Simulation of Gravity Flow of Granular Materials in Silos

Gremaud, Pierre A.; Matthews, John V.

doi:10.1007/978-3-642-59721-3_8

Cited by 6 publications

(3 citation statements)

References 12 publications

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“…Applications of DG methods are predominantly found in fluid/gas dynamics [15,17,22], compressible [23,24]/incompressible flows [25,26], magneto-hydrodynamics [27], granular flows [28], viscoplastic crack growth and chemical transport [29]. Recently, there has been increasing interest in the application of DG methods in solid mechanics.…”

Section: Introductionmentioning

confidence: 99%

On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems

Bayat

Wulfinghoff

Kastian

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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In the present work, the discontinuous Galerkin (DG) method is applied to linear elasticity for two-dimensional and three-dimensional settings. A locking-free element formulation based on reduced integration and physically-based hourglass stabilization (Q1SP) is coupled for the first time with the DG framework. The incomplete interior penalty Galerkin method is chosen, being one example of different variations of DG methods. Several 2D and 3D typical benchmark problems of linear elasticity are investigated. A selection of numerical integration schemes for the boundary terms is presented, namely reduced and mixed integration schemes. The treatment of the surface terms by means of different rules of integration shows a significant influence on the performance of the resulting DG method in combination with the standard Q1 element. This intelligent treatment of the surface part leads to a DG variant with very good convergence properties.

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Section: Introductionmentioning

confidence: 99%

On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems

Bayat

Wulfinghoff

Kastian

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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show abstract

“…The discontinuous Galerkin (DG) methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements. These properties, which render them ideal to be used with hp-adaptive strategies, not only have brought these methods into the main stream of computational fluid dynamics, for example, in gas dynamics [11,14,39], compressible [10,[64][65][66] and incompressible [13,32,33] flows, turbomachinery [12], magneto-hydrodynamics [77], granular flows [52,53], semiconductor device simulation [24,25], viscoplastic crack growth and chemical transport [21], viscoelasticity [5,8,51], and transport of contaminant in porous media [1,28,29,41], but have also prompted their application to a wide variety of problems for which they were not originally intended like, for example, Hamilton-Jacobi equations [59,60,62], second-order elliptic problems [4,6,20,22,31,38,67,70], elasticity [46,54], and Korteweg-deVries equations [72,73].…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin methods

2003

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This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience. We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block‐diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another consequence of the use of discontinuous approximations is that these methods can easily handle irregular meshes with hanging nodes and approximations that have polynomials of different degrees in different elements. They are thus ideal for use with adaptive algorithms. Moreover, the methods are locally conservative (a property highly valued by the computational fluid dynamics community) and, in spite of providing discontinuous approximations, stable, and high‐order accurate. Even more, when applied to non‐linear hyperbolic problems, the discontinuous Galerkin methods are able to capture highly complex solutions presenting discontinuities with high resolution. In this paper, we concentrate on the exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems.

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“…The discontinuous Galerkin (DG) methods are locally conservative, stable, and high-order accurate methods which can easily handle complex geometries, irregular meshes with hanging nodes, and approximations that have polynomials of different degrees in different elements. These properties, which render them ideal to be used with ¢ ¡ -adaptive strategies, not only have brought these methods into the main stream of computational fluid dynamics, for example, in gas dynamics [11,39,14], compressible [10,64,66,65] and incompressible [13,33,32]flows, turbomachinery [12], magneto-hydrodynamics [77], granular flows [53,52], semiconductor device simulation [25,24], viscoplastic crack growth and chemical transport [21], viscoelasticity [51,5,8] and transport of contaminant in porous media [41,1,28,29], but have also prompted their application to a wide variety of problems for which they were not originally intended like, for example, Hamilton-Jacobi equations [60,59,62], second-order elliptic problems [38,67,6,70,20,22,31,4], elasticity [54,46], and Korteweg-deVries equations [73,72].…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin Methods

2000

Lecture Notes in Computational Science and Engineering

614

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Discontinuous Galerkin Methods This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience. We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block-diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another consequence of the use of discontinuous approximations is that these methods can easily handle irregular meshes with hanging nodes and approximations that have polynomials of different degrees in different elements. They are thus ideal for use with adaptive algorithms. Moreover, the methods are locally conservative (a property highly valued by the computational fluid dynamics community) and, in spite of providing discontinuous approximations, stable, and high-order accurate. Even more, when applied to non-linear hyperbolic problems, the discontinuous Galerkin methods are able to capture highly complex solutions presenting discontinuities with high resolution. In this paper, we concentrate on the exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems.

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Simulation of Gravity Flow of Granular Materials in Silos

Cited by 6 publications

References 12 publications

On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems

On the use of reduced integration in combination with discontinuous Galerkin discretization: application to volumetric and shear locking problems

Discontinuous Galerkin methods

Discontinuous Galerkin Methods

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