, Lyes; Cools, Kristof; Andriulli, Francesco P
2016-01-01
In this paper we present a new discretization strategy for the boundary element formulation of the Electroencephalography (EEG) forward problem. Boundary integral formulations, classically solved with the Boundary Element Method (BEM), are widely used in high resolution EEG imaging because of their recognized advantages in several real case scenarios. Unfortunately however, it is widely reported that the accuracy of standard BEM schemes is limited, especially when the current source density is dipolar and its location approaches one of the brain boundary surfaces. This is a particularly limiting problem given that during an high-resolution EEG imaging procedure, several EEG forward problem solutions are required for which the source currents are near or on top of a boundary surface. This work will first present an analysis of standardly discretized EEG forward problems, reporting on a theoretical issue of some of the formulations that have been used so far in the community. We report on the fact that several ...
Institute of Scientific and Technical Information of China (English)
赵学亮; 赫建明; 董高峰; 李腾飞; 吴方华
2012-01-01
Microstructure and micromechanics of granular soils have been of interest to many researchers because of their significant role in the macroscale response. Discrete element method( DEM) is usually simpler, faster, and cheaper than the traditional experimental method and able to obtain some information that is difficult or inaccessible in the experimental method. In this paper, some new developments of the microscale study on granular soil using DEM are briefly reviewed. Some issues in numerical modeling such as density ( mass) scaling and membrane boundary simulation are discussed. The new developments on microstructure study such as particle rotation and displacement and mesoscale void ratio distribution using DEM are analyzed. It is concluded that DEM is a powerful tool that can capture the discrete characteristics of the granular materials.%粒状土的微观结构和微观力学被认为是其宏观力学和体积特性的内在根本因素,近年来得到越来越多的关注和研究.离散单元法作为一种研究颗粒材料的数值模拟计算方法,比试验方法快捷、简便、经济,而且能够容易得到在实验室试验中很难或无法得到的更多重要的微观结构和微观力学的信息,近年来得到越来越多应用.本文介绍了离散单元法对土的微观特性研究的一些最新方法和进展,对数值建模中的一些重要方面如比重(质量)放大、树脂薄膜模拟等方面进行了阐述,对离散单元法在土的微观结构分析(如颗粒旋转、颗粒位移、中尺度孔隙率分布)的一些最新研究作了分析和介绍.分析表明,离散单元法是研究粒状土的微观特性的一个有力工具,可以对土的宏观特性从微观角度得到更好的解释和认识.
Discrete Element Model for Suppression of Coffee-Ring Effect
Xu, Ting; Lam, Miu Ling; Chen, Ting-Hsuan
2017-02-01
When a sessile droplet evaporates, coffee-ring effect drives the suspended particulate matters to the droplet edge, eventually forming a ring-shaped deposition. Because it causes a non-uniform distribution of solid contents, which is undesired in many applications, attempts have been made to eliminate the coffee-ring effect. Recent reports indicated that the coffee-ring effect can be suppressed by a mixture of spherical and non-spherical particles with enhanced particle-particle interaction at air-water interface. However, a model to comprehend the inter-particulate activities has been lacking. Here, we report a discrete element model (particle system) to investigate the phenomenon. The modeled dynamics included particle traveling following the capillary flow with Brownian motion, and its resultant 3D hexagonal close packing of particles along the contact line. For particles being adsorbed by air-water interface, we modeled cluster growth, cluster deformation, and cluster combination. We found that the suppression of coffee-ring effect does not require a circulatory flow driven by an inward Marangoni flow at air-water interface. Instead, the number of new cluster formation, which can be enhanced by increasing the ratio of non-spherical particles and the overall number of microspheres, is more dominant in the suppression process. Together, this model provides a useful platform elucidating insights for suppressing coffee-ring effect for practical applications in the future.
Projected discrete ordinates methods for numerical transport problems
Energy Technology Data Exchange (ETDEWEB)
Larsen, E.W.
1985-01-01
A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.
Discrete/Finite Element Modelling of Rock Cutting with a TBM Disc Cutter
Labra, Carlos; Rojek, Jerzy; Oñate, Eugenio
2017-03-01
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool-rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Institute of Scientific and Technical Information of China (English)
付宏; 吕游; 徐静; 黄山; 于建群
2012-01-01
It needs to establish analysis models of machine parts (boundaries), when use DEM (Discrete Element Method) to analyze the contact action between machine parts and granular materials. There exist irregular surfaces which can not be expressed by the elementary analytic function in the parts' surfaces which contact with granular materials. The AFT (Advancing Front Technique) was used to mesh and discrete irregular surfaces into the triangle planar units,parameters of movement characters and material properties were added in the same time,so the DEM analysis models of irregular surfaces was created. Based on the redevelopment of PRO/E software,the boundary modeling software of irregular surfaces was developed. By application examples,the feasibility of boundary modeling method and the software which based on the AFT was validated,which lays foundations for simulation and analysis of working process for machine parts with complex structure.%在采用离散元法分析机械部件与颗粒材料接触作用时,需要建立机械部件(边界)的离散元法分析模型.分析可知,机械部件中与颗粒材料接触作用的零件表面,存在不能用初等解析函数表达的非规则曲面.为此,采用推进波前法(AFT:Advancing Front Technique)进行非规则曲面网格划分,把非规则曲面离散成三角形平面片的组合,同时添加运动属性和材料特性参数,由此建立非规则曲面边界的离散元法分析模型.在对PRO/E软件进行二次开发的基础上,研制了非规则曲面边界建模软件.通过实例验证,初步证明了基于AFT边界建模方法和软件的可行性,为复杂结构机械部件工作过程的仿真分析奠定了基础.
Nonlocality and discrete cellular methods in optics
Wijers, C.M.J.; Boeij, de P.L.
2001-01-01
A subdivision of space into discrete cells underlies the traditional discrete dipole model. This model presumes that only nonlocal electric interactions between cells govern the electromagnetic response of a condensed matter system. Apart from the case of simple dielectrics, this is not realistic. C
Aorta modeling with the element-based zero-stress state and isogeometric discretization
Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi
2016-11-01
Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight
Aorta modeling with the element-based zero-stress state and isogeometric discretization
Takizawa, Kenji; Tezduyar, Tayfun E.; Sasaki, Takafumi
2017-02-01
Patient-specific arterial fluid-structure interaction computations, including aorta computations, require an estimation of the zero-stress state (ZSS), because the image-based arterial geometries do not come from a ZSS. We have earlier introduced a method for estimation of the element-based ZSS (EBZSS) in the context of finite element discretization of the arterial wall. The method has three main components. 1. An iterative method, which starts with a calculated initial guess, is used for computing the EBZSS such that when a given pressure load is applied, the image-based target shape is matched. 2. A method for straight-tube segments is used for computing the EBZSS so that we match the given diameter and longitudinal stretch in the target configuration and the "opening angle." 3. An element-based mapping between the artery and straight-tube is extracted from the mapping between the artery and straight-tube segments. This provides the mapping from the arterial configuration to the straight-tube configuration, and from the estimated EBZSS of the straight-tube configuration back to the arterial configuration, to be used as the initial guess for the iterative method that matches the image-based target shape. Here we present the version of the EBZSS estimation method with isogeometric wall discretization. With isogeometric discretization, we can obtain the element-based mapping directly, instead of extracting it from the mapping between the artery and straight-tube segments. That is because all we need for the element-based mapping, including the curvatures, can be obtained within an element. With NURBS basis functions, we may be able to achieve a similar level of accuracy as with the linear basis functions, but using larger-size and much fewer elements. Higher-order NURBS basis functions allow representation of more complex shapes within an element. To show how the new EBZSS estimation method performs, we first present 2D test computations with straight
Discrete range clustering using Monte Carlo methods
Chatterji, G. B.; Sridhar, B.
1993-01-01
For automatic obstacle avoidance guidance during rotorcraft low altitude flight, a reliable model of the nearby environment is needed. Such a model may be constructed by applying surface fitting techniques to the dense range map obtained by active sensing using radars. However, for covertness, passive sensing techniques using electro-optic sensors are desirable. As opposed to the dense range map obtained via active sensing, passive sensing algorithms produce reliable range at sparse locations, and therefore, surface fitting techniques to fill the gaps in the range measurement are not directly applicable. Both for automatic guidance and as a display for aiding the pilot, these discrete ranges need to be grouped into sets which correspond to objects in the nearby environment. The focus of this paper is on using Monte Carlo methods for clustering range points into meaningful groups. One of the aims of the paper is to explore whether simulated annealing methods offer significant advantage over the basic Monte Carlo method for this class of problems. We compare three different approaches and present application results of these algorithms to a laboratory image sequence and a helicopter flight sequence.
Coupled discrete element and smoothed particle hydrodynamics simulations of the die filling process
Breinlinger, Thomas; Kraft, Torsten
2016-11-01
Die filling is an important part of the powder compaction process chain, where defects in the final part can be introduced—or prevented. Simulation of this process is therefore a goal for many part producers and has been studied by some researchers already. In this work, we focus on the influence of the surrounding air on the powder flow. We demonstrate the implementing and coupling of the discrete element method for the granular powder and the smoothed particle hydrodynamics method for the gas flow. Application of the method to the die filling process is demonstrated.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)
2005-07-01
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Yang, B; Zika, M R
2005-07-15
We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Institute of Scientific and Technical Information of China (English)
宜晨虹; 慕青松; 苗天德
2009-01-01
The discrete element method is used to research the distribution of forces within the two-dimensional granular system under gravity. The force chains among the particles are generated according to the magnitudes of the forces. Then the simulation results are compared with the well-known q-model, a-model and experimental results obtained through the photoelastic test under the same conditions. According to the computational solution, we conclude that the simulation results are similar to the experimental results are some what different from the two probability models. In addition, we also obtained that the probability distribution of the force is very uneven. The probability of the large force decays exponentially and the distribution of the force chains takes on a fraetal character.%用离散元的方法模拟了仅有重力作用的二维颗粒系统内部力的分布情况,并根据力的大小得到颗粒之间的应力链.模拟结果与颗粒介质研究中的两个著名模型q模型和a模型作了对比,并与光弹实验的结果作了比较.对比结果表明,模拟结果与实验相似,而与两个概率模型有一定的差异.另外计算结果还表明,颗粒介质中力大小的概率分布极为不均匀,较大的力概率呈指数衰减,应力链的分布具有分形特征.
Dual Formulations of Mixed Finite Element Methods with Applications.
Gillette, Andrew; Bajaj, Chandrajit
2011-10-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.
Generation of Random Particle Packings for Discrete Element Models
Abe, S.; Weatherley, D.; Ayton, T.
2012-04-01
An important step in the setup process of Discrete Element Model (DEM) simulations is the generation of a suitable particle packing. There are quite a number of properties such a granular material specimen should ideally have, such as high coordination number, isotropy, the ability to fill arbitrary bounding volumes and the absence of locked-in stresses. An algorithm which is able to produce specimens fulfilling these requirements is the insertion based sphere packing algorithm originally proposed by Place and Mora, 2001 [2] and extended in this work. The algorithm works in two stages. First a number of "seed" spheres are inserted into the bounding volume. In the second stage the gaps between the "seed" spheres are filled by inserting new spheres in a way so they have D+1 (i.e. 3 in 2D, 4 in 3D) touching contacts with either other spheres or the boundaries of the enclosing volume. Here we present an implementation of the algorithm and a systematic statistical analysis of the generated sphere packings. The analysis of the particle radius distribution shows that they follow a power-law with an exponent ≈ D (i.e. ≈3 for a 3D packing and ≈2 for 2D). Although the algorithm intrinsically guarantees coordination numbers of at least 4 in 3D and 3 in 2D, the coordination numbers realized in the generated packings can be significantly higher, reaching beyond 50 if the range of particle radii is sufficiently large. Even for relatively small ranges of particle sizes (e.g. Rmin = 0.5Rmax) the maximum coordination number may exceed 10. The degree of isotropy of the generated sphere packing is also analysed in both 2D and 3D, by measuring the distribution of orientations of vectors joining the centres of adjacent particles. If the range of particle sizes is small, the packing algorithm yields moderate anisotropy approaching that expected for a face-centred cubic packing of equal-sized particles. However, once Rmin 2D and 3D. The analysis demonstrates that this space
Institute of Scientific and Technical Information of China (English)
CHANG Wei-Tze; HSIEH Shang-Hsien; YANG Fu-Ling; CHEN Chuin-Shan
2008-01-01
This paper proposes a numerical scheme that employs the discrete element method (DEM) to simulate the motion of a wet granular flow down an inclined channel.To account for the liquid influences on the dynamics between paired particles,this paper presents a wet soft-sphere contact model with liquid-modified parameters.The developed scheme takes full advantage of DEM and avoids the expensive simula-tion of the solid-liquid interactions with conventional Navier-Stokes equation solver.This wet contact model has been implemented in an in-housed parallel discrete objects simulation system-KNIGHT and ANNE/IRIS口to compute the dynamic behaviors of both dry and wet granular particles flowing down an in-dined channel.
Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo
2015-10-01
The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.
Multiple-contact discrete-element model for simulating dense granular media
Brodu, Nicolas; Dijksman, Joshua A.; Behringer, Robert P.
2015-03-01
This article presents a new force model for performing quantitative simulations of dense granular materials. Interactions between multiple contacts (MC) on the same grain are explicitly taken into account. Our readily applicable MC-DEM method retains all the advantages of discrete-element method simulations and does not require the use of costly finite-element methods. The new model closely reproduces our recent experimental measurements, including contact force distributions in full 3D, at all compression levels of the packing up to the experimental maximum limit of 13%. Comparisons with classic simulations using the nondeformable spheres approach, as well as with alternative models for interactions between multiple contacts, are provided. The success of our model, compared to these alternatives, demonstrates that interactions between multiple contacts on each grain must be included for dense granular packings.
Finite Element Calculation of Discrete Stratified Fluid Vibrations
Directory of Open Access Journals (Sweden)
Ko Ko Win
2016-01-01
Full Text Available Many publications, which consider a problem of small vibrations of an incompressible ideal fluid, completely filling the stationary cylindrical tank, have the long lists of references in the field concerned. This paper uses the finite element method to consider vibrations of three incompressible fluids, defines natural frequencies of vibrations, and builds the vibration forms of the interface surface of fluids for the double-tone vibrations. It shows how the vibration frequency depends on the ratios of vibrating fluid density and thicknesses of fluid layers and compares the numerical calculation results with the analytically obtained exact values.The paper describes a variational formulation of the problem concerning the natural vibrations of immiscible fluids and using the finite element method provides a numerical implementation to define the fixed values of the functional that meets the variational problem. The reliability of the numerical results obtained is proved by their approximation to the result of calculating frequencies derived from the solutions of the problem of natural vibrations of fluid in a cylindrical vessel with a different fluid depth. To perform all numerical calculations was used the Matlab software.
Structure of beef chewing model based on discrete element method%基于离散元法的牛肉咀嚼破碎模型构建
Institute of Scientific and Technical Information of China (English)
王笑丹; 王洪美; 韩云秀; 焦娜; 才英明; 金佳慧; 徐丽萍; 刘爱阳
2016-01-01
Tenderness is one of the most important factors influencing the quality of beef. Traditional evaluation methods have some disadvantages and limitations more or less. In order to predict beef tenderness accurately, conveniently and objectively, in this research, the discrete element method was used to establish the beef chewing model. Beef from the mid-region of longissimus dorsi (LD) was collected from 50 cattle as the samples, in which 30 cattle were used for structuring the beef chewing model, and 20 cattle were prepared for verifying the accuracy. The age of cattle (400-550 kg) was from 30 to 36 months, and the cattle were fattened for more than 6 months. After starving for 24 h, the live cattle were weighed, showered, stunned, killed, and bled blood. The 4 limbs and head of each animal were cut off, and the body of cattle was split into halves, cooled at 4℃for 24 h, and then the carcasses were divided. Each piece of beef was cut into 10 mm × 10 mm × 10 mm sample, but the inter-muscular fat, connective tissues and tendon were deleted. The samples were placed into plastic bags individually in a 75-80℃water bath, and cooked for 15 min until the internal temperature of beef sample reached 70℃. The samples were divided into 3 groups so as to carry out the experiments in triplicate after the samples were cooled to room temperature (20℃). Shear modulus and normal stiffness were detected by Brookfield CT3 texture analyzer (Brookfield Engineering Laboratories, INC. Middleboro Massachusetts, USA). With a two-cycle texture profile analysis (TPA) model (a compression model for normal stiffness) and a TA44 probe (cylinder diameter=4 mm), the size of testing surface of each sample was 10 mm ×10 mm × 10 mm (for normal stiffness). The related parameters settings were: test speed of 0.5 mm/s and deformation quantity of 2.5 mm for shear modulus detection, and test speed of 0.5 mm/s and preload of 2 N for detecting normal stiffness. In addition, density, restitution
Impact of Interaction Laws and Particle Modeling in Discrete Element Simulations
Cao, Hong-Phong; Renouf, Mathieu; Dubois, Frédéric
2009-06-01
To describe the evolution of divided media, Discrete Elements Methods (DEMs) appear as one of the most appropriate tools. Medium evolution is directly related to assumptions about local contact area, body deformations and contact interactions. In some circumstance such assumptions have a strong influence on the macroscopic behaviour of the media and consequently become questionable. Using the Contact Dynamics framework, the paper presents how classical assumptions could be extended to avoid numerical effects. A reflection is proposed taking into account both physical and numerical aspects. Static and dynamic configuration have been used to illustrate the paper purposes.
Karrech, Ali; Bonnet, Guy; Chevoir, François; Roux, Jean-Noel; Canou, Jean; Dupla, Jean-Claude
2008-01-01
This paper deals with the vibration of granular materials due to cyclic external excitation. It highlights the effect of the acceleration on the settlement speed and proves the existence of a relationship between settlement and loss of contacts in partially confined granular materials under vibration. The numerical simulations are carried out using the Molecular Dynamics method, where the discrete elements consist of polygonal grains. The data analyses are conducted based on multivariate autoregressive models to describe the settlement and permanent contacts number with respect to the number of loading cycles.
Indian Academy of Sciences (India)
Rajesh P Nair; C Lakshmana Rao
2012-04-01
One-dimensional discrete element model for the ballistic impact is used to determine the depth of penetration of a bullet on a thick target. Discrete Element Method (DEM) is a numerical tool where a continuum is modelled as a network of masses connected by normal springs. A one-dimensional discrete element model is developed to obtain the displacements and forces associated with the ballistic impact on a thick target. The depth of penetration of the penetrator into the target is calculated from these DEM results. The simulated results of depth of penetration are found to be in reasonable agreement with the simulation results of other numerical approaches that are available in the literature.
Institute of Scientific and Technical Information of China (English)
陈永雄; 梁秀兵; 刘燕; 程江波; 徐滨士
2011-01-01
采用有限元法模拟了高速电弧喷涂枪二维气流场的分布.通过计算比较了收缩型和缩扩型喷管的流场差异,同时分析了不同的丝材夹角、丝交点离喷管出口距离等喷枪结构参数下喷枪气流场行为.结果显示,缩扩型喷管更有利于熔滴的雾化,丝交点离喷管出口距离减小至0、丝夹角为40°时更有利于熔滴的加速.基于以上模拟结果,优化设计了一种新型的高速电弧喷涂枪.喷涂粒子的形貌实验表明,新型喷枪的雾化粒子粒度比原始喷枪更细、分布更均匀.%In order to investigate fracture failure mechanism of asphalt mixture from micro-structure, probability method has been used to present a theoretical formula which develops to convert the aggregate weight gradation into the two-dimension (2D) quantity gradation. Two 2D digital specimens with different thicknesses of asphalt films are generated based on particle generation algorithm. Based on the discrete element method, the fracture process of asphalt mixture beam has been simulated and the effect of asphalt film thickness, cohesive strength of asphalt mastics and adhesive strength between asphalt mastic and aggregate on the fracture failure of asphalt mixture has been also investigated. The results show that the cracking has the tendency to occur in asphalt mastics for asphalt mixture with thick asphalt films and the cohesive strength of asphalt mastics has a great influence on fracture failure of this type mixture. For asphalt mixture with thin films, the early cracking often appears in asphalt mastics and propagation of cracking occurs at the interface between aggregates and mastics. Fracture initiation is dominated by the cohesive strength of asphalt mastics and propagation of cracking is controlled by adhesive strength between asphalt mastic and aggregate for mixture with thin films.
Institute of Scientific and Technical Information of China (English)
张江源; 林福泳
2013-01-01
By constructing a discrete base, multi-resolution analysis methods are applied to denoise the noise signal. The proposed method of discrete base can be explicitly represented, and has symmetric characteristics. The calculation is greatly reduced through the cycle matrix inverse matrix method. Comparing different denoising methods, the signal de-noising effect is assessed from two aspects of signal-to-noise ratio (SNR) and mean square error (MSE). Experimental results indicate that this method shows good characteristics in signal denoising aspect relative to wavelet analysis method. Denoising effect is obvious, and can achieve good signal-to-noise ratio and mean square error when discrete base coefficient is near 0. 75.%通过构造离散基,应用多分辨率分析的方法,对噪声信号进行去噪处理.所提出方法的离散基能够显式表示,且具有对称性等特点,通过循环矩阵求逆矩阵的方法,可以使计算量大大降低.对比不同的去噪方法,并分别从信噪比(SNR)和均方误差(MSE)两个方面对信号去噪效果进行评估.实验结果表明:相对小波分析方法而言,该方法在信号去噪方面表现出较好的特性,去噪效果明显,离散基系数在0.75附近达到较好的信噪比及均方误差.
Institute of Scientific and Technical Information of China (English)
朱立平; 袁竹林; 闫亚明; 罗登山; 王宏生; 李斌
2012-01-01
丝状颗粒作为一类长径比较大的非球形颗粒,其传热特性及相关技术广泛应用于工农业生产的诸多领域.但目前颗粒在运动过程中传热问题的研究还很不充分,特别是对于丝状颗粒,更是缺乏有效的数学模型进行描述.从颗粒传热机理出发,提出了一种基于离散单元法的丝状颗粒传热模型,模型中综合考虑了颗粒碰撞(接触)传热、颗粒的内部导热以及颗粒与气体间的对流换热.利用该模型,对固定床中堆积丝状颗粒的热量迁移过程进行了数值模拟,着重比较了各种传热方式对传热过程的影响.研究表明,对流换热对整体传热量的贡献较大.此外,还获得了不同工况下颗粒温度随时间的变化规律.%Filamentous particle is a kind of non-spherical particles with large aspect ratio. It has been widely applied in industrial and agricultural processes. However, the heat transfer phenomenon about particles is not well understood, especially the filamentous particle. In this study, in order to describe the heat transfer process of filamentous particle, a new mathematical model based on the discrete element method was proposed through the analysis of heat transfer mechanisms. The impact heat transfer between particles, the internal heat conduction and the convection heat exchange between gas and particles were considered in this model, and then it was used to numerically study the heat transfer process of filamentous particles in a fixed bed. Comparing the mechanisms with each other, it showed that the convection heat exchange had greater contribution to the total heat transfer. In addition, the simulation results revealed some internal temperature rules in filamentous particles under different operating conditions.
Institute of Scientific and Technical Information of China (English)
杜欣; 曾亚武; 高睿; 颜敬; 曹源
2012-01-01
In order to reveal the effects of particle shape on friction mechanism, frictions among non-viscous particles were decomposed into the macro biting-force and the mesoscopic biting-force. Impact and angle-of-repose (AOR) numerical tests were conducted to study the effects of particle shape on macro biting-force and mesoscopic biting-force by modeling irregular shape particles using discrete element method. The results of numerical tests show that the friction coefficient of irregularly shaped particles is nearly two times its interface friction coefficient, while the friction coefficient of ellipsoid particles is approximately equal to the interface friction coefficient. Meanwhile, different particle shapes endowed the particles with rolling or slipping characteristics, and influence the macro biting-force and the granular friction behavior.%为了揭示颗粒外形对无粘性散体摩擦机理的影响,将无粘性颗粒材料之间的摩擦作用分解为颗粒间宏观咬合和微观咬合摩擦,运用不规则外形颗粒离散元建模方法,进行撞击模拟和自然安息角模拟,研究颗粒外形对微观咬合摩擦和宏观咬合作用的影响.数值计算结果表明,不规则外形颗粒集料摩擦因数近似为接触面摩擦因数的2倍,椭球体集料摩擦因数与接触面摩擦因数近似相等；颗粒外形不同使得颗粒运动状态呈现出滑动或滚动特征,并影响其宏观咬合特性及颗粒集料的摩擦性能.
A Digital-Discrete Method For Smooth-Continuous Data Reconstruction
Chen, Li
2010-01-01
A systematic digital-discrete method for obtaining continuous functions with smoothness to a certain order (C^(n)) from sample data is designed. This method is based on gradually varied functions and the classical finite difference method. This new method has been applied to real groundwater data and the results have validated the method. This method is independent from existing popular methods such as the cubic spline method and the finite element method. The new digital-discrete method has considerable advantages for a large number of real data applications. This digital method also differs from other classical discrete methods that usually use triangulations. This method can potentially be used to obtain smooth functions such as polynomials through its derivatives f^(k) and the solution for partial differential equations such as harmonic and other important equations.
Energy Technology Data Exchange (ETDEWEB)
Liu, Peiyuan [Univ. of Colorado, Boulder, CO (United States); Brown, Timothy [Univ. of Colorado, Boulder, CO (United States); Fullmer, William D. [Univ. of Colorado, Boulder, CO (United States); Hauser, Thomas [Univ. of Colorado, Boulder, CO (United States); Hrenya, Christine [Univ. of Colorado, Boulder, CO (United States); Grout, Ray [National Renewable Energy Lab. (NREL), Golden, CO (United States); Sitaraman, Hariswaran [National Renewable Energy Lab. (NREL), Golden, CO (United States)
2016-01-29
Five benchmark problems are developed and simulated with the computational fluid dynamics and discrete element model code MFiX. The benchmark problems span dilute and dense regimes, consider statistically homogeneous and inhomogeneous (both clusters and bubbles) particle concentrations and a range of particle and fluid dynamic computational loads. Several variations of the benchmark problems are also discussed to extend the computational phase space to cover granular (particles only), bidisperse and heat transfer cases. A weak scaling analysis is performed for each benchmark problem and, in most cases, the scalability of the code appears reasonable up to approx. 103 cores. Profiling of the benchmark problems indicate that the most substantial computational time is being spent on particle-particle force calculations, drag force calculations and interpolating between discrete particle and continuum fields. Hardware performance analysis was also carried out showing significant Level 2 cache miss ratios and a rather low degree of vectorization. These results are intended to serve as a baseline for future developments to the code as well as a preliminary indicator of where to best focus performance optimizations.
Institute of Scientific and Technical Information of China (English)
WANG Zhuolin; LIN Feng; GU Xianglin
2008-01-01
A two-dimensional mesoscopic numerical method to simulate the failure process of concrete under compression was developed based on the discrete element method by modifying the dgid body-spdng model proposed by Nagai et al.In the calculation model,aggregates or aggregate elements inside the concrete were simplified as rigid bodies with regular polygon profiles,which were surrounded by mortar polygons or mortar elements.All of the adjacent elements were connected by springs.According to the random distribution of aggregates,the mesh was generated by using Voronoi diagram method.Plastic behavior after the elastic limit for a spring was considered to set up the constitutive model of the spring,and Mohr-Coulomb criterion was adopted to judge the failure of a spdng.Simulation examples show that the proposed method can be used to predict the mechanical behavior of concrete under compression descriptively and quantitatively both for small deformation problems and for larger deformation problems.
A minimal coupled fluid-discrete element model for bedload transport
Maurin, R.; Chauchat, J.; Chareyre, B.; Frey, P.
2015-11-01
A minimal Lagrangian two-phase model to study turbulent bedload transport focusing on the granular phase is presented and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively low Shields numbers, for which no suspension occurs. A discrete element method for the granular phase is coupled with a one dimensional volume-averaged two-phase momentum equation for the fluid phase. The coupling between the discrete granular phase and the continuous fluid phase is discussed, and a consistent averaging formulation adapted to bedload transport is introduced. An original simple discrete random walk model is proposed to account for the fluid velocity fluctuations. The model is compared with experiments considering both classical sediment transport rate as a function of the Shields number, and depth profiles of solid velocity, volume fraction, and transport rate density, from existing bedload transport experiments in inclined flume. The results successfully reproduce the classical 3/2 power law, and more importantly describe well the depth profiles of the granular phase, showing that the model is able to reproduce the particle scale mechanisms. From a sensitivity analysis, it is shown that the fluctuation model allows to reproduce a realistic critical Shields number, and that the influence of the granular parameters on the macroscopic results is weak. Nevertheless, the analysis of the corresponding depth profiles reveals an evolution of the depth structure of the granular phase with varying restitution and friction coefficients, which denotes the non-trivial underlying physical mechanisms.
Institute of Scientific and Technical Information of China (English)
Kevin J. Hanley; Catherine O'Sullivan; Edmond P. Byrne; Kevin Cronin
2012-01-01
Infant formula is usually produced in an agglomerated powder form.These agglomerates are subjected to many transient forces following their manufacture.These can be difficult to quantify experimentally because of their small magnitudes and short durations.Numerical models have the potential to address this gap in the experimental data.The objective of the research described here was to calibrate a discrete element model for these agglomerates using experimental data obtained for quasi-static loading,and to use this model to study the mechanics of the particle response in detail.The Taguchi method was previously proposed as a viable calibration approach for discrete element models.In this work,the method was assessed for calibration of the model parameters (e.g.,bond stiffnesses and strengths) considering three responses: the force at failure,strain at failure and agglomerate stiffness.The Weibull moduli for the simulation results and the experimental data were almost identical following calibration and the 37％ characteristic stresses were similar.An analysis of the energy terms in the model provided useful insight into the model response.The bond energy and the normal force exerted on the platens were strongly correlated,and bond breakage events coincided with the highest energy dissipation rates.
Institute of Scientific and Technical Information of China (English)
李永奎; 孙月铢; 白雪卫
2015-01-01
Mechanical behavior in the densification of biomass material is closely related to pellet quality. In order to explore the forming mechanism of typical biomass material from loose state to consolidation, the discrete element method (DEM) was introduced to investigate the movement and interaction of the milled corn stalk particles in the compacting process, and the verification experiments were carried out to test the effectiveness of the DEM simulation in this study. Firstly, the three-dimensional (3D) particle contact model of corn stalk powder based on the soft-sphere model of DEM was established, and the constraining walls in DEM model were completely consistent with the compressing cavity boundary conditions in geometric shape and dimension of experimental tests conducted in December, 2014; the loading speed in simulation was also set as the same value as the DEM model. Secondly, the diameter range of simulated particles was configured to 0.4-1.0 mm in accordance to the particle size distribution acquired through the screening experiment and calculation, and the generated particles were fully filled into the whole cavity at the original state before the compressing force was loaded. The mechanical parameters of the particles, such as normal stiffness, shear stiffness and friction coefficient between the 2 contact particles, were set to the values generated at random in specific range which was determined according to compacting experimental data. Thirdly, the comparison of compression stress relaxation data between tests and simulation was carried out and the validity of the simulation was verified by the hypothesis test. It was found that the force data with time from the hypothesis tests and DEM simulation followed the similar tendency, and the absolute error was not higher than 100 N in both initial loading stage and 20 seconds after stress relaxation. In the first 20 seconds of stress relaxation course, the values of absolute error were obviously higher
Zohdi, T. I.
2016-03-01
In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach.
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Laboratory
2012-07-13
We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
Energy-pointwise discrete ordinates transport methods
Energy Technology Data Exchange (ETDEWEB)
Williams, M.L.; Asgari, M.; Tashakorri, R.
1997-06-01
A very brief description is given of a one-dimensional code, CENTRM, which computes a detailed, space-dependent flux spectrum in a pointwise-energy representation within the resolved resonance range. The code will become a component in the SCALE system to improve computation of self-shielded cross sections, thereby enhancing the accuracy of codes such as KENO. CENTRM uses discrete-ordinates transport theory with an arbitrary angular quadrature order and a Legendre expansion of scattering anisotropy for moderator materials and heavy nuclides. The CENTRM program provides capability to deterministically compute full energy range, space-dependent angular flux spectra, rigorously accounting for resonance fine-structure and scattering anisotropy effects.
Institute of Scientific and Technical Information of China (English)
陈俊; 黄晓明
2011-01-01
为了从细观角度深入分析沥青混凝土的断裂机理,根据概率理论,建立了集料质量级配与二维数量级配的关系,并通过计算机随机投放技术生成了具有2种不同沥青膜厚度的沥青混合料二维数字试件;利用离散元方法,模拟了沥青混合料小梁试件的断裂过程,分析了沥青砂浆抗拉强度、砂浆与集料黏结强度和沥青膜厚度对沥青混合料断裂过程的影响.结果表明:对于沥青膜较厚的沥青混合料而言,起裂阶段和扩展阶段的裂纹主要出现在沥青砂浆中,沥青砂浆的抗拉强度是影响混合料断裂的主要因素;当沥青膜较薄时,起裂和扩展阶段的裂纹在沥青砂浆内部和砂浆与集料界面中都有发现,砂浆抗拉强度决定着混合料的破坏应力和应变,砂浆与集料的黏结强度决定着混合料裂纹扩展的速率.%In order to investigate fracture failure mechanism of asphalt mixture from micro-structure, probability method has been used to present a theoretical formula which develops to convert the aggregate weight gradation into the two-dimension (2D) quantity gradation. Two 2D digital specimens with different thicknesses of asphalt films are generated based on particle generation algorithm. Based on the discrete element method, the fracture process of asphalt mixture beam has been simulated and the effect of asphalt film thickness, cohesive strength of asphalt mastics and adhesive strength between asphalt mastic and aggregate on the fracture failure of asphalt mix ture has been also investigated. The results show that the cracking has the tendency to occur in asphalt mastics for asphalt mixture with thick asphalt films and the cohesive strength of asphalt mastics has a great influence on fracture failure of this type mixture. For asphalt mixture with thin films, the early cracking often appears in as phalt mastics and propagation of cracking occurs at the interface between aggregates and mastics
Institute of Scientific and Technical Information of China (English)
蒋明镜; 张望城; 王剑锋
2013-01-01
砂土等散粒体在剪切过程中的能量存储及耗散是其宏观力学响应的深层原因,但因量测难度较大而研究较少.将考虑抗转动的接触模型引入离散元软件PFC2D,基于热力学第一定律建立各种能量量测方法,并在平面应变双轴压缩试验中采用该方法统计密实散粒体在剪切过程中的能量演化规律.采取了4种耗散类型,即滑动-滚动(S-R)、滑动-非滚动(S-NR)、非滑动-滚动(NS-R)和非滑动-非滚动(NS-NR).结果表明:密实散粒体加载时能量耗散以滑动摩擦为主；且小应变加载阶段,外力功主要转化为弹性应变能,但同时也存在均布于试样的耗散能；随着应变的增加,外力功的转化形式逐渐过渡为以耗散能为主,且集中分布在带状区域内；各个加载阶段的摩擦耗散均存在各向异性.%Energy storing and dissipation are the underlying mechanisms of the macromechanical responses of granular materials subjected to shear failure, while they are difficult to measure in laboratory. We implemented a user-defined contact model considering rolling resistance to the commercial software PFC2D, and made a calculable method to count the energy components based on the first law of thermodynamics. Then the energy storing and dissipation through the whole sample are investigated in a series of numerical biaxial compression tests by discrete element method (DEM). Four kinds of friction are adopted, i.e. sliding and rolling (S-R), sliding and non-rolling (S-NR), non-sliding and rolling (NS-R) and non-sliding and non-rolling (NS-NR). The results show that the energy is mainly dissipated in the type of sliding rather than rolling. And at a small biaxial strain, the input energy is mainly stored as elastic energy with a small portion dissipated and the dissipated energy is globally distributed through the whole sample. While a large biaxial strain is achieved, the dissipated energy gradually turns dominant and the majority
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
Two Dynamic Discrete Choice Estimation Problems and Simulation Method Solutions
Steven Stern
1994-01-01
This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in bot...
Charging behavior in a bell-less blast furnace based on 3D discrete element method%基于三维离散元法的无钟高炉装料行为
Institute of Scientific and Technical Information of China (English)
张建良; 邱家用; 国宏伟; 刘征建; 孙辉; 王广伟; 高征铠
2013-01-01
利用三维离散元法建立了无钟高炉布料模型，分析了料罐、旋转溜槽中的颗粒流动行为以及颗粒离开溜槽后的下落轨迹和料堆形成，可视化再现了装料过程。结果发现：炉料在流动过程中始终存在粒度偏析，料罐排料流为漏斗流，小颗粒由于偏析而倾向于后期排出；溜槽倾角对颗粒流动行为和料堆形成影响较大；溜槽内颗粒流由于溜槽旋转而向侧上部偏离和翻动，小颗粒因靠近壁面而位于料流内侧，大颗粒因聚集在溜槽上部而处在料流外侧，炉料颗粒偏析、偏转翻动和速度分布影响下落轨迹；在炉料下落到料面的堆积过程中，大颗粒易于向炉喉中心和边缘偏析，小颗粒因位于料流内侧和渗透作用而分布在堆尖下方且偏向中心侧。结合激光网格炉内测量技术料流轨迹测量结果，验证了模型的适用性。%A bell-less blast furnace charging model was established by using 3D discrete element method. The flow behavior of particles in the hopper and rotating chute, the falling trajectory and heaping process of particles discharged from the rotating chute were modeled and analyzed by using this model. Consequently, the charging process was reproduced visually. It is found that size segregation is always prevalent throughout the flow process of particles. The discharging flow from the hopper is funnel flow, and small particles tend to be discharged in the later stage due to size segregation. It is proved that the influence of chute inclination angle on the particle behavior and heaping process is very significance. The granular flow in the chute deviates upward to one side and tumbles attributing to rotation. Small particles close to the chute wall surface move to the inside of the stream, while large ones staying at the upper part of the chute flow move to the outside. The falling tra jectory of particles is affected by particle size segregation
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
Influence of discretization method on the digital control system performance
Directory of Open Access Journals (Sweden)
Futás József
2003-12-01
Full Text Available The design of control system can be divided into two steps. First the process or plant have to be convert into mathematical model form, so that its behavior can be analyzed. Then an appropriate controller have to be design in order to get the desired response of the controlled system. In the continuous time domain the system is represented by differential equations. Replacing a continuous system into discrete time form is always an approximation of the continuous system. The different discretization methods give different digital controller performance. The methods presented on the paper are Step Invariant or Zero Order Hold (ZOH Method, Matched Pole-Zero Method, Backward difference Method and Bilinear transformation. The above mentioned discretization methods are used in developing PI position controller of a dc motor. The motor model was converted by the ZOH method. The performances of the different methods are compared and the results are presented.
Discrete element modeling of ice loads on ship hulls in broken ice fields
Institute of Scientific and Technical Information of China (English)
JI Shunying; LI Zilin; LI Chunhua; SHANG Jie
2013-01-01
Ice loads on a ship hull affect the safety of the hull structure and the ship maneuvering performance in ice-covered regions. A discrete element method (DEM) is used to simulate the interaction between drifting ice floes and a moving ship. The pancake ice floes are modelled with three-dimensional (3-D) dilated disk elements considering the buoyancy, drag force and additional mass induced by the current. The ship hull is modelled with 3D disks with overlaps. Ice loads on the ship hull are determined through the contact detection between ice floe element and ship hull element and the contact force calculation. The influences of different ice conditions (current velocities and directions, ice thicknesses, concentrations and ice floe sizes) and ship speeds are also examined on the dynamic ice force. The simulated results are compared qualitatively well with the existing field data and other numerical results. This work can be helpful in the ship structure design and the navigation security in ice-covered fields.
Institute of Scientific and Technical Information of China (English)
张涛; 刘飞; 赵满全; 刘月琴; 李凤丽; 陈晨; 张勇
2016-01-01
domain of vibration signal is conducted with the MATLAB software. Then the time domain and frequency domain results are taken as input parameters of seed metering device model in discrete element software, and the movement law of maize populations under the condition of vibration is simulated in the field work of no-till planter. Seed suction performance bench test verification is performed with the JPS-12 computer vision test bench and LKD-P type suction electromagnetic vibration table, and the analysis on seed metering performance of air-suction seed metering device is conducted under different operation speed and vibration amplitude. Field vibration signal analysis results show that when the field operation speed of planter increases from 2 to 7 km/h, the frequency of the main vibration power of seed metering device is basically kept at 5, 6 and 7 Hz; the vibration amplitude of the seed metering device shows a linear increase from 2.4 to 7.9 mm. Discrete element method simulation results show that the fitting curve between the maximum speed of corn population in seed room and the forward speed of planter has a fitting determination coefficient (R2) of 0.9671. The fitting straight line between the average speed of corn population and the speed of planter has a fitting determination coefficient (R2) of 0.9325. Bench test results show that the operation speed for good seed metering performance of the air-suction seed metering device is 3-5 km/h, and the good vibration amplitude is 6 mm; the maximum speed range of the population is 0.1203-0.2243 m/s, the population average speed range is 0.0807-0.1413 m/s, the maximum speed range of the population in seed suction area is 0.127-0.26 m/s, and the air-suction seed metering device has a good performance. The results can provide theoretical basis for improving the seed suction performance of air-suction seed metering device of no-tillage planter.%高寒干旱地区免耕地表播种作业时，排种器振动与种群运动
Institute of Scientific and Technical Information of China (English)
刘凡一; 张舰; 李博; 陈军
2016-01-01
In this study, we determined the parameters of wheat required in discrete element method (DEM) simulation by the response surface method. The repose angle is a macroscopic parameter, which is used to describe the friction and flow properties of particle material and widely applied in DEM parameter calibration for it can be measured easily. In this research, the heap of wheat was formed through the bottomless cylinder method and the repose angle was measured using a computer graphic technology. The calibration tests were conducted in laboratory and by simulation using EDEM 2.7.0 software. According to previous research, an acrylic cylinder with an inner diameter of 39 mm and a height of 120 mm was used. The wheat particles were filled into the cylinder using the "rainy method" through a square-opening sieve with 12 mm aperture and lifted with a speed of 0.05 m/s. For DEM simulation, different parameter combination tests were designed. Specifically, the Plackett-Burman test was performed to screen the significant parameters from the 8 selected parameters. It was found that the static friction for wheat-wheat and wheat-acrylic contact and the rolling friction for wheat-wheat contact had a significant effect on the repose angle, while the other 5 parameters' influence was negligible. Then the steepest ascent test was used to determine the optimal value range of the significant parameters. In the steepest ascent test, the 5 non-significant parameters were the mid-value of the corresponding initial region, while the 3 significant parameters increased progressively until the relative errors between the simulated and the test value reached the minimum. Based on the result of the Box-Behnken test, a quadratic polynomial model for the repose angle and the 3 significant parameters was created. The analysis of variance (ANOVA) of the quadratic polynomial model showed that the model was significant and the lack-of-fit was non-significant. This means the model can be used to
An Efficient Approach for Identifying Stable Lobes with Discretization Method
Directory of Open Access Journals (Sweden)
Baohai Wu
2013-01-01
Full Text Available This paper presents a new approach for quick identification of chatter stability lobes with discretization method. Firstly, three different kinds of stability regions are defined: absolute stable region, valid region, and invalid region. Secondly, while identifying the chatter stability lobes, three different regions within the chatter stability lobes are identified with relatively large time intervals. Thirdly, stability boundary within the valid regions is finely calculated to get exact chatter stability lobes. The proposed method only needs to test a small portion of spindle speed and cutting depth set; about 89% computation time is savedcompared with full discretization method. It spends only about10 minutes to get exact chatter stability lobes. Since, based on discretization method, the proposed method can be used for different immersion cutting including low immersion cutting process, the proposed method can be directly implemented in the workshop to promote machining parameters selection efficiency.
Discrete-Roughness-Element-Enhanced Swept-Wing Natural Laminar Flow at High Reynolds Numbers
Malik, Mujeeb; Liao, Wei; Li, Fei; Choudhari, Meelan
2015-01-01
Nonlinear parabolized stability equations and secondary-instability analyses are used to provide a computational assessment of the potential use of the discrete-roughness-element technology for extending swept-wing natural laminar flow at chord Reynolds numbers relevant to transport aircraft. Computations performed for the boundary layer on a natural-laminar-flow airfoil with a leading-edge sweep angle of 34.6 deg, freestream Mach number of 0.75, and chord Reynolds numbers of 17 × 10(exp 6), 24 × 10(exp 6), and 30 × 10(exp 6) suggest that discrete roughness elements could delay laminar-turbulent transition by about 20% when transition is caused by stationary crossflow disturbances. Computations show that the introduction of small-wavelength stationary crossflow disturbances (i.e., discrete roughness element) also suppresses the growth of most amplified traveling crossflow disturbances.
An overset mesh approach for 3D mixed element high-order discretizations
Brazell, Michael J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.
2016-10-01
A parallel high-order Discontinuous Galerkin (DG) method is used to solve the compressible Navier-Stokes equations in an overset mesh framework. The DG solver has many capabilities including: hp-adaption, curved cells, support for hybrid, mixed-element meshes, and moving meshes. Combining these capabilities with overset grids allows the DG solver to be used in problems with bodies in relative motion and in a near-body off-body solver strategy. The overset implementation is constructed to preserve the design accuracy of the baseline DG discretization. Multiple simulations are carried out to validate the accuracy and performance of the overset DG solver. These simulations demonstrate the capability of the high-order DG solver to handle complex geometry and large scale parallel simulations in an overset framework.
Discrete Element Simulation of Elastoplastic Shock Wave Propagation in Spherical Particles
Directory of Open Access Journals (Sweden)
M. Shoaib
2011-01-01
Full Text Available Elastoplastic shock wave propagation in a one-dimensional assembly of spherical metal particles is presented by extending well-established quasistatic compaction models. The compaction process is modeled by a discrete element method while using elastic and plastic loading, elastic unloading, and adhesion at contacts with typical dynamic loading parameters. Of particular interest is to study the development of the elastoplastic shock wave, its propagation, and reflection during entire loading process. Simulation results yield information on contact behavior, velocity, and deformation of particles during dynamic loading. Effects of shock wave propagation on loading parameters are also discussed. The elastoplastic shock propagation in granular material has many practical applications including the high-velocity compaction of particulate material.
Discrete element modeling of inherently anisotropic granular assemblies with polygonal particles
Institute of Scientific and Technical Information of China (English)
Ehsan Seyedi Hosseininia
2012-01-01
In the present article,we study the effect of inherent anisotropy,i.e.,initial bedding angle of particles and associated voids on macroscopic mechanical behavior of granular materials,by numerical simulation of several biaxial compression tests using the discrete element method (DEM).Particle shape is considered to be irregular convex-polygonal.The effect of inherent anisotropy is investigated by following the evolution of mobilized shear strength and volume change during loading.As experimental tests have already shown,numerical simulations also indicate that initial anisotropic condition has a great influence on the strength and deformational behavior of granular assemblies.Comparison of simulations with tests using oval particles,shows that angularity influences both the mobilized shear strength and the volume change regime,which originates from the interlocking resistance between particles.
Discrete element modelling approach to assessment of granular properties in concrete
Institute of Scientific and Technical Information of China (English)
Piet STROEVEN; Huan HE; Martijn STROEVEN
2011-01-01
This paper presents the technological relevance of a concurrent algorithm-based discrete element modelling (DEM)system, HADES. This new system is the successor of SPACE that is limited to spherical grains only. It can realistically simulate the packing of arbitrary-shaped particles up to the fully compacted state. Generation of families of such particles, i.e., generally representing aggregate of fluvial origin and crushed rock, respectively, and the forming way of particulate structure are described.Similarly shaped particles are proposed for simulation of cement paste because of conformity with experimental results obtained by the X-ray tomography method. Technologically relevant territories inside and outside concrete technology are presently explored in this efficient, reliable, and economic way. Some results obtained by this DEM approach are presented.
DEFF Research Database (Denmark)
Hærvig, Jakob; Kleinhans, Ulrich; Wieland, Christoph
2017-01-01
Discrete Element Method (DEM) simulations are a promising approach to accurately predict agglomeration and deposition of micron-sized adhesive particles. However, the mechanistic models in DEM combined with high particle stiffness for most common materials require time step sizes in the order...... particle stiffness to experimental data. Then two well-defined test cases are investigated to show the applicability of the guidelines. When introducing a reduced particle stiffness in DEM simulations by reducing the effective Young's modulus from E to Emod, the surface energy density γ in the adhesive...... is important, the commonly used adhesive rolling resistance torque model proposed by Dominik and Tielens [2,3], Krijt et al. [4] can be used by modifying the contact radius ratio (a/a0)3/2 to (amod/a0,mod)3/2, while keeping the other terms unaltered in the description of the rolling resistance torque Mr...
Institute of Scientific and Technical Information of China (English)
贾富国; 姚丽娜; 韩燕龙; 王会; 史宇菲; 曾勇; 蒋龙伟
2016-01-01
Humidifying evenly is the key to moisture conditioning technology. The uniformity of moisture content depends on the material distribution uniformity. Material uniform plate is the chief work part for increasing the material uniformity, and it has an immediate influence on the follow-up material processing quality and production efficiency. In order to improve the humidifying uniformity in the process of brown rice moisture conditioning, a new type of plate called curved-surface material uniform plate was designed on the basis of existing technology. Combined with the material movement rule on the cone material uniform plate, the parabola was set as the curved generatrix of curved-surface material uniform plate. One of the characteristics of the curved-surface material uniform plate was that it enhanced the uniformity of the material thickness by controlling the floating velocity of the material and offered a favorable condition for uniform humidification of brown rice, and moreover it couldn’t damage brown rice. In this study, on the basis of the theoretical analysis, the working process of the curved-surface material uniform plate was simulated with the discrete element method (DEM), and it was found that the structure parameters and operating conditions of curved-surface refining plate were the key factors affecting its wok performance through the analysis based on the orthogonal design. DEM is a numerical method used for modelling the mechanical behavior of granular materials. Using the EDEM software, the influence laws of the rotation rate of material uniform plate, the curved-surface form and the feeding rateon the material thickness uniformity were simulated and analyzed. According to the performance evaluation indices of evenly distributing material, the structure of curved-surface material uniform plate was optimized. By the response surface analysis method, the mathematical model between each factor and coefficient of variation was established. The
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
RESEARCH METHODS OF LOCATIVE ELEMENT
Directory of Open Access Journals (Sweden)
SULAYMANOVA N.J.
2012-01-01
Full Text Available The article is devoted to the methods of investigation of locative elements. Sentence analysis with locative elements is taken according to the results of component analysis in the system of contradicting – opposition. More over the article is full of examples related to the description of various syntactic units.
Gilev, Konstantin V; Eremina, Elena; Yurkin, Maxim A; Maltsev, Valeri P
2010-03-15
The discrete sources method (DSM) and the discrete dipole approximation (DDA) were compared for simulation of light scattering by a red blood cell (RBC) model. We considered RBCs with diameters up to 8 mum (size parameter up to 38), relative refractive indices 1.03 and 1.06, and two different orientations. The agreement in the angle-resolved S(11) element of the Mueller matrix obtained by these methods is generally good, but it deteriorates with increasing scattering angle, diameter and refractive index of a RBC. Based on the DDA simulations with very fine discretization (up to 93 dipoles per wavelength) for a single RBC, we attributed most of the disagreement to the DSM, which results contain high-frequency ripples. For a single orientation of a RBC the DDA is comparable to or faster than the DSM. However, the relation is reversed when a set of particle orientations need to be simulated at once. Moreover, the DSM requires about an order of magnitude less computer memory. At present, application of the DSM for massive calculation of light scattering patterns of RBCs is hampered by its limitations in size parameter of a RBC due to the high number of harmonics used for calculations.
Discrete gradient methods for solving variational image regularisation models
Grimm, V.; McLachlan, Robert I.; McLaren, David I.; Quispel, G. R. W.; Schönlieb, C.-B.
2017-07-01
Discrete gradient methods are well-known methods of geometric numerical integration, which preserve the dissipation of gradient systems. In this paper we show that this property of discrete gradient methods can be interesting in the context of variational models for image processing, that is where the processed image is computed as a minimiser of an energy functional. Numerical schemes for computing minimisers of such energies are desired to inherit the dissipative property of the gradient system associated to the energy and consequently guarantee a monotonic decrease of the energy along iterations, avoiding situations in which more computational work might lead to less optimal solutions. Under appropriate smoothness assumptions on the energy functional we prove that discrete gradient methods guarantee a monotonic decrease of the energy towards stationary states, and we promote their use in image processing by exhibiting experiments with convex and non-convex variational models for image deblurring, denoising, and inpainting.
Digital functions and data reconstruction digital-discrete methods
Chen, Li M
2012-01-01
Digital Functions and Data Reconstruction: Digital-Discrete Methods provides a solid foundation to the theory of digital functions and its applications to image data analysis, digital object deformation, and data reconstruction. This new method has a unique feature in that it is mainly built on discrete mathematics with connections to classical methods in mathematics and computer sciences. Digitally continuous functions and gradually varied functions were developed in the late 1980s. A. Rosenfeld (1986) proposed digitally continuous functions for digital image analysis, especially to describe
The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil
Meade, Andrew J., Jr.
1992-01-01
A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.
An innovative lossless compression method for discrete-color images.
Alzahir, Saif; Borici, Arber
2015-01-01
In this paper, we present an innovative method for lossless compression of discrete-color images, such as map images, graphics, GIS, as well as binary images. This method comprises two main components. The first is a fixed-size codebook encompassing 8×8 bit blocks of two-tone data along with their corresponding Huffman codes and their relative probabilities of occurrence. The probabilities were obtained from a very large set of discrete color images which are also used for arithmetic coding. The second component is the row-column reduction coding, which will encode those blocks that are not in the codebook. The proposed method has been successfully applied on two major image categories: 1) images with a predetermined number of discrete colors, such as digital maps, graphs, and GIS images and 2) binary images. The results show that our method compresses images from both categories (discrete color and binary images) with 90% in most case and higher than the JBIG-2 by 5%-20% for binary images, and by 2%-6.3% for discrete color images on average.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
2015-05-01
We derive a numerical method for Darcy flow, and also for Poisson's equation in mixed (first order) form, based on discrete exterior calculus (DEC). Exterior calculus is a generalization of vector calculus to smooth manifolds and DEC is one of its discretizations on simplicial complexes such as triangle and tetrahedral meshes. DEC is a coordinate invariant discretization, in that it does not depend on the embedding of the simplices or the whole mesh. We start by rewriting the governing equations of Darcy flow using the language of exterior calculus. This yields a formulation in terms of flux differential form and pressure. The numerical method is then derived by using the framework provided by DEC for discretizing differential forms and operators that act on forms. We also develop a discretization for a spatially dependent Hodge star that varies with the permeability of the medium. This also allows us to address discontinuous permeability. The matrix representation for our discrete non-homogeneous Hodge star is diagonal, with positive diagonal entries. The resulting linear system of equations for flux and pressure are saddle type, with a diagonal matrix as the top left block. The performance of the proposed numerical method is illustrated on many standard test problems. These include patch tests in two and three dimensions, comparison with analytically known solutions in two dimensions, layered medium with alternating permeability values, and a test with a change in permeability along the flow direction. We also show numerical evidence of convergence of the flux and the pressure. A convergence experiment is included for Darcy flow on a surface. A short introduction to the relevant parts of smooth and discrete exterior calculus is included in this article. We also include a discussion of the boundary condition in terms of exterior calculus.
Finite-element discretization of 3D energy-transport equations for semiconductors
Energy Technology Data Exchange (ETDEWEB)
Gadau, Stephan
2007-07-01
In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Institute of Scientific and Technical Information of China (English)
ZHANG Xiang-wei; TAKEUCHI Kuniyoshi; CHEN Jing
2007-01-01
In this article, the finite element solution of quasi-three-dimensional (quasi-3-D) groundwater flow was mathematically analyzed. The research shows that the spurious oscillation solution to the Finite Element Model (FEM) is the results choosing the small time step or the large element size L and using the non-diagonal storage matrix. The mechanism for this phenomenon is explained by the negative weighting factor of implicit part in the discretized equations. To avoid spurious oscillation solution, the criteria on the selection of and L for quasi-3-D groundwater flow simulations were identified. An application example of quasi-3-D groundwater flow simulation was presented to verify the criteria. The results indicate that temporal discretization scale has significant impact on the spurious oscillations in the finite-element solutions, and the spurious oscillations can be avoided in solving practical quasi-3-D groundwater flow problems if the criteria are satisfied.
Discrete element study of granulation in a spout-fluidized bed
Link, J.M.; Godlieb, W.; Deen, N.G.; Kuipers, J.A.M.
2007-01-01
In this work a discrete element model (DEM) is presented for the description of the gas–liquid–solid flow in a spout-fluidized bed including all relevant phenomena for the study of granulation. The model is demonstrated for the case of a granulation process in a flat spout-fluidized bed, containing
On Some Versions of the Element Agglomeration AMGe Method
Energy Technology Data Exchange (ETDEWEB)
Lashuk, I; Vassilevski, P
2007-08-09
The present paper deals with element-based AMG methods that target linear systems of equations coming from finite element discretizations of elliptic PDEs. The individual element information (element matrices and element topology) is the main input to construct the AMG hierarchy. We study a number of variants of the spectral agglomerate element based AMG method. The core of the algorithms relies on element agglomeration utilizing the element topology (built recursively from fine to coarse levels). The actual selection of the coarse degrees of freedom (dofs) is based on solving large number of local eigenvalue problems. Additionally, we investigate strategies for adaptive AMG as well as multigrid cycles that are more expensive than the V-cycle utilizing simple interpolation matrices and nested conjugate gradient (CG) based recursive calls between the levels. The presented algorithms are illustrated with an extensive set of experiments based on a matlab implementation of the methods.
Institute of Scientific and Technical Information of China (English)
ZHANG; Lei; WEI; Zuoan; LIU; Xiaoyu; LI; Shihai
2005-01-01
Three-dimensional discrete element face-to-face contact model with fissure water pressure is established in this paper and the model is used to simulate three-stage process of landslide under fissure water pressure in the opencast mine, according to the actual state of landslide in Panluo iron mine where landslide happened in 1990 and was fathered in 1999. The calculation results show that fissure water pressure on the sliding surface is the main reason causing landslide and the local soft interlayer weakens the stability of slope. If the discrete element method adopts the same assumption as the limit equilibrium method, the results of two methods are in good agreement; while if the assumption is not adopted in the discrete element method, the critical φ numerically calculated is less than the one calculated by use of the limit equilibrium method for the sameC. Thus, from an engineering point of view, the result from the discrete element model simulation is safer and has more widely application since the discrete element model takes into account the effect of rock mass structures.
A Fully Discrete Galerkin Method for a Nonlinear Space-Fractional Diffusion Equation
Directory of Open Access Journals (Sweden)
Yunying Zheng
2011-01-01
Full Text Available The spatial transport process in fractal media is generally anomalous. The space-fractional advection-diffusion equation can be used to characterize such a process. In this paper, a fully discrete scheme is given for a type of nonlinear space-fractional anomalous advection-diffusion equation. In the spatial direction, we use the finite element method, and in the temporal direction, we use the modified Crank-Nicolson approximation. Here the fractional derivative indicates the Caputo derivative. The error estimate for the fully discrete scheme is derived. And the numerical examples are also included which are in line with the theoretical analysis.
Multilevel Fast Multipole Method for Higher Order Discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik;
2014-01-01
The multi-level fast multipole method (MLFMM) for a higher order (HO) discretization is demonstrated on high-frequency (HF) problems, illustrating for the first time how an efficient MLFMM for HO can be achieved even for very large groups. Applying several novel ideas, beneficial to both lower or...
Improved Multilevel Fast Multipole Method for Higher-Order discretizations
DEFF Research Database (Denmark)
Borries, Oscar Peter; Meincke, Peter; Jorgensen, Erik
2014-01-01
The Multilevel Fast Multipole Method (MLFMM) allows for a reduced computational complexity when solving electromagnetic scattering problems. Combining this with the reduced number of unknowns provided by Higher-Order discretizations has proven to be a difficult task, with the general conclusion b...
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
DMTO – a method for Discrete Material and Thickness Optimization of laminated composite structures
DEFF Research Database (Denmark)
Sørensen, Søren Nørgaard; Sørensen, Rene; Lund, Erik
2014-01-01
are optimized simultaneously through interpolation functions with penalization. Numerical results for several parameterizations of a finite element model of a generic main spar from a wind turbine blade are presented. The different parameterizations represent different levels of complexity with respect......This paper presents a gradient based topology optimization method for Discrete Material and Thickness Optimization of laminated composite structures, labelled the DMTOmethod. The capabilities of the proposed method are demonstrated on mass minimization, subject to constraints on the structural...
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Application of network methods for understanding evolutionary dynamics in discrete habitats.
Greenbaum, Gili; Fefferman, Nina H
2017-02-16
In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population genetics literature; however, these models have usually addressed relatively simple settings of habitable patches, and have stopped short of providing general methodologies for addressing non-trivial gene flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modeling gene flow between habitat patches using networks. Here we present the idea and concepts of modeling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network-theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. This article is protected by copyright. All rights reserved.
Matsuyama, Eri; Tsai, Du-Yih; Lee, Yongbum; Takahashi, Noriyuki
2013-01-01
The purpose of this study was to evaluate the performance of a conventional discrete wavelet transform (DWT) method and a modified undecimated discrete wavelet transform (M-UDWT) method applied to mammographic image denoising. Mutual information, mean square error, and signal to noise ratio were used as image quality measures of images processed by the two methods. We examined the performance of the two methods with visual perceptual evaluation. A two-tailed F test was used to measure statistical significance. The difference between the M-UDWT processed images and the conventional DWT-method processed images was statistically significant (P<0.01). The authors confirmed the superiority and effectiveness of the M-UDWT method. The results of this study suggest the M-UDWT method may provide better image quality as compared to the conventional DWT.
Calibration of Discrete Element Heat Transfer Parameters by Central Composite Design
Deng, Zongquan; Cui, Jinsheng; Hou, Xuyan; Jiang, Shengyuan
2017-03-01
The efficiency and precision of parameter calibration in discrete element method (DEM) are not satisfactory, and parameter calibration for granular heat transfer is rarely involved. Accordingly, parameter calibration for granular heat transfer with the DEM is studied. The heat transfer in granular assemblies is simulated with DEM, and the effective thermal conductivity (ETC) of these granular assemblies is measured with the transient method in simulations. The measurement testbed is designed to test the ETC of the granular assemblies under normal pressure and a vacuum based on the steady method. Central composite design (CCD) is used to simulate the impact of the DEM parameters on the ETC of granular assemblies, and the heat transfer parameters are calibrated and compared with experimental data. The results show that, within the scope of the considered parameters, the ETC of the granular assemblies increases with an increasing particle thermal conductivity and decreases with an increasing particle shear modulus and particle diameter. The particle thermal conductivity has the greatest impact on the ETC of granular assemblies followed by the particle shear modulus and then the particle diameter. The calibration results show good agreement with the experimental results. The error is less than 4%, which is within a reasonable range for the scope of the CCD parameters. The proposed research provides high efficiency and high accuracy parameter calibration for granular heat transfer in DEM.
Surface processing methods for point sets using finite elements
Clarenz, Ulrich; Rumpf, Martin; Telea, Alexandru
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs
A Geometrical Approach to the Boundary Element Method
Auchmann, B; Rjasanow, S
2008-01-01
We introduce a geometric formulation of the boundary element method (BEM), using concepts of the discrete electromagnetic theory. Geometric BEM is closely related to Galerkin-BEM and to the generalized collocation scheme. It is easy to implement, accurate, and computationally efficient. We validate our approach with 2-D examples and give an outlook to 3-D results.
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
Anssari-Benam, Afshin; Bucchi, Andrea; Bader, Dan L
2015-09-18
Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues. Copyright © 2015 Elsevier Ltd. All rights reserved.
CASCADIC MULTIGRID METHODS FOR MORTAR WILSON FINITE ELEMENT METHODS ON PLANAR LINEAR ELASTICITY
Institute of Scientific and Technical Information of China (English)
陈文斌; 汪艳秋
2003-01-01
Cascadic multigrid technique for mortar Wilson finite element method ofhomogeneous boundary value planar linear elasticity is described and analyzed. Firstthe mortar Wilson finite element method for planar linear elasticity will be analyzed,and the error estimate under L2 and H1 norm is optimal. Then a cascadic multigridmethod for the mortar finite element discrete problem is described. Suitable grid trans-fer operator and smoother are developed which lead to an optimal cascadic multigridmethod. Finally, the computational results are presented.
Energy Technology Data Exchange (ETDEWEB)
Herrmann, K.P. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik; Mueller, W.H. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mechanical and Chemical Engineering; Neumann, S. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik
2001-07-01
The objective of our contribution is to present the discrete Fouriertransformation (DFT) as a serious alternative for the numerical computation of local stresses and strains in a two dimensional representative volume element (RVE) containing heterogeneities of complex shape and high volume fractions. The methodology is based on the application of the so-called ''equivalent inclusion method'' (Mura 1987). This method is used to devolve the original problem onto the determination of an auxiliary strain field which is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. The resulting partial differential equations (PDE) are firstly approximated by difference schemes leading to a linear system of equations (LSE) to solve. Two different types of difference schemes for an approximation are presented, a 9-pixelstar which is well-known in this context and a new one which uses 21 pixel for the numerical approach in order to increase the quality of the numerical solution. In a second step the DFT has been used which allows to solve the LSE analytically, obtaining a functional relation for the auxiliary strain field. Finally the solution of this equation is determined approximately by virtue of a Neumann iteration procedure. Different heterogeneity problems are considered where the accuracy of both difference stars is checked by existing analytical solutions. (orig.)
Discrete element simulation of charging and mixed layer formation in the ironmaking blast furnace
Mitra, Tamoghna; Saxén, Henrik
2016-11-01
The burden distribution in the ironmaking blast furnace plays an important role for the operation as it affects the gas flow distribution, heat and mass transfer, and chemical reactions in the shaft. This work studies certain aspects of burden distribution by small-scale experiments and numerical simulation by the discrete element method (DEM). Particular attention is focused on the complex layer-formation process and the problems associated with estimating the burden layer distribution by burden profile measurements. The formation of mixed layers is studied, and a computational method for estimating the extent of the mixed layer, as well as its voidage, is proposed and applied on the results of the DEM simulations. In studying a charging program and its resulting burden distribution, the mixed layers of coke and pellets were found to show lower voidage than the individual burden layers. The dynamic evolution of the mixed layer during the charging process is also analyzed. The results of the study can be used to gain deeper insight into the complex charging process of the blast furnace, which is useful in the design of new charging programs and for mathematical models that do not consider the full behavior of the particles in the burden layers.
Discrete-element model for the interaction between ocean waves and sea ice.
Xu, Zhijie; Tartakovsky, Alexandre M; Pan, Wenxiao
2012-01-01
We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds α increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.
Dry granular avalanche down a flume: Choice of discrete element simulation parameters
Yang, F.-L.; Chang, W. T.; Huang, Y. T.; Hsieh, S. H.; Chen, C. S.
2013-12-01
This paper presents a method to assign soft-sphere contact model parameters in a discrete-element simulation with which we can reproduce the experimentally measured avalanche dynamics of finite dry granular mass down a flume. We adopt the simplest linear model in which interaction force is decomposed along or tangent to the contact normal. The model parameters are chosen uniquely to satisfy theoretical models or to meet experimental evidences at either the particle or the bulk size level. The normal mode parameters are chosen specifically to ensure Hertzian contact time (but not its force-displacement history) and the resulting loss of particle kinetic energy, characterized by a measured coefficient of restitution, for each pair of colliding surfaces. We follow the literature to assign the tangential spring constant according to an elasticity model but propose a method to assign the friction coefficient using a measured bulk property that characterizes the bulk discharge volume flow rate. The linear contact model with the assigned parameters are evaluated by comparing the simulated bulk avalanche dynamics down three slopes to the experimental data, including instantaneous particle trajectories and bulk unsteady velocity profile. Satisfying quantitative agreement can be obtained except at the free surface and the early-time front propagation velocity.
Monteiro, André O.
2013-09-25
The mechanical response to a uniaxial compressive force of a single carbon nanotube (CNT) filled (or partially-filled) with ZnS has been modelled. A semi-empirical approach based on the finite element method was used whereby modelling outcomes were closely matched to experimental observations. This is the first example of the use of the continuum approach to model the mechanical behaviour of discrete filled CNTs. In contrast to more computationally demanding methods such as density functional theory or molecular dynamics, our approach provides a viable and expedite alternative to model the mechanics of filled multi-walled CNTs. © 2013 Springer Science+Business Media New York.
Chebyshev-Legendre method for discretizing optimal control problems
Institute of Scientific and Technical Information of China (English)
ZHANG Wen; MA He-ping
2009-01-01
In this paper, a numerical method for solving the optimal control (OC) problems is presented. The method is enlightened by the Chebyshev-Legendre (CL) method for solving the partial differential equations (PDEs). The Legen-dre expansions are used to approximate both the control and the state functions. The constraints are discretized over the Chebyshev-Gauss-Lobatto (CGL) collocation points. A Legendre technique is used to approximate the integral involved in the performance index. The OC problem is changed into an equivalent nonlinear programming problem which is directly solved. The fast Legendre transform is employed to reduce the computation time. Several further illustrative examples demonstrate the efficiency of the proposed method.
A lumped mass finite element method for vibration analysis of elastic plate-plate structures
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The fully discrete lumped mass finite element method is proposed for vibration analysis of elastic plate-plate structures.In the space directions,the longitudinal displacements on plates are discretized by conforming linear elements,and the transverse displacements are discretized by the Morley element.By means of the second order central difference for discretizing the time derivative and the technique of lumped masses,a fully discrete lumped mass finite element method is obtained,and two approaches to choosing the initial functions are also introduced.The error analysis for the method in the energy norm is established,and some numerical examples are included to validate the theoretical analysis.
The continuum discretized coupled-channels method and its applications
Yahiro, Masanobu; Matsumoto, Takuma; Minomo, Kosho
2012-01-01
This is a review on recent developments of the continuum discretized coupled-channels method (CDCC) and its applications to nuclear physics, cosmology and astrophysics, and nuclear engineering. The theoretical foundation of CDCC is shown, and a microscopic reaction theory for nucleus-nucleus scattering is constructed as an underlying theory of CDCC. CDCC is then extended to treat Coulomb breakup and four-body breakup. We also propose a new theory that makes CDCC applicable to inclusive reactions
Discrete Direct Methods in the Fractional Calculus of Variations
Pooseh, Shakoor; Almeida, Ricardo; Torres, Delfim F. M.
2012-01-01
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends on the left Riemann– Liouville fractional derivative. Using the Gr¨unwald–Letnikov definition, we approximate the objective functional in...
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Selective Smoothed Finite Element Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
Sun, Zhuang; Espinoza, D. Nicolas; Balhoff, Matthew T.
2016-11-01
During CO2 injection into geological formations, petrophysical and geomechanical properties of host formations can be altered due to mineral dissolution and precipitation. Field and laboratory results have shown that sandstone and siltstone can be altered by CO2-water mixtures, but few quantitative studies have been performed to fully investigate underlying mechanisms. Based on the hypothesis that CO2-water mixtures alter the integrity of rock structure by attacking cements rather than grains, we attempt to explain the degradation of cementation due to long-term contact with CO2 and water and mechanisms for changes in rock mechanical properties. Many sandstones, including calcite-cemented quartzitic sandstone, chlorite-cemented quartzitic sandstone, and hematite-cemented quartzitic sandstone, contain interparticle cements that are more readily affected by CO2-water mixtures than grains. A model that couples the discrete element method and the bonded-particle model is used to perform simulations of indentation tests on synthetic rocks with crystal and random packings. The model is verified against the analytical cavity expansion model and validated against laboratory indentation tests on Entrada sandstone with and without CO2 alteration. Sensitivity analysis is performed for cementation microscopic parameters including stiffness, size, axial, and shear strength. The simulation results indicate that the CO2-related degradation of mechanical properties in bleached Entrada sandstone can be attributed to the reduction of cement size rather than cement strength. Our study indicates that it is possible to describe the CO2-related rock alteration through particle-scale mechanisms.
Yan, Zilin; Wilkinson, Sam K; Stitt, Edmund H; Marigo, Michele
2016-11-20
Mixing and segregation in a Freeman FT4 powder rheometer, using binary mixtures with varied particle size ratio and volume fraction, were studied using the Discrete Element Method (DEM). As the blade moves within the particle bed, size induced segregations can occur via a sifting mechanism. A larger particle size ratio and/or a larger volume fraction of large particles lead to a quicker segregation process. A higher particle velocity magnitude can promote the segregation process and the rate for the segregation index increases in the radial direction: from the centre towards the outer layer. In the current DEM simulations, it is shown that the change in flow energy associated with segregation and mixing depends on the choice of frictional input parameters. FT4 is proposed as a potential tool to compare and rank the segregation tendency for particulate materials with distinct differences in flow energy of each component. This is achieved by measuring the flow energy gradient after a number of test cycles for mixing powders with different flow properties. Employing the FT4 dynamic powder characterisation can be advantageous to establish blending performances in an industrial context.
Yushi, Zou; Xinfang, Ma; Tong, Zhou; Ning, Li; Ming, Chen; Sihai, Li; Yinuo, Zhang; Han, Li
2017-09-01
Hydraulic fracture (HF) height containment tends to occur in layered formations, and it significantly influences the entire HF geometry or the stimulated reservoir volume. This study aims to explore the influence of preexisting bedding planes (BPs) on the HF height growth in layered formations. Laboratory fracturing experiments were performed to confirm the occurrence of HF height containment in natural shale that contains multiple weak and high-permeability BPs under triaxial stresses. Numerical simulations were then conducted to further illustrate the manner in which vertical stress, BP permeability, BP density(or spacing), pump rate, and fluid viscosity control HF height growth using a 3D discrete element method-based fracturing model. In this model, the rock matrix was considered transversely isotropic and multiple BPs can be explicitly represented. Experimental and numerical results show that the vertically growing HF tends to be limited by multi-high-permeability BPs, even under higher vertical stress. When the vertically growing HF intersects with the multi-high-permeability BPs, the injection pressure will be sharply reduced. If a low pumping rate or a low-viscosity fluid is used, the excess fracturing fluid leak-off into the BPs obviously decreases the rate of pressure build up, which will then limit the growth of HF. Otherwise, a higher pumping rate and/or a higher viscosity will reduce the leak-off time and fluid volume, but increase the injection pressure to drive the HF to grow and to penetrate through the BPs.
Discrete element modeling of sand behavior in a biaxial shear test
Institute of Scientific and Technical Information of China (English)
Zhi-yi HUANG; Zhong-xuan YANG; Zhen-yu WANG
2008-01-01
The mechanical behavior of sand is very complex,and depends on factors including confining pressure,density,and drainage condition.A soil mass Call be contractive or dilative when subjected to shear loading,and eventually reaches an ultimate state,referred to as the critical state in soil mechanics.Conventional approach to explore the mechanical behavior of sand mainly relies on the experimental tests in laboratory.This paper gives an alternative view to this subject using discrete element method (DEM),which has attracted much attention in recent years.The implementation of the DEM is carried out by a series of numerical tests on granular assemblies with varying initial densities and confining pressures,under different test configurations.The results demonstrate that such numerical simulations can produce correct responses of the sand behavior in general,including the critical state response,as compared to experimental observations.In addition,the DEM can further provide details of the microstructure evolutions during shearing processes,and the resulting induced anisotropy can be fully captured and quantified in the particle scale.
A discrete element based simulation framework to investigate particulate spray deposition processes
Mukherjee, Debanjan
2015-06-01
© 2015 Elsevier Inc. This work presents a computer simulation framework based on discrete element method to analyze manufacturing processes that comprise a loosely flowing stream of particles in a carrier fluid being deposited on a target surface. The individual particulate dynamics under the combined action of particle collisions, fluid-particle interactions, particle-surface contact and adhesive interactions is simulated, and aggregated to obtain global system behavior. A model for deposition which incorporates the effect of surface energy, impact velocity and particle size, is developed. The fluid-particle interaction is modeled using appropriate spray nozzle gas velocity distributions and a one-way coupling between the phases. It is found that the particle response times and the release velocity distribution of particles have a combined effect on inter-particle collisions during the flow along the spray. It is also found that resolution of the particulate collisions close to the target surface plays an important role in characterizing the trends in the deposit pattern. Analysis of the deposit pattern using metrics defined from the particle distribution on the target surface is provided to characterize the deposition efficiency, deposit size, and scatter due to collisions.
New numerical analysis method in computational mechanics: composite element method
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF's description after discretizing the structure, i.e. the nodal coordinate system UFEM(ξ) for employing the conventional FEM, and the field coordinate system UCT(ξ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ξ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
New numerical analysis method in computational mechanics: composite element method
Institute of Scientific and Technical Information of China (English)
曾攀
2000-01-01
A new type of FEM, called CEM (composite element method), is proposed to solve the static and dynamic problems of engineering structures with high accuracy and efficiency. The core of this method is to define two sets of coordinate systems for DOF’ s description after discretizing the structure, i.e. the nodal coordinate system UFEM(ζ) for employing the conventional FEM, and the field coordinate system UCT(ζ) for utilizing classical theory. Then, coupling these two sets of functional expressions could obtain the composite displacement field U(ζ) of CEM. The computations of the stiffness and mass matrices can follow the conventional procedure of FEM. Since the CEM inherents some good properties of the conventional FEM and classical analytical method, it has the powerful versatility to various complex geometric shapes and excellent approximation. Many examples are presented to demonstrate the ability of CEM.
Optimization of Zoom Lens with Discrete State of Liquid Lens Elements by Using Genetic Algorithm
Directory of Open Access Journals (Sweden)
Cheng-Mu Tsai
2015-01-01
Full Text Available This paper is to employ liquid lens elements to design a lens with zoom function by using the genetic algorithm (GA optimization. The liquid lens elements used in the proposal can apply voltage adjustment to generate the electrical field that induces the liquid with electric conductivity to vary the surface curvature between two different kinds of liquids. According to the voltage level, the liquid lens element makes the discrete variation of the curvature and thickness realize the zoom function without moving the lens groups so that the overall length can be reduced. However, it is difficult to design the zoom lens under the discrete variation of the curvature and thickness in the liquid lens elements and the mechanical space that is constantly limited. The GA offers a flexible way for lens optimization. We regarded the spot size as the fitness function to look for the optimum curvatures, thickness, and the corresponding statuses of liquid lens elements for the zoom lens. As a result, the zoom lens with constant space can be realized by running the selection, crossover, and mutation operation in the GA optimization.
Korneev, V. G.
2012-09-01
BPS is a well known an efficient and rather general domain decomposition Dirichlet-Dirichlet type preconditioner, suggested in the famous series of papers Bramble, Pasciak and Schatz (1986-1989). Since then, it has been serving as the origin for the whole family of domain decomposition Dirichlet-Dirichlet type preconditioners-solvers as for h so hp discretizations of elliptic problems. For its original version, designed for h discretizations, the named authors proved the bound O(1 + log2 H/ h) for the relative condition number under some restricting conditions on the domain decomposition and finite element discretization. Here H/ h is the maximal relation of the characteristic size H of a decomposition subdomain to the mesh parameter h of its discretization. It was assumed that subdomains are images of the reference unite cube by trilinear mappings. Later similar bounds related to h discretizations were proved for more general domain decompositions, defined by means of coarse tetrahedral meshes. These results, accompanied by the development of some special tools of analysis aimed at such type of decompositions, were summarized in the book of Toselli and Widlund (2005). This paper is also confined to h discretizations. We further expand the range of admissible domain decompositions for constructing BPS preconditioners, in which decomposition subdomains can be convex polyhedrons, satisfying some conditions of shape regularity. We prove the bound for the relative condition number with the same dependence on H/ h as in the bound given above. Along the way to this result, we simplify the proof of the so called abstract bound for the relative condition number of the domain decomposition preconditioner. In the part, related to the analysis of the interface sub-problem preconditioning, our technical tools are generalization of those used by Bramble, Pasciak and Schatz.
Kovács, M; Lindgren, F
2012-01-01
We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation.
Boutt, D. F.; McPherson, B. J.
2001-12-01
The micromechanics of sedimentary rock deformation are a fundamental aspect of many research fields, ranging from geotechnical engineering to petroleum recovery and hazardous waste disposal. Laboratory triaxial tests yield information concerning macroscopic behaviors but are not capable of quantifying micromechanical processes such as microcracking and localization. Thus, to quantify micromechanical processes we employed the discrete element method (DEM) of rock deformation, calibrated with triaxial test results. This DEM simulates rock using rigid disc shaped particles bonded at contacts between particles. Previous studies demonstrated that this type of DEM can qualitatively and quantitatively mimic macroscopic behaviors of triaxial tests. An important conclusion of these studies is that a number of particles must be bonded together with higher bond strengths than the surrounding particles to achieve a steeper strength envelope of rocks. This process, termed clustering, is the focus of this study. We hypothesize that since clusters posses a more complicated geometry, they may increase failure strength at elevated confining pressures by interlocking and creating a higher apparent friction. An alternative hypothesis is that the clusters change force chain development by allowing chains to persist longer in specimens. This ultimately causes failure to occur at higher strengths compared to unclustered material. A systematic study comparing effects of cluster shape, particle friction, and force chain development was undertaken. Several model simulations with various cluster shapes and sizes were compared with each other as well as single particle models with high friction coefficients (>1). Preliminary results suggest that the organization of the particle clusters play a key role in increasing the strength envelope. Particle friction coefficients needed to increase slopes of the strength envelopes are well beyond those of geological materials measured in the laboratory
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
A Nuclear Reactor Transient Methodology Based on Discrete Ordinates Method
Directory of Open Access Journals (Sweden)
Shun Zhang
2014-01-01
Full Text Available With the rapid development of nuclear power industry, simulating and analyzing the reactor transient are of great significance for the nuclear safety. The traditional diffusion theory is not suitable for small volume or strong absorption problem. In this paper, we have studied the application of discrete ordinates method in the numerical solution of space-time kinetics equation. The fully implicit time integration was applied and the precursor equations were solved by analytical method. In order to improve efficiency of the transport theory, we also adopted some advanced acceleration methods. Numerical results of the TWIGL benchmark problem presented demonstrate the accuracy and efficiency of this methodology.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Discontinuous finite element method for vector radiative transfer
Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping
2017-03-01
The discontinuous finite element method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into finite non-overlapped discontinuous elements. The elements in the whole solution domain are connected by modelling the boundary numerical flux between adjacent elements, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.
Institute of Scientific and Technical Information of China (English)
Habib Ammari; Gang Bao
2008-01-01
Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.
Institute of Scientific and Technical Information of China (English)
Dongyang Shi; Haihong Wang; Yuepeng Du
2009-01-01
An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.
Casas, Guillermo; Mukherjee, Debanjan; Celigueta, Miguel Angel; Zohdi, Tarek I.; Onate, Eugenio
2015-11-01
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Casas, Guillermo; Mukherjee, Debanjan; Celigueta, Miguel Angel; Zohdi, Tarek I.; Onate, Eugenio
2017-04-01
A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.
Discrete element modeling approach to porosimetry for durability risk estimation of concrete
Stroeven, P.; Le, N.L.B.; Stroeven, M.; Sluys, L.J.
2011-01-01
The paper introduces a novel approach to porosimetry in virtual concrete, denoted as random node structuring (RNS). The fresh state of this particulate material is produced by the DEM system HADES. Hydration simulation is a hybrid approach making use of wellknown discretization and vector methods. P
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems
Knabner, Peter; Summ, Gerhard
2016-01-01
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixe...
Directory of Open Access Journals (Sweden)
Ji Wei
2010-10-01
Full Text Available Abstract Background Microarray data discretization is a basic preprocess for many algorithms of gene regulatory network inference. Some common discretization methods in informatics are used to discretize microarray data. Selection of the discretization method is often arbitrary and no systematic comparison of different discretization has been conducted, in the context of gene regulatory network inference from time series gene expression data. Results In this study, we propose a new discretization method "bikmeans", and compare its performance with four other widely-used discretization methods using different datasets, modeling algorithms and number of intervals. Sensitivities, specificities and total accuracies were calculated and statistical analysis was carried out. Bikmeans method always gave high total accuracies. Conclusions Our results indicate that proper discretization methods can consistently improve gene regulatory network inference independent of network modeling algorithms and datasets. Our new method, bikmeans, resulted in significant better total accuracies than other methods.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The soil plug phenomenon involving the rising of the surface soil inside the bucket chamber under the suction pressure and seepage forces was simulated and calculated by deformable discrete element method (DDEM) models. The seepage forces, the effective gravity of soil, the friction on the chamber wall and the suction inside the chamber are considered as the main external forces of DDEM specimen. Three typical types of soil (silty clay, silt and sand) in the Bohai Sea are set as the main environmental conditions in the formation process of soil plug. It is found that the heights of soil plug simulated by DDEM models are 161.85 mm in silty clay, 125.22 mm in silt and 167.56 mm in sand, which are close to model test results and higher than those estimated by discrete element method (DEM). DDEM is an effective method to estimate and predict the heights of soil plug before suction penetration of bucket foundations on site.
Description of Four-Body Breakup Reaction with the Method of Continuum-Discretized Coupled-Channels
Egami, Tomoaki; Ogata, Kazuyuki; Yahiro, Masanobu
2008-01-01
We present a method for smoothing discrete breakup $S$-matrix elements calculated by the method of continuum-discretized coupled-channels (CDCC). This smoothing method makes it possible to apply CDCC to four-body breakup reactions. The reliability of the smoothing method is confirmed for two cases, $^{58}$Ni($d$, $p n$) at 80 MeV and the $E1$ transition of $^6$He. We apply CDCC with the smoothing method to $^6$He breakup reaction at 22.5 MeV. Multi-step breakup processes are found to be important.
Energy Technology Data Exchange (ETDEWEB)
Svyatskiy, Daniil [Los Alamos National Laboratory; Shashkov, Mikhail [Los Alamos National Laboratory; Kuzmin, D [DORTMUND UNIV
2008-01-01
A new approach to the design of constrained finite element approximations to second-order elliptic problems is introduced. This approach guarantees that the finite element solution satisfies the discrete maximum principle (DMP). To enforce these monotonicity constrains the sufficient conditions for elements of the stiffness matrix are formulated. An algebraic splitting of the stiffness matrix is employed to separate the contributions of diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L{sub 2} projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.
Constructing exact solutions to discrete systems with the trial function method
Institute of Scientific and Technical Information of China (English)
Taogetusang Sirendaoerji
2008-01-01
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear (2+1) dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.
Energy Technology Data Exchange (ETDEWEB)
Yu, Dequan [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Cong, Shu-Lin, E-mail: shlcong@dlut.edu.cn [School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024 (China); Sun, Zhigang, E-mail: zsun@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023 (China); Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technology, University of Science and Technology of China, 96 Jinzhai Road, Hefei 230026 (China)
2015-09-08
Highlights: • An optimised finite element discrete variable representation method is proposed. • The method is tested by solving one and two dimensional Schrödinger equations. • The method is quite efficient in solving the molecular Schrödinger equation. • It is very easy to generalise the method to multidimensional problems. - Abstract: The Lobatto discrete variable representation (LDVR) proposed by Manoloupolos and Wyatt (1988) has unique features but has not been generally applied in the field of chemical dynamics. Instead, it has popular application in solving atomic physics problems, in combining with the finite element method (FE-DVR), due to its inherent abilities for treating the Coulomb singularity in spherical coordinates. In this work, an efficient phase optimisation and variable mapping procedure is proposed to improve the grid efficiency of the LDVR/FE-DVR method, which makes it not only be competing with the popular DVR methods, such as the Sinc-DVR, but also keep its advantages for treating with the Coulomb singularity. The method is illustrated by calculations for one-dimensional Coulomb potential, and the vibrational states of one-dimensional Morse potential, two-dimensional Morse potential and two-dimensional Henon–Heiles potential, which prove the efficiency of the proposed scheme and promise more general applications of the LDVR/FE-DVR method.
Method of securing filter elements
Energy Technology Data Exchange (ETDEWEB)
Brown, Erik P.; Haslam, Jeffery L.; Mitchell, Mark A.
2016-10-04
A filter securing system including a filter unit body housing; at least one tubular filter element positioned in the filter unit body housing, the tubular filter element having a closed top and an open bottom; a dimple in either the filter unit body housing or the top of the tubular filter element; and a socket in either the filter unit body housing or the top of the tubular filter element that receives the dimple in either the filter unit body housing or the top of the tubular filter element to secure the tubular filter element to the filter unit body housing.
A TWO-SCALE HIGHER-ORDER FINITE ELEMENT DISCRETIZATION FOR SCHRODINGER EQUATION
Institute of Scientific and Technical Information of China (English)
Huajie Chen; Fang Liu; Aihui Zhou
2009-01-01
In this paper,a two-scale higher-order finite element discretization scheme is proposed and analyzed for a Schr(o)dinger equation on tensor product domains.With the scheme,the solution of the eigenvalue problem on a fine grid can be reduced to an eigenvalue problem on a much coarser grid together with some eigenvalue problems on partially fine grids.It is shown theoretically and numerically that the proposed two-scale higher-order scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.
Coupled discrete element modeling of fluid injection into dense granular media
Zhang, Fengshou; Damjanac, Branko; Huang, Haiying
2013-06-01
The coupled displacement process of fluid injection into a dense granular medium is investigated numerically using a discrete element method (DEM) code PFC2D® coupled with a pore network fluid flow scheme. How a dense granular medium behaves in response to fluid injection is a subject of fundamental and applied research interests to better understand subsurface processes such as fluid or gas migration and formation of intrusive features as well as engineering applications such as hydraulic fracturing and geological storage in unconsolidated formations. The numerical analysis is performed with DEM executing the mechanical calculation and the network model solving the Hagen-Poiseuille equation between the pore spaces enclosed by chains of particles and contacts. Hydromechanical coupling is realized by data exchanging at predetermined time steps. The numerical results show that increase in the injection rate and the invading fluid viscosity and decrease in the modulus and permeability of the medium result in fluid flow behaviors displaying a transition from infiltration-governed to infiltration-limited and the granular medium responses evolving from that of a rigid porous medium to localized failure leading to the development of preferential paths. The transition in the fluid flow and granular medium behaviors is governed by the ratio between the characteristic times associated with fluid injection and hydromechanical coupling. The peak pressures at large injection rates when fluid leakoff is limited compare well with those from the injection experiments in triaxial cells in the literature. The numerical analysis also reveals intriguing tip kinematics field for the growth of a fluid channel, which may shed light on the occurrence of the apical inverted-conical features in sandstone and magma intrusion in unconsolidated formations.
Energy Technology Data Exchange (ETDEWEB)
Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu
2010-07-01
An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)
A new full discrete stabilized viscosity method for transient Navier-Stokes equations
Institute of Scientific and Technical Information of China (English)
Yan-mei QIN; Min-fu FENG; Tian-xiao ZHOU
2009-01-01
A new full discrete stabilized viscosity method for the transient Navier-Stokes equations with the high Reynolds number (small viscosity coefficient) is proposed based on the pressure projection and the extrapolated trapezoidal rule.The transient NavierStokes equations are fully discretized by the continuous equal-order finite elements in space and the reduced Crank-Nicolson scheme in time.The new stabilized method is stable and has many attractive properties.First,the system is stable for the equal-order combination of discrete continuous velocity and pressure spaces because of adding a pressure projection term.Second,the artifical viscosity parameter is added to the viscosity coefficient as a stability factor,so the system is antidiffusive.Finally,the method requires only the solution to a linear system at every time step.Stability and convergence of the method is proved.The error estimation results show that the method has a second-order accuracy,and the constant in the estimation is independent of the viscosity coefficient.The numerical results are given,which demonstrate the advantages of the method presented.
MULTIGRID FOR THE MORTAR ELEMENT METHOD WITH LOCALLY P1 NONCONFORMING ELEMENTS
Institute of Scientific and Technical Information of China (English)
毕春加; 李立康
2003-01-01
In this paper we study the theoretical properties of multigrid algorithm for discretization of the Poisson equation in 2D using a mortar element method under the assumption that the triangulations on every subdomain are uniform.We prove the convergence of the W-cycle with a sufficiently large number of smoothing steps.The variable V-cycle multigrid preconditioner are also available.
Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods
Zampieri, Elena; Pavarino, Luca F.
2006-01-01
A numerical approximation of the acoustic wave equation is presented. The spatial discretization is based on conforming spectral elements, whereas we use finite difference Newmark's explicit integration schemes for the temporal discretization. A rigorous stability analysis is developed for the discretized problem providing an upper bound for the time step [Delta]t. We present several numerical results concerning stability and convergence properties of the proposed numerical methods.
Probabilistic methods for discrete nonlinear Schr\\"odinger equations
Chatterjee, Sourav
2010-01-01
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher. A number of explicit formulas are derived. The probabilistic results, combined with dynamical information, prove the existence and typicality of solutions to the discrete NLS with highly stable localized modes that are sometimes called discrete breathers.
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Improved stochastic approximation methods for discretized parabolic partial differential equations
Guiaş, Flavius
2016-12-01
We present improvements of the stochastic direct simulation method, a known numerical scheme based on Markov jump processes which is used for approximating solutions of ordinary differential equations. This scheme is suited especially for spatial discretizations of evolution partial differential equations (PDEs). By exploiting the full path simulation of the stochastic method, we use this first approximation as a predictor and construct improved approximations by Picard iterations, Runge-Kutta steps, or a combination. This has as consequence an increased order of convergence. We illustrate the features of the improved method at a standard benchmark problem, a reaction-diffusion equation modeling a combustion process in one space dimension (1D) and two space dimensions (2D).
Xue, W.-M.; Atluri, S. N.
1985-01-01
In this paper, all possible forms of mixed-hybrid finite element methods that are based on multi-field variational principles are examined as to the conditions for existence, stability, and uniqueness of their solutions. The reasons as to why certain 'simplified hybrid-mixed methods' in general, and the so-called 'simplified hybrid-displacement method' in particular (based on the so-called simplified variational principles), become unstable, are discussed. A comprehensive discussion of the 'discrete' BB-conditions, and the rank conditions, of the matrices arising in mixed-hybrid methods, is given. Some recent studies aimed at the assurance of such rank conditions, and the related problem of the avoidance of spurious kinematic modes, are presented.
Simulation of a soil loosening process by means of the modified distinct element method
Momuzu, M.; Oida, A.; Yamazaki, M.; Koolen, A.J.
2002-01-01
We apply the Distinct Element Method (DEM) to analyze the dynamic behavior of soil. However, the conventional DEM model for calculation of contact forces between elements has some problems; for example, the movement of elements is too discrete to simulate real soil particle movement. Therefore, we m
Discrete Dipole Approximation Aided Design Method for Nanostructure Arrays
Institute of Scientific and Technical Information of China (English)
ZHU Shao-Li; LUO Xian-Gang; DU Chun-Lei
2007-01-01
A discrete dipole approximation (DDA) aided design method is proposed to determine the parameters of nanostructure arrays. The relationship between the thickness, period and extinction efficiency of nanostructure arrays for the given shape can be calculated using the DDA. Based on the calculated curves, the main parameters of the nanostructure arrays such as thickness and period can be determined. Using this aided method, a rhombic sliver nanostructure array is designed with the determinant parameters of thickness (40 nm) and period (440 nm).We further fabricate the rhombic sliver nanostructure arrays and testify the character of the extinction spectra.The obtained extinction spectra is within the visible range and the full width at half maximum is 99nm, as is expected.
Energy Technology Data Exchange (ETDEWEB)
Romero Gomez, Pedro DJ; Richmond, Marshall C.
2014-04-17
Evaluating the consequences from blade-strike of fish on marine hydrokinetic (MHK) turbine blades is essential for incorporating environmental objectives into the integral optimization of machine performance. For instance, experience with conventional hydroelectric turbines has shown that innovative shaping of the blade and other machine components can lead to improved designs that generate more power without increased impacts to fish and other aquatic life. In this work, we used unsteady computational fluid dynamics (CFD) simulations of turbine flow and discrete element modeling (DEM) of particle motion to estimate the frequency and severity of collisions between a horizontal axis MHK tidal energy device and drifting aquatic organisms or debris. Two metrics are determined with the method: the strike frequency and survival rate estimate. To illustrate the procedure step-by-step, an exemplary case of a simple runner model was run and compared against a probabilistic model widely used for strike frequency evaluation. The results for the exemplary case showed a strong correlation between the two approaches. In the application case of the MHK turbine flow, turbulent flow was modeled using detached eddy simulation (DES) in conjunction with a full moving rotor at full scale. The CFD simulated power and thrust were satisfactorily comparable to experimental results conducted in a water tunnel on a reduced scaled (1:8.7) version of the turbine design. A cloud of DEM particles was injected into the domain to simulate fish or debris that were entrained into the turbine flow. The strike frequency was the ratio of the count of colliding particles to the crossing sample size. The fish length and approaching velocity were test conditions in the simulations of the MHK turbine. Comparisons showed that DEM-based frequencies tend to be greater than previous results from Lagrangian particles and probabilistic models, mostly because the DEM scheme accounts for both the geometric
Institute of Scientific and Technical Information of China (English)
CHEN Jun; PAN Tongyan; HUANG Xiaoming
2011-01-01
We established a user-defined micromechanical model using discrete element method (DEM) to investigate the cracking behavior of asphalt concrete (AC).Using the “Fish” language provided in the particle flow code in 3-Demensions (PFC3D),the air voids and mastics in asphalt concrete were realistically built as two distinct phases.With the irregular shape of individual aggregate particles modeled using a clump of spheres of different sizes,the three-dimensional (3D) discrete element model was able to account for aggregate gradation and fraction.Laboratory uniaxial complex modulus test and indirect tensile strength test were performed to obtain input material parameters for the numerical simulation.A set of the indirect tensile test were simulated to study the cracking behavior of AC at two levels of temperature,i e,-10 ℃ and 15 ℃.The predicted results of the numerical simulation were compared with laboratory experimental measurements.Results show that the 3D DEM model is able to predict accurately the fracture pattern of different asphalt mixtures.Based on the DEM model,the effects of air void content and aggregate volumetric fraction on the cracking behavior of asphalt concrete were evaluated.
Institute of Scientific and Technical Information of China (English)
HOU Shuguang; ZHANG Dong; HUANG Xiaoming; ZHAO Yongli
2015-01-01
The micro-mechanical response of asphalt mixtures was studied using the discrete element method. The discrete element sample of stone mastic asphalt was generated first and the vehicle load was applied to the sample. A user-written program was coded with the FISH language in PFC3D to extract the contact forces within the sample and the displacements of the particles. Then, the contact forces within the whole sample, in asphalt mastic, in coarse aggregates and between asphalt mastic and coarse aggregates were investigated. Finally, the movement of the particles in the sample was analyzed. The sample was divided into 15 areas and a figure was drawn to show how the balls move in each area according to the displacements of the balls in each area. The displacements of asphalt mastic balls and coarse aggregates were also analyzed. The experimental results explain how the asphalt mixture bears vehicle load and the potential reasons why the rutting forms from a micro-mechanical view.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Institute of Scientific and Technical Information of China (English)
2008-01-01
A discrete ordinates method for a threedimensional first-order neutron transport equation based on unstructured-meshes that avoids the singularity of the second-order neutron transport equation in void regions was derived.The finite element variation equation was obtained using the least-squares method.A three-dimensional transport calculation code was developed.Both the triangular-z and the tetrahedron elements were included.The numerical results of some benchmark problems demonstrated that this method can solve neutron transport problems in unstructuredmeshes very well.For most problems,the error of the eigenvalue and the angular flux is less than 0.3% and 3.0% respectively.
A Stable Parametric Finite Element Discretization of Two-Phase Navier--Stokes Flow
Barrett, John W; Nürnberg, Robert
2013-01-01
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier--Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuous-in-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be uncondit...
Discrete Element Modeling Results of Proppant Rearrangement in the Cooke Conductivity Cell
Energy Technology Data Exchange (ETDEWEB)
Earl Mattson; Hai Huang; Michael Conway; Lisa O' Connell
2014-02-01
The study of propped fracture conductivity began in earnest with the development of the Cooke cell which later became part of the initial API standard. Subsequent developments included a patented multicell design to conduct 4 tests in a press at the same time. Other modifications have been used by various investigators. Recent studies by the Stim-Lab proppant consortium have indicated that the flow field across a Cooke proppant conductivity testing cell may not be uniform as initially believed which resulted is significantly different conductivity results. Post test analysis of low temperature metal alloy injections at the termination of proppant testing prior to the release of the applied stress suggest that higher flow is to be expected along the sides and top of the proppant pack than compared to the middle of the pack. To evaluate these experimental findings, a physics-based two-dimensional (2-D) discrete element model (DEM) was developed and applied to simulate proppant rearrangement during stress loading in the Cooke conductivity cell and the resulting porosity field. Analysis of these simulations are critical to understanding the impact of modification to the testing cell as well as understanding key proppant conductivity issues such as how these effects are manifested in proppant concentration testing results. The 2-D DEM model was constructed to represent a realistic cross section of the Cooke cell with a distribution of four material properties, three that represented the Cooke cell (steel, sandstone,square rings), and one representing the proppant. In principle, Cooke cell materials can be approximated as assemblies of independent discrete elements (particles) of various sizes and material properties that interact via cohesive interactions, repulsive forces, and frictional forces. The macroscopic behavior can then be modeled as the collective behavior of many interacting discrete elements. This DEM model is particularly suitable for modeling proppant
The Role of Qualitative Research Methods in Discrete Choice Experiments
Vass, Caroline; Rigby, Dan; Payne, Katherine
2017-01-01
Background. The use of qualitative research (QR) methods is recommended as good practice in discrete choice experiments (DCEs). This study investigated the use and reporting of QR to inform the design and/or interpretation of healthcare-related DCEs and explored the perceived usefulness of such methods. Methods. DCEs were identified from a systematic search of the MEDLINE database. Studies were classified by the quantity of QR reported (none, basic, or extensive). Authors (n = 91) of papers reporting the use of QR were invited to complete an online survey eliciting their views about using the methods. Results. A total of 254 healthcare DCEs were included in the review; of these, 111 (44%) did not report using any qualitative methods; 114 (45%) reported “basic” information; and 29 (11%) reported or cited “extensive” use of qualitative methods. Studies reporting the use of qualitative methods used them to select attributes and/or levels (n = 95; 66%) and/or pilot the DCE survey (n = 26; 18%). Popular qualitative methods included focus groups (n = 63; 44%) and interviews (n = 109; 76%). Forty-four studies (31%) reported the analytical approach, with content (n = 10; 7%) and framework analysis (n = 5; 4%) most commonly reported. The survey identified that all responding authors (n = 50; 100%) found that qualitative methods added value to their DCE study, but many (n = 22; 44%) reported that journals were uninterested in the reporting of QR results. Conclusions. Despite recommendations that QR methods be used alongside DCEs, the use of QR methods is not consistently reported. The lack of reporting risks the inference that QR methods are of little use in DCE research, contradicting practitioners’ assessments. Explicit guidelines would enable more clarity and consistency in reporting, and journals should facilitate such reporting via online supplementary materials. PMID:28061040
Carbonate fracture stratigraphy: An integrated outcrop and 2D discrete element modelling study
Spence, Guy; Finch, Emma
2013-04-01
Constraining fracture stratigraphy is important as natural fractures control primary fluid flow in low matrix permeability naturally fractured carbonate hydrocarbon reservoirs. Away from the influence of folds and faults, stratigraphic controls are known to be the major control on fracture networks. The fracture stratigraphy of carbonate nodular-chert rhythmite successions are investigated using a Discrete Element Modelling (DEM) technique and validated against observations from outcrops. Comparisons are made to the naturally fractured carbonates of the Eocene Thebes Formation exposed in the west central Sinai of Egypt, which form reservoir rocks in the nearby East Ras Budran Field. DEM allows mechanical stratigraphy to be defined as the starting conditions from which forward numerical modelling can generate fracture stratigraphy. DEM can incorporate both stratigraphic and lateral heterogeneity, and enable mechanical and fracture stratigraphy to be characterised separately. Stratally bound stratified chert nodules below bedding surfaces generate closely spaced lateral heterogeneity in physical properties at stratigraphic mechanical interfaces. This generates extra complexity in natural fracture networks in addition to that caused by bed thickness and lithological physical properties. A series of representative geologically appropriate synthetic mechanical stratigraphic models were tested. Fracture networks generated in 15 DEM experiments designed to isolate and constrain the effects of nodular chert rhythmites on carbonate fracture stratigraphy are presented. The discrete element media used to model the elastic strengths of rocks contain 72,866 individual elements. Mechanical stratigraphies and the fracture networks generated are placed in a sequence stratigraphic framework. Nodular chert rhythmite successions are shown to be a distinct type of naturally fractured carbonate reservoir. Qualitative stratigraphic rules for predicting the distribution, lengths, spacing
Discrete Direct Methods in the Fractional Calculus of Variations
Pooseh, Shakoor; Torres, Delfim F M
2012-01-01
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann-Liouville fractional derivative. Using Grunwald-Letnikov definition, we approximate the objective functional in an equispaced grid as a multi-variable function of the values of the unknown function on mesh points. The problem is then transformed to an ordinary static optimization problem. The solution to the latter problem gives an approximation to the original fractional problem on mesh points.
Hashemnia, Kamyar
A new laser displacement probe was developed to measure the impact velocities of particles within vibrationally-fluidized beds. The sensor output was also used to measure bulk flow velocity along the probe window and to provide a measure of the media packing. The displacement signals from the laser sensors were analyzed to obtain the probability distribution functions of the impact velocity of the particles. The impact velocity was affected by the orientation of the laser probe relative to the bulk flow velocity, and the density and elastic properties of the granular media. The impact velocities of the particles were largely independent of their bulk flow speed and packing density. Both the local impact and bulk flow velocities within a tub vibratory finisher were predicted using discrete element modelling (DEM) and compared to the measured values for spherical steel media. It was observed that the impact and bulk flow velocities were relatively insensitive to uncertainties in the contact coefficients of friction and restitution. It was concluded that the predicted impact and bulk flow velocities were dependent on the number of layers in the model. Consequently, the final DE model mimicked the key aspects of the experimental setup, including the submerged laser sensor. The DE method predictions of both impact velocity and bulk flow velocity were in reasonable agreement with the experimental measurements, with maximum differences of 20% and 30%, respectively. Discrete element modeling of granular flows is effective, but requires large numerical models. In an effort to reduce computational effort, this work presents a finite element (FE) continuum model of a vibrationally-fluidized granular flow. The constitutive equations governing the continuum model were calibrated using the discrete element method (DEM). The bulk flow behavior of the equivalent continuum media was then studied using both Lagrangian and Eulerian FE formulations. The bulk flow velocities predicted
INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
郭书祥; 吕震宙
2001-01-01
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters,median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
The Role of Qualitative Research Methods in Discrete Choice Experiments.
Vass, Caroline; Rigby, Dan; Payne, Katherine
2017-04-01
The use of qualitative research (QR) methods is recommended as good practice in discrete choice experiments (DCEs). This study investigated the use and reporting of QR to inform the design and/or interpretation of healthcare-related DCEs and explored the perceived usefulness of such methods. DCEs were identified from a systematic search of the MEDLINE database. Studies were classified by the quantity of QR reported (none, basic, or extensive). Authors ( n = 91) of papers reporting the use of QR were invited to complete an online survey eliciting their views about using the methods. A total of 254 healthcare DCEs were included in the review; of these, 111 (44%) did not report using any qualitative methods; 114 (45%) reported "basic" information; and 29 (11%) reported or cited "extensive" use of qualitative methods. Studies reporting the use of qualitative methods used them to select attributes and/or levels ( n = 95; 66%) and/or pilot the DCE survey ( n = 26; 18%). Popular qualitative methods included focus groups ( n = 63; 44%) and interviews ( n = 109; 76%). Forty-four studies (31%) reported the analytical approach, with content ( n = 10; 7%) and framework analysis ( n = 5; 4%) most commonly reported. The survey identified that all responding authors ( n = 50; 100%) found that qualitative methods added value to their DCE study, but many ( n = 22; 44%) reported that journals were uninterested in the reporting of QR results. Despite recommendations that QR methods be used alongside DCEs, the use of QR methods is not consistently reported. The lack of reporting risks the inference that QR methods are of little use in DCE research, contradicting practitioners' assessments. Explicit guidelines would enable more clarity and consistency in reporting, and journals should facilitate such reporting via online supplementary materials.
Influence of mobile shale on thrust faults: Insights from discrete element simulations
Dean, S. L.; Morgan, J. K.
2013-12-01
We use two-dimensional discrete element method (DEM) simulations to study the effects of a two-layer mechanical stratigraphy on a gravitationally collapsing passive margin. The system consists of an upslope sedimentary wedge, overlying an extensional zone that is linked at depth with a downslope fold and thrust belt. The behavior of the system is dependent on the material properties and thickness of the competent units. The models are initially composed of a mobile shale unit overlain by a pre-delta unit. In DEM materials, the bulk rheology of the granular material is a product of the particle interactions, depending on a range of parameters, including friction and elastic moduli. Natural mobile shales underlying deltas are presumed to be viscous, and are therefore represented in DEM as very weak non-cohesive particles. The unbonded particles respond to loading by moving to areas of lower stress, i.e. out from beneath a growing sediment wedge. The bulk motion of the particles therefore flows away from the upslope extensional zone. Apparent viscosity is introduced in DEM materials due to time dependent numerical parameters such as viscous damping of particle motions. We characterized this apparent viscosity of this mobile shale unit with a series of shear box tests, with varying shear strain rates. The mobile shale particles have a viscosity of about 108 Pa*s, which is low for mobile shale. The low viscosity of our numerical materials can be compensated for by scaling time in our models, because the simulations are driven by sedimentary loading. By increasing the sedimentation rate by many orders of magnitude, we can approximate the natural values of shear stress in our simulations. Results are compared with the Niger Delta type locale for shale tectonics. The simulations succeed in creating an overall linked extensional-contractional system, as well as creating individual structures such as popups and intersecting forethrusts and backthrusts. In addition, toe
A practical guide to boundary element methods with the software library BEMLIB
Pozrikidis, C
2002-01-01
LAPLACE'S EQUATION IN ONE DIMENSIONGreen's First and Second Identities and the Reciprocal Relation Green's FunctionsBoundary-Value Representation Boundary-Value EquationLAPLACE'S EQUATION IN TWO DIMENSIONS Green's First and Second Identities and the Reciprocal RelationGreen's Functions Integral Representation Integral Equations Hypersingular Integrals Irrotational FlowGeneralized Single- and Double-Layer Representations BOUNDARY-ELEMENT METHODS FOR LAPLACE'S EQUATION IN TWO DIMENSIONSBoundary Element Discretization .Discretization of
Institute of Scientific and Technical Information of China (English)
陈普庆; 夏伟; 周照耀; 朱权利; 李元元
2004-01-01
The application of a combined finite-discrete element modeling approach to simulate the three-dimensional microscopic compaction behavior of single-layer metal powder system was described. The process was treated as a static problem, with kinematical component being neglected. Due to ill condition, Cholesky's method failed to solve the system equations, while conjugate gradient method was tried and yielded good results. Deformation of the particles was examined and compared with the results of physical modeling experiments. In both cases, the inner particles were deformed from sphere to polygonal column, with the edges turning from arc to straight line. The edge number of a particle was equal to the number of particles surrounding it. And the experiments show that the ductile metal particles can be densified only by their plastic deformation without the occurrence of rearrangement phenomenon.
Institute of Scientific and Technical Information of China (English)
LI; Shihai; LIAN; Zhenzhong; J.; G.; Wang
2005-01-01
This paper studies the stability of jointed rock slopes by using our improved three-dimensional discrete element methods (DEM) and physical modeling. Results show that the DEM can simulate all failure modes of rock slopes with different joint configurations. The stress in each rock block is not homogeneous and blocks rotate in failure development. Failure modes depend on the configuration of joints. Toppling failure is observed for the slope with straight joints and sliding failure is observed for the slope with staged joints. The DEM results are also compared with those of limit equilibrium method (LEM). Without considering the joints in rock masses, the LEM predicts much higher factor of safety than physical modeling and DEM. The failure mode and factor of safety predicted by the DEM are in good agreement with laboratory tests for any jointed rock slope.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper we continue our effort in Liu-Shu (2004) and Liu-Shu (2007) for developing local discontinuous Galerkin (LDG) finite element methods to discretize moment models in semiconductor device simulations. We consider drift-diffusion (DD) and high-field (HF) models of one-dimensional devices, which involve not only first derivative convection terms but also second derivative diffusion terms, as well as a coupled Poisson potential equation. Error estimates are obtained for both models with smooth solutions. The main technical difficulties in the analysis include the treatment of the inter-element jump terms which arise from the discontinuous nature of the numerical method, the nonlinearity, and the coupling of the models. A simulation is also performed to validate the analysis.
Bosch, Jessica
2014-04-01
We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.
Energy Technology Data Exchange (ETDEWEB)
Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
Le Hardy, D.; Favennec, Y.; Rousseau, B.; Hecht, F.
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
FINITE ELEMENT METHOD ON NUMERICAL SIMULATION OF STRATUM CORNEUM'S PENETRATION PROPERTY
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
How the outer substance could penetrate through the skin lies in the stratum corneum, because it is the main barrier in the multi-layers of the skin. Supposing the keratin cell with a special geometry as tetrakaidecahedron, the penetration property of stratum corneum was the key problem which was numerically simulated with finite element method. At first the discretization of the stratum corneum region was given in two steps: first, the discretization of the keratin cell; second, the discretization of fattiness that surrounds the keratin. Then there was the work of numerical simulation. In this procedure, the finite element method and the multi-grid method were used. The former was to obtain the discretization of basic elements; the latter was to decrease the high frequency error. At last the visualization of the numerical simulation was shown.
Institute of Scientific and Technical Information of China (English)
陈蔚
2003-01-01
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by a mixed finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The schemes are very efficient.The optimal order error estimates both in time and space are derived.
On Sumudu Transform Method in Discrete Fractional Calculus
Directory of Open Access Journals (Sweden)
Fahd Jarad
2012-01-01
Full Text Available In this paper, starting from the definition of the Sumudu transform on a general time scale, we define the generalized discrete Sumudu transform and present some of its basic properties. We obtain the discrete Sumudu transform of Taylor monomials, fractional sums, and fractional differences. We apply this transform to solve some fractional difference initial value problems.
A discrete element model for soil-sweep interaction in three different soils
DEFF Research Database (Denmark)
Chen, Y; Munkholm, Lars Juhl; Nyord, Tavs
2013-01-01
Soil–tool interactions are at the centre of many agricultural field operations, including slurry injection. Understanding of soil–tool interaction behaviours (soil cutting forces and soil disturbance) is important for designing high performance injection tools. A discrete element model was develo....... The calibrated model was validated using the soil disturbance characteristics measured in those three soils. The simulations agreed well with the measurements with relative errors below 10% in most cases....... were measured. The measured draught and vertical forces were used in calibrations of the most sensitive model parameter, particle stiffness. The calibrated particle stiffness was 0.75 × 103 N m−1 for the coarse sand, 2.75 × 103 N m−1 for the loamy sand, and 6 × 103 N m−1 for the sandy loam...
A Discrete Element Model of Armor Glass Fragmentation and Comminution Failure Under Compression
Energy Technology Data Exchange (ETDEWEB)
Xu, Wei [Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland Washington 99354; Sun, Xin [Advanced Computing, Mathematics, and Data Division, Pacific Northwest National Laboratory, Richland Washington 99354
2016-02-15
Because of its exceptional compressive resistance and crystal-clear appearance, lightweight glass has been traditionally used in transparent armor applications. However, due to its brittle nature, glass fails differently from ductile materials in the sense that glass fragmentation occurs instantly ahead of the projectile tip upon penetration. The effective residual strength of the armor glass then inevitably relies on the damaged glass strength within such comminuted zones with confinement from the surrounding intact materials. Physical understanding of damaged glass strength therefore becomes highly critical to the further development of armor designs. In the present study, a discrete element based modeling framework has been developed to understand and predict the evolution of compressive damages and residual strength of armor glasses. With the characteristic fragmentation and comminution failures explicitly resolved, their influences on the mechanical degradation of the loaded glass materials have been evaluated. The effects of essential loading conditions and material properties have also been investigated.
Arteaga, Santiago Egido
1998-12-01
The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the
Discrete Method of Images for 3D Radio Propagation Modeling
Novak, Roman
2016-09-01
Discretization by rasterization is introduced into the method of images (MI) in the context of 3D deterministic radio propagation modeling as a way to exploit spatial coherence of electromagnetic propagation for fine-grained parallelism. Traditional algebraic treatment of bounding regions and surfaces is replaced by computer graphics rendering of 3D reflections and double refractions while building the image tree. The visibility of reception points and surfaces is also resolved by shader programs. The proposed rasterization is shown to be of comparable run time to that of the fundamentally parallel shooting and bouncing rays. The rasterization does not affect the signal evaluation backtracking step, thus preserving its advantage over the brute force ray-tracing methods in terms of accuracy. Moreover, the rendering resolution may be scaled back for a given level of scenario detail with only marginal impact on the image tree size. This allows selection of scene optimized execution parameters for faster execution, giving the method a competitive edge. The proposed variant of MI can be run on any GPU that supports real-time 3D graphics.
Extension of silo discharge model based on discrete element method
Energy Technology Data Exchange (ETDEWEB)
Oldal, Istvan; Safranyil, Ferenc [Szent Istvan University, Goedoelloe (Hungary)
2015-09-15
Silos are containers used by almost all fields of industry for storing granular materials and generally classified in two types: mass flow and funnel flow. One of the most important design parameter of these equipment is the discharge rate which depends on the flow mode. There are high numbers of analytical and empirical models used for determine this parameter, however none of them is suitable for both flow modes; moreover the accuracy of mass flow models is not acceptable. Recently a few numerical discharge models are made for certain geometries; but the applicability of these models in case of different flow modes was not examined. Aim of our work is the creation of an experimentally validated numerical discharge model based on others work and examination of this in term of different flow modes. We prove that our modified model is suitable for determine silos discharge rate independently from flow mode.
Discrete Spectral Local Measurement Method for Testing Solar Concentrators
Directory of Open Access Journals (Sweden)
Huifu Zhao
2012-01-01
Full Text Available In order to compensate for the inconvenience and instability of outdoor photovoltaic concentration test system which are caused by the weather changes, we design an indoor concentration test system with a large caliber and a high parallelism, and then verify its feasibility and scientificity. Furthermore, we propose a new concentration test method: the discrete spectral local measurement method. A two-stage Fresnel concentration system is selected as the test object. The indoor and the outdoor concentration experiments are compared. The results show that the outdoor concentration efficiency of the two-stage Fresnel concentration system is 85.56%, while the indoor is 85.45%. The two experimental results are so close that we can verify the scientificity and feasibility of the indoor concentration test system. The light divergence angle of the indoor concentration test system is 0.267° which also matches with sunlight divergence angle. The indoor concentration test system with large diameter (145 mm, simple structure, and low cost will have broad applications in solar concentration field.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...... element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have...
Mixed time discontinuous space-time finite element method for convection diffusion equations
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A mixed time discontinuous space-time finite element scheme for second-order convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
SPACE-TIME FINITE ELEMENT METHOD FOR SCHR(O)DINGER EQUATION AND ITS CONSERVATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Energy conservation of nonlinear Schr(o)dinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.
Directory of Open Access Journals (Sweden)
Dayanne Aline de Souza Fidelis
2006-07-01
Full Text Available The space and time discretization of the finite element method was optimized for following application in multicomponent diffusion simulation during Prato cheese salting, a traditional and much consumed foodstuff in Brazil originated from the European Gouda cheese. It was ascertained that the correct choice of the time intervals and mesh is fundamental in applying the method. After optimization the simulated results were in agreement with the experimental and calculated results by the analytical method, showing that the method is a promising tool for simulation of diffusive processes when two solutes are considered, and is also a much less restrictive technique than the analytical method.Neste trabalho foi realizada a otimização da discretização espaço-temporal do método de elementos finitos para sua posterior aplicação na simulação da difusão multicomponente durante a salda de queijo prato, um alimento tradicional e muito consumido no Brasil e similar ao queijo Gouda. Foi verificado que a escolha correta dos intervalos de tempo e da malha é fundamental para a aplicação do método. Após a otimização os resultados simulados concordaram com os experimentais e estimados pelo método analítico. Mostrando que o método é uma ferramenta promissora para a simulação de processos difusivos quando dois solutos são considerados, além de ser uma técnica muito menosrestritiva que o método analítico.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Institute of Scientific and Technical Information of China (English)
Xiao-Ting Rui; Edwin Kreuzer; Bao Rong; Bin He
2012-01-01
In this paper,by defining new state vectors and developing new transfer matrices of various elements moving in space,the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of muhibody system with flexible beams moving in space.Formulations and numerical example of a rigidflexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov ing in space,the global dynamics equations of system are not needed,the orders of involved matrices of the system are very low and the computational speed is high,irrespective of the size of the system.The new method is simple,straightforward,practical,and provides a powerful tool for multi-rigid-flexible-body system dynamics.
Multiscale modeling of rapid granular flow with a hybrid discrete-continuum method
Chen, Xizhong; Li, Jinghai
2015-01-01
Both discrete and continuum models have been widely used to study rapid granular flow, discrete model is accurate but computationally expensive, whereas continuum model is computationally efficient but its accuracy is doubtful in many situations. Here we propose a hybrid discrete-continuum method to profit from the merits but discard the drawbacks of both discrete and continuum models. Continuum model is used in the regions where it is valid and discrete model is used in the regions where continuum description fails, they are coupled via dynamical exchange of parameters in the overlap regions. Simulation of granular channel flow demonstrates that the proposed hybrid discrete-continuum method is nearly as accurate as discrete model, with much less computational cost.
Rubtsova, O A; Moro, A M
2008-01-01
The direct comparison of two different continuum discretization methods towards the solution of a composite particle scattering off a nucleus is presented. The first approach -- the Continumm-Discretized Coupled Channel method -- is based on the differential equation formalism, while the second one -- the Wave-Packet Continuum Discretization method -- uses the integral equation formulation for the composite-particle scattering problem. As benchmark calculations we have chosen the deuteron off \
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
DEFF Research Database (Denmark)
Stolpe, Mathias; Bendsøe, Martin P.
2007-01-01
This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...
Note on governing equations for a discrete vortex method
Energy Technology Data Exchange (ETDEWEB)
Arai, Norio; Taguchi, Katsuhiko
1987-11-04
The characteristic of a coefficient matrix, which is derived from governing equations used in a discrete vortex method was investigated. The purpose of this note is to show the reduction of the rank of coefficient matrix when the vortices on the body are arranged symmetrically. When singular points are arranged symmetrically, the rank of the coefficient matrix derived from equation is reduced from m to (m-1). Then if Kelvin's theorem on circulation is introduced in equations, the rank becomes m. The uniqueness of the solution by using Cramer's theorem was obtained. The following three cases were taken into consideration:(1) even vortices, none on the symmetrial axis; (2) even vortices, two vortices on the symmetrical axis; (3) odd vortices, only one vortex on the symmetrical asix. The singularity of the coefficient matrix in the above-mentioned cases were proved. Firstly, the immutability of the characteristic of the coefficient matrix by the rotation of the coordinate system and the parallel transformation of that were proved. Then the x-axis was specified as symmetrical. (4 figs, 4 refs)
Macroscopic model and truncation error of discrete Boltzmann method
Hwang, Yao-Hsin
2016-10-01
A derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete Boltzmann method is proffered in this paper. Essential presumptions of two time scales and a small parameter in the Chapman-Enskog expansion are disposed of in the present formulation. Equilibrium particle distribution function instead of its original non-equilibrium form is chosen as key variable in the derivation route. Taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart. A self-contained and comprehensive practice for the linear one-dimensional convection-diffusion equation is illustrated in details. Numerical validations on the incurred truncation error in one- and two-dimensional cases with various distribution functions are conducted to verify present formulation. As shown in the computational results, excellent agreement between numerical result and theoretical prediction are found in the test problems. Straightforward extensions to more complicated systems including convection-diffusion-reaction, multi-relaxation times in collision operator as well as multi-dimensional Navier-Stokes equations are also exposed in the Appendix to point out its expediency in solving complicated flow problems.
A spatial discretization of the MHD equations based on the finite volume - spectral method
Energy Technology Data Exchange (ETDEWEB)
Miyoshi, Takahiro [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment
2000-05-01
Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA{sub {phi}}, is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)
Institute of Scientific and Technical Information of China (English)
Hong-ying Man; Zhong-ci Shi
2006-01-01
In this paper, we discuss the finite volume element method of P1-nonconforming quadrilateral element for elliptic problems and obtain optimal error estimates for general quadrilateral partition. An optimal cascadic multigrid algorithm is proposed to solve the nonsymmetric large-scale system resulting from such discretization. Numerical experiments are reported to support our theoretical results.
LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM
Institute of Scientific and Technical Information of China (English)
Lie-heng Wang; Huo-yuan Duan
2000-01-01
In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived.
In-plane Material Filters for the Discrete Material Optimization Method
DEFF Research Database (Denmark)
Sørensen, Rene; Lund, Erik
2015-01-01
This paper presents in-plane material filters for the Discrete Material Optimization method used for optimizing laminated composite structures. The filters make it possible for engineers to specify a minimum length scale which governs the minimum size of areas with constant material continuity....... Consequently, engineers can target the available production methods, and thereby increase its manufacturability while the optimizer is free to determine which material to apply together with an optimum location, shape, and size of these areas with constant material continuity. By doing so, engineers no longer...... have to group elements together in so-called patches, so to statically impose a minimum length scale. The proposed method imposes the minimum length scale through a standard density filter known from topology optimization of isotropic materials. This minimum length scale is generally referred...
Ji, S.; Hanes, D.M.; Shen, H.H.
2009-01-01
In this study, we report a direct comparison between a physical test and a computer simulation of rapidly sheared granular materials. An annular shear cell experiment was conducted. All parameters were kept the same between the physical and the computational systems to the extent possible. Artificially softened particles were used in the simulation to reduce the computational time to a manageable level. Sensitivity study on the particle stiffness ensured such artificial modification was acceptable. In the experiment, a range of normal stress was applied to a given amount of particles sheared in an annular trough with a range of controlled shear speed. Two types of particles, glass and Delrin, were used in the experiment. Qualitatively, the required torque to shear the materials under different rotational speed compared well with those in the physical experiments for both the glass and the Delrin particles. However, the quantitative discrepancies between the measured and simulated shear stresses were nearly a factor of two. Boundary conditions, particle size distribution, particle damping and friction, including a sliding and rolling, contact force model, were examined to determine their effects on the computational results. It was found that of the above, the rolling friction between particles had the most significant effect on the macro stress level. This study shows that discrete element simulation is a viable method for engineering design for granular material systems. Particle level information is needed to properly conduct these simulations. However, not all particle level information is equally important in the study regime. Rolling friction, which is not commonly considered in many discrete element models, appears to play an important role. ?? 2009 Elsevier Ltd.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Guan, P. B.; Tingatinga, E. A.; Longalong, R. E.; Saguid, J.
2016-09-01
During the past decades, the complexity of conventional methods to perform seismic performance assessment of buildings led to the development of more effective approaches. The rigid body spring-discrete element method (RBS-DEM) is one of these approaches and has recently been applied to the study of the behavior of reinforced concrete (RC) buildings subjected to strong earthquakes. In this paper, the governing equations of RBS-DEM planar elements subjected to lateral loads and horizontal ground motion are presented and used to replicate the hysteretic behavior of experimental RC columns. The RBS-DEM models of columns are made up of rigid components connected by systems of springs that simulate axial, shear, and bending behavior of an RC section. The parameters of springs were obtained using Response-2000 software and the hysteretic response of the models of select columns from the Pacific Earthquake Engineering Research (PEER) Structural Performance Database were computed numerically. Numerical examples show that one-component models were able to simulate the initial stiffness reasonably, while the displacement capacity of actual columns undergoing large displacements were underestimated.
Toward Distinct Element Method Simulations of Carbon Nanotube Systems
Akatyeva, Evgeniya; Anderson, Tyler; Nikiforov, Ilia; Potyondy, David; Ballarini, Roberto; Dumitrica, Traian
2011-03-01
We propose distinct element method modeling of carbon nanotube systems. The atomic-level description of an individual nanotube is coarse-grained into a chain of spherical elements that interact by parallel bonds located at their contacts. The spherical elements can lump multiple translational unit cells of the carbon nanotube and have both translational and rotational degrees of freedom. The discrete long ranged interaction between nanotubes is included in a van der Waals contact of nonmechanical nature that acts simultaneously with the parallel bonds. The created mesoscopic model is put into service by simulating a realistic carbon nanotube ring. The ring morphology arises from the energy balance stored in both parallel and van der Waals bonds. We thank NSF CAREER under Grant No. CMMI-0747684, NSF under Grant No. CMMI 0800896.
Error estimates of H1-Galerkin mixed finite element method for Schr(o)dinger equation
Institute of Scientific and Technical Information of China (English)
LIU Yang; LI Hong; WANG Jin-feng
2009-01-01
An H1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
Gardiner, Bruce S; Wong, Kelvin K L; Joldes, Grand R; Rich, Addison J; Tan, Chin Wee; Burgess, Antony W; Smith, David W
2015-10-01
This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus) and extracellular matrix (e.g. collagen) are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties). Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings). Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Directory of Open Access Journals (Sweden)
Bruce S Gardiner
2015-10-01
Full Text Available This paper presents a framework for modelling biological tissues based on discrete particles. Cell components (e.g. cell membranes, cell cytoskeleton, cell nucleus and extracellular matrix (e.g. collagen are represented using collections of particles. Simple particle to particle interaction laws are used to simulate and control complex physical interaction types (e.g. cell-cell adhesion via cadherins, integrin basement membrane attachment, cytoskeletal mechanical properties. Particles may be given the capacity to change their properties and behaviours in response to changes in the cellular microenvironment (e.g., in response to cell-cell signalling or mechanical loadings. Each particle is in effect an 'agent', meaning that the agent can sense local environmental information and respond according to pre-determined or stochastic events. The behaviour of the proposed framework is exemplified through several biological problems of ongoing interest. These examples illustrate how the modelling framework allows enormous flexibility for representing the mechanical behaviour of different tissues, and we argue this is a more intuitive approach than perhaps offered by traditional continuum methods. Because of this flexibility, we believe the discrete modelling framework provides an avenue for biologists and bioengineers to explore the behaviour of tissue systems in a computational laboratory.
Heege, J.H. ter; Orlic, B.; Hoedeman, G.C.
2015-01-01
Wellbore zonal isolation is particularly important for subsurface storage of CO2, where well integrity must be ensured for very long time spans. In this study, three dimensional discrete element models of wellbore systems have been used to simulate failure and damage of wellbore cement and surroundi
Calvert, S.C.; Taale, H.; Hoogendoorn, S.P.
2014-01-01
In this contribution the Core Probability Framework (CPF) is introduced with the application of the Discrete-Element Core Probability Model (DE-CPM) as a new DNL for dynamic macroscopic modelling of stochastic traffic flow. The model is demonstrated for validation in a test case and for computationa
Bokhove, O.
2003-01-01
Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symm
An improved optimal elemental method for updating finite element models
Institute of Scientific and Technical Information of China (English)
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
Institute of Scientific and Technical Information of China (English)
Ding Rui; Jiang Meiqun; Peng Daping
2005-01-01
The boundary element approximation of the parabolic variational inequalities of the second kind is discussed. First, the parabolic variational inequalities of the second kind can be reduced to an elliptic variational inequality by using semidiscretization and implicit method in time; then the existence and uniqueness for the solution of nonlinear non-differentiable mixed variational inequality is discussed. Its corresponding mixed boundary variational inequality and the existence and uniqueness of its solution are yielded. This provides the theoretical basis for using boundary element method to solve the mixed variational inequality.
MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS
Institute of Scientific and Technical Information of China (English)
Qing-ping Deng; Xiao-ping Feng
2002-01-01
Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion.To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
Mixed finite element methods for linear elasticity with weakly imposed symmetry
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2007-12-01
In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.
Particle Discrete Method Based on Manifold Cover for Crack Propagation of Jointed Rock Mass
Directory of Open Access Journals (Sweden)
Yang Ping
2014-01-01
Full Text Available The rock mass can be assumed to be homogeneous material from a macroscopic view; however, it is the heterogeneous material in mesoscopic scale and its physicomechanical properties are discontinuous in space. The failure of jointed rock mass was usually caused by the initiation, propagation, and coalescence of new wing cracks derived from primary joint. In order to further study the rock fracture instability, we need to study the expansion of rock cracks under external loads from the macro-meso perspective. This paper, based on the manifold cover concept, proposes a new discrete element numerical method, manifold particle discrete (MPD, combined with the particle contact model and the introduced concept of stress boundary. The proposed method can easily simulate the crack generation, propagation, and coalescence of jointed rock mass from the macro-meso perspective. The whole process of rock fragmentation is thereafter reproduced. By analyzing the manifold cover and sphere particle model, this paper constitutes the sphere unit cover function of three-dimensional manifold cover, establishes tetrahedron units, and obtains the equilibrium equation and compatible equation of the MPD model. For rock-like brittle material, crack propagation process can be simulated, and it also verifies the accuracy of the proposed numerical method.
Coupled Large Eddy Simulation and Discrete Element Model for Particle Saltation
Liu, X.; Liu, D.; Fu, X.
2016-12-01
Particle saltation is the major mode of motion for sediment transport. The quantification of the characteristics of saltation, either as an individual particle or as a group, is of great importance to our understanding of the transport process. In the past, experiments and numerical models have been performed to study the saltation length, height, and velocity under different turbulent flow and rough bed conditions. Most previous numerical models have very restrictive assumptions. For example, many models assumed Log-law flow velocity profiles to drive the motion of particles. Others assumed some "splash-function" which assigns the reflection angle for the rebounding of the saltating particle after each collision with bed. This research aims to relax these restrictions by a coupled eddy-resolving flow solver and a discrete element model. The model simulates the fully four-way coupling among fluid, particles, and wall. The model is extensively validated on both the turbulent flow field and saltation statistics. The results show that the two controlling factors for particle saltation are turbulent fluctuations and bed collision. Detailed quantification of these two factors will be presented. Through the statistics of incidence reflection angles, a more physical "splash-function" is obtained in which the reflection angle follows an asymmetric bimodal distribution for a given incidence angle. The higher mode is always located on the upstream side of the bed particle, while the lower one is always on the downstream surface.
High-speed laminar-turbulent boundary layer transition induced by a discrete roughness element
Iyer, Prahladh; Mahesh, Krishnan
2013-11-01
Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy et al. (AIAA Paper 2009-394, 2009) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in Cf and Ch (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in Cf until 20 D downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered. Partially supported by NASA.
Borehole Breakouts Induced in Arkosic Sandstones and a Discrete Element Analysis
Lee, H.; Moon, T.; Haimson, B. C.
2016-04-01
A series of laboratory drilling experiments were conducted on two arkosic sandstones (Tenino and Tablerock) under polyaxial far-field stress conditions (σ h ≠ σ H ≠ σ v ). V-shaped breakouts, aligned with the σ h direction and revealing stress-dependent dimensions (width and length), were observed in the sandstones. The microscale damage pattern leading to the breakouts, however, is different between the two, which is attributed to the difference in their cementation. The dominant micromechanism in Tenino sandstone is intergranular microcracking occurring in clay minerals filling the spaces between clastic grains. On the other hand, intra- and transgranular microcracking taking place in the grain itself prevails in Tablerock sandstone. To capture the grain-scale damage and reproduce the failure localization observed around the borehole in the laboratory, we used a discrete element (DE) model in which a grain breakage algorithm was implemented. The microparameters needed in the numerical model were calibrated by running material tests and comparing the macroscopic responses of the model to the ones measured in the laboratory. It is shown that DE modeling is capable of simulating the microscale damage of the rock and replicating the localized damage zone observed in the laboratory. In addition, the numerically induced breakout width is determined at a very early stage of the damage localization and is not altered for the rest of the failure process.
Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations
Institute of Scientific and Technical Information of China (English)
Christoph R. Müller; Daniel J. Holland; James R. Third; Andrew J. Sederman; John S. Dennis; Lynn F. Gladden
2011-01-01
This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and twophase granular systems,such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes.The unique capability of MR to not only image the solids' distribution (voidage) but also the velocity of the particulate phase is clearly shown,it is demonstrated that MR can provide measurements over different length and time scales.With the MR equipment used for the studies summarized here,temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres,respectively.Besides providing crucial data required for an improved understanding of the underlying physics of granular flows,multi-scale MR measurements were also used to validate numerical simulations of granular systems.It is shown that predictions of time-averaged properties,such as voidage and velocity of the particulate phase,made using the Discrete Element Model agree very well with MR measurements.
Institute of Scientific and Technical Information of China (English)
石连栓; 孙焕纯; 冯恩民
2001-01-01
A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Karampinos, Efstratios; Hadjigeorgiou, John; Turcotte, Pascal
2016-12-01
Structurally defined squeezing mechanisms in hard rock mining often result in buckling failures and large deformations. In mining drives, the primary objective is to mitigate and manage, in a cost-effective way, as opposed to arrest the deformation. This paper is a contribution to an improved understanding of the impact of several reinforcement scenarios in structurally controlled deformations in hard rock mines. The influence of reinforcement in the 3D discrete element method is explored, extending previous numerical work that has captured the squeezing buckling mechanism driven by foliation and high stresses in the selected mine site. A comprehensive strategy for explicitly modelling rock reinforcement using the DEM was developed and implemented in a series of 3D numerical models. The models were calibrated based on field testing of reinforcement and observations at the LaRonde Mine. They were used to investigate the influence of different reinforcement strategies at different deformation stages. The numerical results were in agreement with the field observations and demonstrated the practical implications of using yielding reinforcement elements. This was supported by field data where the use of yielding bolts reduced the drift convergence and rehabilitation. The methodology is applicable to other mine sites facing structurally controlled large deformations.
Lagrangian Finite-Element Method for the Simulation of K-BKZ Fluids with Third Order Accuracy
DEFF Research Database (Denmark)
Marin, José Manuel Román; Rasmussen, Henrik K.
2009-01-01
system attached to the particles is discretized by ten-node quadratic tetrahedral elements using Cartesian coordinates and the pressure by linear interpolation inside these elements. The spatial discretization of the governing equations follows the mixed Galerkin finite element method. The time integral...... is discretized by a quadratic interpolation in time. The convergence of the method in time and space was demonstrated on the free surface problem of a filament stretched between two plates, considering the axisymmetric case as well as the growth of non-axisymmetric disturbances on the free surface. The scheme...
van der Vegt, Jacobus J.W.; van der Ven, H.
1998-01-01
A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Coupled large eddy simulation and discrete element model of bedload motion
Furbish, D.; Schmeeckle, M. W.
2011-12-01
We combine a three-dimensional large eddy simulation of turbulence to a three-dimensional discrete element model of turbulence. The large eddy simulation of the turbulent fluid is extended into the bed composed of non-moving particles by adding resistance terms to the Navier-Stokes equations in accordance with the Darcy-Forchheimer law. This allows the turbulent velocity and pressure fluctuations to penetrate the bed of discrete particles, and this addition of a porous zone results in turbulence structures above the bed that are similar to previous experimental and numerical results for hydraulically-rough beds. For example, we reproduce low-speed streaks that are less coherent than those over smooth-beds due to the episodic outflow of fluid from the bed. Local resistance terms are also added to the Navier-Stokes equations to account for the drag of individual moving particles. The interaction of the spherical particles utilizes a standard DEM soft-sphere Hertz model. We use only a simple drag model to calculate the fluid forces on the particles. The model reproduces an exponential distribution of bedload particle velocities that we have found experimentally using high-speed video of a flat bed of moving sand in a recirculating water flume. The exponential distribution of velocity results from the motion of many particles that are nearly constantly in contact with other bed particles and come to rest after short distances, in combination with a relatively few particles that are entrained further above the bed and have velocities approaching that of the fluid. Entrainment and motion "hot spots" are evident that are not perfectly correlated with the local, instantaneous fluid velocity. Zones of the bed that have recently experienced motion are more susceptible to motion because of the local configuration of particle contacts. The paradigm of a characteristic saltation hop length in riverine bedload transport has infused many aspects of geomorphic thought, including
Energy Technology Data Exchange (ETDEWEB)
Vaillon, R.; Lallemand, M.; Lemonnier, D. [Ecole Nationale Superieure de Mecanique et d`Aerotechnique (ENSMA), 86 - Poitiers (France)
1996-12-31
The method of discrete ordinates, which is more and more widely used in radiant heat transfer studies, is mainly developed in Cartesian, (r,z) and (r,{Theta}) cylindrical, and spherical coordinates. In this study, the approach of this method is performed in orthogonal curvilinear coordinates: determination of the radiant heat transfer equation, treatment of the angular redistribution terms, numerical procedure. Some examples of application are described in 2-D geometry defined in curvilinear coordinates along a curve and at the thermal equilibrium. A comparison is made with the discrete ordinates method in association with the finite-volumes method in non structured mesh. (J.S.) 27 refs.
Atkins, H. L.; Helenbrook, B. T.
2005-01-01
This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.
Institute of Scientific and Technical Information of China (English)
张理论; 宋君强; 李晓梅
2004-01-01
Semi-implicit spectral element schemes for 2-D shallow water equation are given, and numerical techniques are discussed. The EBE (element by element) idea is generalized to unsymmetric caes. We design mass-matrix diagonal pre-conditioned conjugate gradient method. The parallel computing is covered, and implemented on PC cluster. The research shows that spectral element has high precision and good scalability for shallow water simulation, and fits on the high-latency PC cluster perfectly.
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
In-plane material continuity for the discrete material optimization method
DEFF Research Database (Denmark)
Sørensen, Rene; Lund, Erik
2015-01-01
When performing discrete material optimization of laminated composite structures, the variation of the in-plane material continuity is typically governed by the size of the finite element discretization. For a fine mesh, this can lead to designs that cannot be manufactured due to the complexity...... of the material distribution. In order to overcome this problem, engineers typically group elements together into socalled patches which share design variables. However, because the shape and size of a patch are fixed during the optimization procedure, a poor patch layout may drastically limit the design space...
Duan, K.; Kwok, C. Y.
2016-04-01
The aim of this study is to better understand the mechanisms controlling the initiation, propagation, and ultimate pattern of borehole breakouts in shale formation when drilled parallel with and perpendicular to beddings. A two-dimensional discrete element model is constructed to explicitly represent the microstructure of inherently anisotropic rocks by inserting a series of individual smooth joints into an assembly of bonded rigid discs. Both isotropic and anisotropic hollow square-shaped samples are generated to represent the wellbores drilled perpendicular to and parallel with beddings at reduced scale. The isotropic model is validated by comparing the stress distribution around borehole wall and along X axis direction with analytical solutions. Effects of different factors including the particle size distribution, borehole diameter, far-field stress anisotropy, and rock anisotropy are systematically evaluated on the stress distribution and borehole breakout propagation. Simulation results reveal that wider particle size distribution results in the local stress perturbations which cause localization of cracks. Reduction of borehole diameter significantly alters the crack failure from tensile to shear and raises the critical pressure. Rock anisotropy plays an important role on the stress state around wellbore which lead to the formation of preferred cracks under hydrostatic stress. Far-field stress anisotropy plays a dominant role in the shape of borehole breakout when drilled perpendicular to beddings while a secondary role when drilled parallel with beddings. Results from this study can provide fundamental insights on the underlying particle-scale mechanisms for previous findings in laboratory and field on borehole stability in anisotropic rock.
Domain decomposition for a mixed finite element method in three dimensions
Cai, Z.; Parashkevov, R.R.; Russell, T.F.; Wilson, J.D.; Ye, X.
2003-01-01
We consider the solution of the discrete linear system resulting from a mixed finite element discretization applied to a second-order elliptic boundary value problem in three dimensions. Based on a decomposition of the velocity space, these equations can be reduced to a discrete elliptic problem by eliminating the pressure through the use of substructures of the domain. The practicality of the reduction relies on a local basis, presented here, for the divergence-free subspace of the velocity space. We consider additive and multiplicative domain decomposition methods for solving the reduced elliptic problem, and their uniform convergence is established.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
On Hybrid and mixed finite element methods
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Novel boundary element method for resolving plate bending problems
Institute of Scientific and Technical Information of China (English)
陈颂英; 王乐勤; 焦磊
2003-01-01
This paper discusses the application of the boundary contour method for resolving plate bending problems. The exploitation of the integrand divergence free property of the plate bending boundary integral equation based on the Kirchhoff hypothesis and a very useful application of Stokes' Theorem are presented to convert surface integrals on boundary elements to the computation of bending potential functions on the discretized boundary points, even for curved surface elements of arbitrary shape. Singularity and treatment of the discontinued corner point are not needed at all. The evaluation of the physics variant at internal points is also shown in this article. Numerical results are presented for some plate bending problems and compared against analytical and previous solutions.
Jensen, K. A.; Ripoll, J.-F.; Wray, A. A.; Joseph, D.; ElHafi, M.
2004-01-01
Five computational methods for solution of the radiative transfer equation in an absorbing-emitting and non-scattering gray medium were compared on a 2 m JP-8 pool fire. The temperature and absorption coefficient fields were taken from a synthetic fire due to the lack of a complete set of experimental data for fires of this size. These quantities were generated by a code that has been shown to agree well with the limited quantity of relevant data in the literature. Reference solutions to the governing equation were determined using the Monte Carlo method and a ray tracing scheme with high angular resolution. Solutions using the discrete transfer method, the discrete ordinate method (DOM) with both S(sub 4) and LC(sub 11) quadratures, and moment model using the M(sub 1) closure were compared to the reference solutions in both isotropic and anisotropic regions of the computational domain. DOM LC(sub 11) is shown to be the more accurate than the commonly used S(sub 4) quadrature technique, especially in anisotropic regions of the fire domain. This represents the first study where the M(sub 1) method was applied to a combustion problem occurring in a complex three-dimensional geometry. The M(sub 1) results agree well with other solution techniques, which is encouraging for future applications to similar problems since it is computationally the least expensive solution technique. Moreover, M(sub 1) results are comparable to DOM S(sub 4).
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Furihata, Daisuke
2010-01-01
Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be used to effectively model multidimensional systems. The methods put forward in Discrete Variational Derivative Method concentrate on a new class of ""structure-preserving numerical equations"" which improves the qualitative behaviour of the PDE solutions and allows for stable computing. The authors have also taken care to present their methods in an accessible manner, which means that the book will be useful to engineer
Energy Technology Data Exchange (ETDEWEB)
Feng, Xiaobing [Univ. of Tennessee, Knoxville, TN (United States)
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
Institute of Scientific and Technical Information of China (English)
LUO Zhen-dong; MAO Yun-kui; ZHU Jiang
2007-01-01
The Galerkin-Petrov least squares method is combined with the mixed finite element method to deal with the stationary, incompressible magnetohydrodynamics system of equations with viscosity. A Galerkin-Petrov least squares mixed finite element format for the stationary incompressible magnetohydrodynamics equations is presented.And the existence and error estimates of its solution are derived. Through this method,the combination among the mixed finite element spaces does not demand the discrete Babu(s)ka-Brezzi stability conditions so that the mixed finite element spaces could be chosen arbitrartily and the error estimates with optimal order could be obtained.
Finite element method for solving geodetic boundary value problems
Fašková, Zuzana; Čunderlík, Róbert; Mikula, Karol
2010-02-01
The goal of this paper is to present the finite element scheme for solving the Earth potential problems in 3D domains above the Earth surface. To that goal we formulate the boundary-value problem (BVP) consisting of the Laplace equation outside the Earth accompanied by the Neumann as well as the Dirichlet boundary conditions (BC). The 3D computational domain consists of the bottom boundary in the form of a spherical approximation or real triangulation of the Earth’s surface on which surface gravity disturbances are given. We introduce additional upper (spherical) and side (planar and conical) boundaries where the Dirichlet BC is given. Solution of such elliptic BVP is understood in a weak sense, it always exists and is unique and can be efficiently found by the finite element method (FEM). We briefly present derivation of FEM for such type of problems including main discretization ideas. This method leads to a solution of the sparse symmetric linear systems which give the Earth’s potential solution in every discrete node of the 3D computational domain. In this point our method differs from other numerical approaches, e.g. boundary element method (BEM) where the potential is sought on a hypersurface only. We apply and test FEM in various situations. First, we compare the FEM solution with the known exact solution in case of homogeneous sphere. Then, we solve the geodetic BVP in continental scale using the DNSC08 data. We compare the results with the EGM2008 geopotential model. Finally, we study the precision of our solution by the GPS/levelling test in Slovakia where we use terrestrial gravimetric measurements as input data. All tests show qualitative and quantitative agreement with the given solutions.
Boundary element-free method for elastodynamics
Institute of Scientific and Technical Information of China (English)
CHENG; Yumin; PENG; Miaojuan
2005-01-01
The moving least-square approximation is discussed first. Sometimes the method can form an ill-conditioned equation system, and thus the solution cannot be obtained correctly. A Hilbert space is presented on which an orthogonal function system mixed a weight function is defined. Next the improved moving least-square approximation is discussed in detail. The improved method has higher computational efficiency and precision than the old method, and cannot form an ill-conditioned equation system. A boundary element-free method (BEFM) for elastodynamics problems is presented by combining the boundary integral equation method for elastodynamics and the improved moving least-square approximation. The boundary element-free method is a meshless method of boundary integral equation and is a direct numerical method compared with others, in which the basic unknowns are the real solutions of the nodal variables and the boundary conditions can be applied easily. The boundary element-free method has a higher computational efficiency and precision. In addition, the numerical procedure of the boundary element-free method for elastodynamics problems is presented in this paper. Finally, some numerical examples are given.
High-order solution methods for grey discrete ordinates thermal radiative transfer
Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.
2016-12-01
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge-Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
High-order solution methods for grey discrete ordinates thermal radiative transfer
Energy Technology Data Exchange (ETDEWEB)
Maginot, Peter G., E-mail: maginot1@llnl.gov [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States); Morel, Jim E., E-mail: morel@tamu.edu [Department of Nuclear Engineering, Texas A& M University, College Station, TX 77843 (United States)
2016-12-15
This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation is accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 谢正辉; 张桂芳
2003-01-01
The non-stationary natural convection problem is studied. A lowest order finite difference scheme based on mixed finite element method for non-stationary natural convection problem, by the spatial variations discreted with finite element method and time with finite difference scheme was derived, where the numerical solution of velocity, pressure, and temperature can be found together, and a numerical example to simulate the close square cavity is given, which is of practical importance.
Accelerated Matrix Element Method with Parallel Computing
Schouten, Doug; Stelzer, Bernd
2014-01-01
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current collider experiments. However, the computational complexity of this method for final states with many particles and degrees of freedom sets it at a disadvantage compared to supervised classification methods such as decision trees, k nearest-neighbour, or neural networks. This note presents a concrete implementation of the matrix element technique using graphics processing units. Due to the intrinsic parallelizability of multidimensional integration, dramatic speedups can be readily achieved, which makes the matrix element technique viable for general usage at collider experiments.
Lei, Qinghua; Latham, John-Paul; Xiang, Jiansheng
2016-12-01
An empirical joint constitutive model (JCM) that captures the rough wall interaction behaviour of individual fractures associated with roughness characteristics observed in laboratory experiments is combined with the solid mechanical model of the finite-discrete element method (FEMDEM). The combined JCM-FEMDEM formulation gives realistic fracture behaviour with respect to shear strength, normal closure, and shear dilatancy and includes the recognition of fracture length influence as seen in experiments. The validity of the numerical model is demonstrated by a comparison with the experimentally established empirical solutions. A 2D plane strain geomechanical simulation is conducted using an outcrop-based naturally fractured rock model with far-field stresses loaded in two consecutive phases, i.e. take-up of isotropic stresses and imposition of two deviatoric stress conditions. The modelled behaviour of natural fractures in response to various stress conditions illustrates a range of realistic behaviour including closure, opening, shearing, dilatancy, and new crack propagation. With the increase in stress ratio, significant deformation enhancement occurs in the vicinity of fracture tips, intersections, and bends, where large apertures can be generated. The JCM-FEMDEM model is also compared with conventional approaches that neglect the scale dependency of joint properties or the roughness-induced additional frictional resistance. The results of this paper have important implications for understanding the geomechanical behaviour of fractured rocks in various engineering activities.
Method of classification of integumentary landscape elements
Voloshyn, V. I.; Bushuyev, Ye. I.; Parshina, O. I.; Fedorov, O. P.
We develop the method for the determination of technology for creation of thematic map of landscape elements of the territory of Ukraine using remotely sensed data. The purpose of our investigation is maximum formalization and accessibility of the method for many users.
Discrete vortex method simulations of aerodynamic admittance in bridge aerodynamics
DEFF Research Database (Denmark)
Rasmussen, Johannes Tophøj; Hejlesen, Mads Mølholm; Larsen, Allan
, and to determine aerodynamic forces and the corresponding ﬂutter limit. A simulation of the three-dimensional bridge responseto turbulent wind is carried out by quasi steady theory by modelling the bridge girder as a line like structure [2], applying the aerodynamic load coefﬁcients found from the current version...... of DVMFLOW in a strip wise fashion. Neglecting the aerodynamic admittance, i.e. the correlation of the instantaneous lift force to the turbulent ﬂuctuations in the vertical velocities, leads to higher response to high frequency atmospheric turbulence than would be obtained from wind tunnel tests....... In the present work we have extended the laminar oncoming ﬂow in DVMFLOW to a turbulent one, modelled by seeding the upstream ﬂow with vortex particles synthesized from prescribed atmospheric turbulence velocity spectra [3] . The discrete spectrum is sampled from the continuous spectrum subject to a lower cutoff...
Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
On the eigenvalue-eigenvector method for solution of the stationary discrete matrix Riccati equation
DEFF Research Database (Denmark)
Michelsen, Michael Locht
1979-01-01
The purpose of this correspondence is to point out that certain numerical problems encountered in the solution of the stationary discrete matrix Riccati equation by the eigenvalue-eigenvector method of Vanghan [1] can be avoided by a simple reformulation....
Evaluation of the discrete complex-image method for a NEC-like moment-method solution
Energy Technology Data Exchange (ETDEWEB)
Burke, G.J.
1996-01-05
The discrete image approximation for the field of a half-space is tested in the NEC antenna modeling program as an alternative to the interpolation method presently used. The accuracy and speed of the discrete image approximation are examined for varying number of images and approximation contour, and the solution for current is obtained on a horizontal wire approaching the interface.
Institute of Scientific and Technical Information of China (English)
高红利; 陈友川; 赵永志; 郑津洋
2011-01-01
Using the four-equation of linear spring-dashpot discrete element method and considering effect of the liquid bridge,the mixing and segregation process of size-type binary wet particulate system in a rotating horizontal drum is simulated.The effect of interstitial liquid on the mixing and segregation process is discussed.To assess the accuracy of the simulation result,some comparisons are made with the experimental date in the literature.The simulation results show that the liquid bridge between particles plays an important role in mixing and segregation process,and that the cohesion force induced by liquid-bridge leads to the formation of agglomerates of particles.As a result,segregation may be mitigated and mixing may be enhanced,and the network distribution of the contact forces is more uniform in wet particulate system.%采用所建立的四方程线性弹性-阻尼离散单元模型,同时考虑了液桥力的作用,对填充量为40%、含液量为3%的水平薄滚筒内S型（不同直径颗粒）二元湿颗粒体系混合过程进行了数值模拟,并与同等操作条件下不含液的干颗粒体系的混合行为进行了比较,分析了液体对颗粒体系混合行为的影响.同时还将计算结果与文献中的实验结果进行了比较.结果表明,由于湿颗粒间液桥力的牵引作用使不同性质的颗粒不易分离,使部分颗粒聚结成团,减弱了离析作用的影响,使得滚筒内湿颗粒的混合程度高于相同条件下的干颗粒体系,且接触力的分布较干颗粒体系更加均匀.通过对混合过程的模拟,直观地反映了混合过程中颗粒的微观运动特性和内部的力学结构,为研究湿颗粒体系混合过程机理提供了依据和参考.
Pindza, Edson; Maré, Eben
2017-03-01
A modified discrete singular convolution method is proposed. The method is based on the single (SE) and double (DE) exponential transformation to speed up the convergence of the existing methods. Numerical computations are performed on a wide variety of singular boundary value and singular perturbed problems in one and two dimensions. The obtained results from discrete singular convolution methods based on single and double exponential transformations are compared with each other, and with the existing methods too. Numerical results confirm that these methods are considerably efficient and accurate in solving singular and regular problems. Moreover, the method can be applied to a wide class of nonlinear partial differential equations.
Institute of Scientific and Technical Information of China (English)
LI Xikui; YAO Dongmei
2004-01-01
A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed. As compared with the existing discontinuous Galerkin finite element methods, the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured, whereas the discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously reduced,particularly, for material non-linear problems. Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed. Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
Directory of Open Access Journals (Sweden)
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
The edge-based face element method for 3D-stream function and flux calculations in porous media flow
Zijl, W.; Nawalany, M.
2004-01-01
We present a velocity-oriented discrete analog of the partial differential equations governing porous media flow: the edge-based face element method. Conventional finite element techniques calculate pressures in the nodes of the grid. However, such methods do not satisfy the requirement of flux cont
A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation
2013-05-01
examples of nonstan- dard discretizations include higher order continuity basis functions (splines and NURBS [34]), and discontinuous functions (DG...analysis: CAD, finite elements, NURBS , exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39–41):4135
The Superconvergence of Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
Imprioved L2-error estimates are computed for mixed finte element methods for second order nonlinear hyperbolic equations.Superconvergence results,L∞ in time and discrete L2 in space,are derived for both the solution and gradients on the rectangular domain.Results are given for the continuous-time case.
Dynamics of parabolic equations via the finite element method I. Continuity of the set of equilibria
Figueroa-López, R. N.; Lozada-Cruz, G.
2016-11-01
In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds.
Residual-based Methods for Controlling Discretization Error in CFD
2015-08-24
cjroy@vt.edu Co-I: Jeff Borggaard, Interdisciplinary Center for Applied Mathematics , jborggaard@vt.edu Virginia Tech, Blacksburg, Virginia Students...2008). Mathematically rigorous approaches for driving mesh adaptation are discussed in this proposal. Once the strategy for driving the adaption is...GTEE given in Equation (3) gives the continuous residual )()( hhh uuL (8) which is analogous to the finite element residual (Ainsworth and
Directory of Open Access Journals (Sweden)
Jingjun Zhao
2013-01-01
Full Text Available A finite element method (FEM for multiterm fractional partial differential equations (MT-FPDEs is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM, based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the main conclusions.
Deng, Yongbo; Korvink, Jan G.
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Deng, Yongbo; Korvink, Jan G
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Korvink, Jan G.
2016-01-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766
Chen, Jiefu; Zeng, Shubin; Dong, Qiuzhao; Huang, Yueqin
2017-02-01
An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.
LOW ORDER NONCONFORMING RECTANGULAR FINITE ELEMENT METHODS FOR DARCY-STOKES PROBLEMS
Institute of Scientific and Technical Information of China (English)
Shiquan Zhang; Xiaoping Xie; Yumei Chen
2009-01-01
In this paper, we consider lower order rectangular finite element methods for the singularly perturbed Stokes problem. The model problem reduces to a linear Stokes problem when the perturbation parameter is large and degenerates to a mixed formulation of Poisson's equation as the perturbation parameter tends to zero. We propose two 2D and two 3D nonconforming rectangular finite elements, and derive robust discretization error estimates. Numerical experiments are carried out to verify the theoretical results.
A new approach in cascade flow analysis using the finite element method
Baskharone, E.; Hamed, A.
1980-01-01
A new approach in analyzing the potential flow past cascades and single airfoils using the finite element method is developed. In this analysis the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils.
Directory of Open Access Journals (Sweden)
Yang Liu
2012-01-01
Full Text Available A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.
CASCADIC MULTIGRID METHOD FOR THE MORTAR ELEMENT METHOD FOR P1 NONCONFORMING ELEMENT
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Dan-hui Hong
2005-01-01
In this paper, we consider the cascadic multigrid method for the mortar P1 nonconforming element which is used to solve the Poisson equation and prove that the cascadic conjugate gradient method is accurate with optimal complexity.
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
A posteriori error estimator and AMR for discrete ordinates nodal transport methods
Energy Technology Data Exchange (ETDEWEB)
Duo, Jose I. [The Pennsylvania State University, 138 Reber Bldg, University Park (United States); Azmy, Yousry Y. [The Pennsylvania State University, 229 Reber Bldg, University Park (United States); Zikatanov, Ludmil T. [The Pennsylvania State University, 218 McAllister Bldg, University Park (United States)
2008-07-01
In the development of high fidelity transport solvers, optimization of the use of available computational resources and access to a tool for assessing quality of the solution are key to the success of large-scale nuclear systems' simulation. Error control provides the analyst with a confidence level in the numerical solution and enables for optimization of resources through Adaptive Mesh Refinement (AMR). In this paper, we derive an a posterior error estimator based on the nodal solution of the Arbitrarily High Order Transport Method of the Nodal type (AHOT-N). Furthermore, by making assumptions on the regularity of the solution, we represent the error estimator as a function of computable volume and element-edges residuals. The global L{sub 2} error norm is proved to be bound by the estimator. To lighten the computational load, we present a numerical approximation to the aforementioned residuals and split the global norm error estimator into local error indicators. These indicators are used to drive an AMR strategy for the spatial discretization. However, the indicators based on forward solution residuals alone do not bound the cell-wise error. The estimator and AMR strategy are tested in two problems featuring strong heterogeneity and highly transport streaming regime with strong flux gradients. The results show that the error estimator indeed bounds the global error norms and that the error indicator follows the cell-error's spatial distribution pattern closely. The AMR strategy proves beneficial to optimize resources, primarily by reducing the number of discrete variables unknowns solved for to achieve a prescribed solution accuracy in global L{sub 2} error norm. Likewise, AMR achieves higher accuracy compared to uniform refinement when resolving sharp flux gradients, for the same number of unknowns. (authors)
A local level set method based on a finite element method for unstructured meshes
Energy Technology Data Exchange (ETDEWEB)
Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)
2016-12-15
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.
Error analysis of finite element method for Poisson-Nernst-Planck equations
Energy Technology Data Exchange (ETDEWEB)
Sun, Yuzhou; Sun, Pengtao; Zheng, Bin; Lin, Guang
2016-08-01
A priori error estimates of finite element method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear element, and optimal error estimates in L∞(L2) norm with quadratic or higher-order element, for both semi- and fully discrete finite element approximations. Numerical experiments are also given to validate the theoretical results.
On conforming mixed finite element methods for incompressible viscous flow problems
Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.
1982-01-01
The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
A Teaching Experience: Aeroelasticity and the Finite Element Method
Directory of Open Access Journals (Sweden)
Mario Lázaro
2015-07-01
Full Text Available The aeroelastic modelling of aircraft structures is a fundamental area for the students of Aerospace Engineering Degree. This subject has a strongly multidisciplinary character and involves other several subjects like mechanics, vibrations, aerodynamics, structural analysis. Consequently, the students find stimulating the challenge of merging their knowledge at different areas. In this paper, a teaching experience on the solution of the aeroelastic problem of a 3D-wing through six different computer tasks is presented. The main objective is to attempt a relatively complex problem using a simple version of the Finite Element Method with only four degrees of freedom. The students begin creating the shape functions of the discrete model and finish solving the flutter instability problem.
Viscous incompressible flow simulation using penalty finite element method
Directory of Open Access Journals (Sweden)
Sharma R.L.
2012-04-01
Full Text Available Numerical analysis of Navier–Stokes equations in velocity– pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flowwidely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.
Vibration analysis of composite pipes using the finite element method with B-spline wavelets
Energy Technology Data Exchange (ETDEWEB)
Oke, Wasiu A.; Khulief, Yehia A. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2016-02-15
A finite element formulation using the B-spline wavelets on the interval is developed for modeling the free vibrations of composite pipes. The composite FRP pipe element is treated as a beam element. The finite pipe element is constructed in the wavelet space and then transformed to the physical space. Detailed expressions of the mass and stiffness matrices are derived for the composite pipe using the Bspline scaling and wavelet functions. Both Euler-Bernoulli and Timoshenko beam theories are considered. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the composite pipe. The developed wavelet-based finite element discretization scheme utilizes significantly less elements compared to the conventional finite element method for modeling composite pipes. Numerical solutions are obtained to demonstrate the accuracy of the developed element, which is verified by comparisons with some available results in the literature.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Institute of Scientific and Technical Information of China (English)
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
A dynamic model of mobile concrete pump boom based on discrete time transfer matrix method
Ren, Wu; Wu, Yunxin; Zhang, Zhaowei
2013-12-01
Mobile concrete pump boom is typical multibody large-scale motion manipulator. Due to posture constantly change in working process, kinematic rule and dynamic characteristic are difficult to solve. A dynamics model of a mobile concrete pump boom is established based on discrete time transfer matrix method (DTTMM). The boom system is divided into sub-structure A and substructure B. Sub-structure A is composed by the 1st boom and hydraulic actuator as well as the support. And substructure B is consists of the other three booms and corresponding hydraulic actuators. In the model, the booms and links are regarded as rigid elements and the hydraulic cylinders are equivalent to spring-damper. The booms are driven by the controllable hydraulic actuators. The overall dynamic equation and transfer matrix of the model can be assembled by sub-structures A and B. To get a precise result, step size and integration parameters are studied then. Next the tip displacement is calculated and compared with the result of ADAMS software. The displacement and rotation angle curves of the proposed method fit well with the ADAMS model. Besides it is convenient in modeling and saves time. So it is suitable for mobile concrete pump boom real-time monitoring and dynamic analysis. All of these provide reference to boom optimize and engineering application of such mechanisms.
Cluster analysis of European Y-chromosomal STR haplotypes using the discrete Laplace method
DEFF Research Database (Denmark)
Andersen, Mikkel Meyer; Eriksen, Poul Svante; Morling, Niels
2014-01-01
method can be used for cluster analysis to further validate the discrete Laplace method. A very important practical fact is that the calculations can be performed on a normal computer. We identified two sub-clusters of the Eastern and Western European Y-STR haplotypes similar to results of previous...... studies. We also compared pairwise distances (between geographically separated samples) with those obtained using the AMOVA method and found good agreement. Further analyses that are impossible with AMOVA were made using the discrete Laplace method: analysis of the homogeneity in two different ways......The European Y-chromosomal short tandem repeat (STR) haplotype distribution has previously been analysed in various ways. Here, we introduce a new way of analysing population substructure using a new method based on clustering within the discrete Laplace exponential family that models...
Lisjak, Andrea; Tatone, Bryan S. A.; Mahabadi, Omid K.; Grasselli, Giovanni; Marschall, Paul; Lanyon, George W.; Vaissière, Rémi de la; Shao, Hua; Leung, Helen; Nussbaum, Christophe
2016-05-01
The analysis and prediction of the rock mass disturbance around underground excavations are critical components of the performance and safety assessment of deep geological repositories for nuclear waste. In the short term, an excavation damaged zone (EDZ) tends to develop due to the redistribution of stresses around the underground openings. The EDZ is associated with an increase in hydraulic conductivity of several orders of magnitude. In argillaceous rocks, sealing mechanisms ultimately lead to a partial reduction in the effective hydraulic conductivity of the EDZ with time. The goal of this study is to strengthen the understanding of the phenomena involved in the EDZ formation and sealing in Opalinus Clay, an indurated claystone currently being assessed as a host rock for a geological repository in Switzerland. To achieve this goal, hybrid finite-discrete element method (FDEM) simulations are performed. With its explicit consideration of fracturing processes, FDEM modeling is applied to the HG-A experiment, an in situ test carried out at the Mont Terri underground rock laboratory to investigate the hydro-mechanical response of a backfilled and sealed microtunnel. A quantitative simulation of the EDZ formation process around the microtunnel is first carried out, and the numerical results are compared with field observations. Then, the re-compression of the EDZ under the effect of a purely mechanical loading, capturing the increase of swelling pressure from the backfill onto the rock, is considered. The simulation results highlight distinctive rock failure kinematics due to the bedded structure of the rock mass. Also, fracture termination is simulated at the intersection with a pre-existing discontinuity, representing a fault plane oblique to the bedding orientation. Simulation of the EDZ re-compression indicates an overall reduction of the total fracture area as a function of the applied pressure, with locations of ineffective sealing associated with self
Falkingham, Peter L; Gatesy, Stephen M
2014-12-23
Locomotion over deformable substrates is a common occurrence in nature. Footprints represent sedimentary distortions that provide anatomical, functional, and behavioral insights into trackmaker biology. The interpretation of such evidence can be challenging, however, particularly for fossil tracks recovered at bedding planes below the originally exposed surface. Even in living animals, the complex dynamics that give rise to footprint morphology are obscured by both foot and sediment opacity, which conceals animal-substrate and substrate-substrate interactions. We used X-ray reconstruction of moving morphology (XROMM) to image and animate the hind limb skeleton of a chicken-like bird traversing a dry, granular material. Foot movement differed significantly from walking on solid ground; the longest toe penetrated to a depth of ∼5 cm, reaching an angle of 30° below horizontal before slipping backward on withdrawal. The 3D kinematic data were integrated into a validated substrate simulation using the discrete element method (DEM) to create a quantitative model of limb-induced substrate deformation. Simulation revealed that despite sediment collapse yielding poor quality tracks at the air-substrate interface, subsurface displacements maintain a high level of organization owing to grain-grain support. Splitting the substrate volume along "virtual bedding planes" exposed prints that more closely resembled the foot and could easily be mistaken for shallow tracks. DEM data elucidate how highly localized deformations associated with foot entry and exit generate specific features in the final tracks, a temporal sequence that we term "track ontogeny." This combination of methodologies fosters a synthesis between the surface/layer-based perspective prevalent in paleontology and the particle/volume-based perspective essential for a mechanistic understanding of sediment redistribution during track formation.
A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES
A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...
Discrete vortex method simulations of the aerodynamic admittance in bridge aerodynamics
DEFF Research Database (Denmark)
Rasmussen, Johannes Tophøj; Hejlesen, Mads Mølholm; Larsen, Allan;
2010-01-01
We present a novel method for the simulation of the aerodynamic admittance in bluff body aerodynamics. The method introduces a model for describing oncoming turbulence in two-dimensional discrete vortex method simulations by seeding the upstream ﬂow with vortex particles. The turbulence...