hpGEM---A software framework for discontinuous Galerkin finite element methods

Pesch, Lars; Bell, Alexander Graham; Sollie, Henk; Ambati, V.R.; Bokhove, Onno; Vegt, J.J.W. van der

doi:10.1145/1268776.1268778

Cited by 24 publications

(24 citation statements)

References 14 publications

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“…Alternatively, a multi-scale modelling approach might be adopted such as the heterogeneuous, multiscale methodology [50], among others, in which closure relations for discretisations (e.g., [37]) depth-averaged shallow-layer models are coupled to DPM simulations in selected regions in space and time. Thus computational costs would be diminished while accurate closure relations are gathered 'on the fly' in time and space.…”

Section: Discussionmentioning

confidence: 99%

Closure relations for shallow granular flows from particle simulations

et al. 2012

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The discrete particle method (DPM) is used to model granular flows down an inclined chute with varying basal roughness, thickness and inclination. We observe three major regimes: arresting flows, steady uniform flows and accelerating flows. For flows over a smooth base, other (quasi-steady) regimes are observed: for small inclinations the flow can be highly energetic and strongly layered in depth; whereas, for large inclinations it can be non-uniform and oscillating. For steady uniform flows, depth profiles of density, velocity and stress are obtained using an improved coarse-graining method, which provides accurate statistics even at the base of the flow. A shallow-layer model for granular flows is completed with macro-scale closure relations obtained from micro-scale DPM simulations of steady flows. We obtain functional relations for effective basal friction, velocity shape factor, mean density, and the normal stress anisotropy as functions of layer thickness, flow velocity and basal roughness. Granular avalanche flows are common in both the natural environments and industry. They occur across many orders of magnitude. Examples range from rock slides, containing upwards of 1,000 m 3 of material; to the flow of sinter, pellets and coke into a blast furnace for iron-ore melting; down to the flow of sand in an hour-glass. The dynamics of these flows are influenced by many factors such as: polydispersity; variations in density; non-uniform shape; complex basal topography; surface contact properties; coexistence of static, steady and accelerating material; and, flow obstacles and constrictions. KeywordsDiscrete particle methods (DPMs) are an extremely powerful way to investigate the effects of these and other factors. With the rapid recent improvement in computational power the full simulation of the flow in a small hour glass of millions of particles is now feasible. However, complete DPM simulations of large-scale geophysical mass flow will, probably, never be possible.One of the main goals of the present research is to simulate large scale and complex industrial flows using granular shallow-layer equations. In this paper we will take the first step of using the DPM [9,34,42,43,46] to simulate small granular flows of mono-dispersed spherical particles in steady flow situations. We will use a refined and novel analysis to investigate three particular aspects of shallow chute flows: (i) how to obtain meaningful macro-scale fields from the DPM simulation, (ii) how to assess the flow dependence on the basal roughness, and (iii) how to validate the assumptions made in depth-averaged theory.The DPM simulations presented here will enable the construction of the mapping between the micro-scale and 123

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Section: Discussionmentioning

confidence: 99%

Closure relations for shallow granular flows from particle simulations

et al. 2012

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“…The first twelve of the basis functions used here are not the same as those that form the first-order second-family of Nédélec elements, defined in [23], but they span exactly the same space and have the same approximation properties as those. All numerical computations have been carried out in the framework of hpGEM [24], a software environment for DG discretisations suitable for a variety of physical problems. To solve the linear system that results from the DG discretisations, we use PETSc [3] and opt for MINRES as a suitable linear solver with incomplete Cholesky factorisation (ICC) 1 as preconditioners.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Optimal Penalty Parameters for Symmetric Discontinuous Galerkin Discretisations of the Time-Harmonic Maxwell Equations

2010

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We provide optimal parameter estimates and a priori error bounds for symmetric discontinuous Galerkin (DG) discretisations of the second-order indefinite time-harmonic Maxwell equations. More specifically, we consider two variations of symmetric DG methods: the interior penalty DG (IP-DG) method and one that makes use of the local lifting operator in the flux formulation. As a novelty, our parameter estimates and error bounds are (i) valid in the pre-asymptotic regime; (ii) solely depend on the geometry and the polynomial order; and (iii) are free of unspecified constants. Such estimates are particularly important in three-dimensional (3D) simulations because in practice many 3D computations occur in the pre-asymptotic regime. Therefore, it is vital that our numerical experiments that accompany the theoretical results are also in 3D. They are carried out on tetrahedral meshes with high-order (p = 1, 2, 3, 4) hierarchic H (curl)-conforming polynomial basis functions.

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“…Discretisations for linear compressible and incompressible flows were implemented for discontinuous Galerkin methods in the hpGEM C++ software framework [80]. The developed applications are consequently highly object-oriented, easy to maintain and extend.…”

Section: Tests Of Numerical Schemementioning

confidence: 99%

“…In this Appendix, the second version of hpGEM, a C++ software framework for DGFEM discretisations [80], will be introduced. As a particular example, an implementation of the application based on the Hamiltonian DGFEM discretisation discussed in Chapter 2 will be presented.…”

Section: Appendix a Design And Implementation Of A Dgfem Applicationmentioning

hpGEM---A software framework for discontinuous Galerkin finite element methods

Cited by 24 publications

References 14 publications

Closure relations for shallow granular flows from particle simulations

Closure relations for shallow granular flows from particle simulations

Optimal Penalty Parameters for Symmetric Discontinuous Galerkin Discretisations of the Time-Harmonic Maxwell Equations

Discrete and continuous hamiltonian systems for wave modelling

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