Discrete and continuous hamiltonian systems for wave modelling

Nurijanyan, S.

doi:10.3990/1.9789036511544

Cited by 2 publications

(2 citation statements)

References 84 publications

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“…The details of the numerical method used can be found in appendix A. The method is implemented in the hpGEM software package (Pesch et al 2007;Nurijanyan 2013), which provides a framework for DGFEM simulations. Due to the wetting and drying treatment and the small but finite gradients of the height in the front, the accuracy of the method is reduced to first order.…”

Section: Time-dependent Numerical Solutionmentioning

confidence: 99%

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

et al. 2019

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Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger material is transported to the flow front. This causes size segregation in the downstream direction, resulting in a flow front composed of large particles. Since the large particles are often more frictional than the small, the mobility of the flow front is reduced, resulting in a so-called bulbous head. This study focuses on the formation and evolution of this bulbous head, which we show to emerge in both a depth-averaged continuum framework and discrete particle simulations. Furthermore, our numerical solutions of the continuum model converge to a travelling wave solution, which allows for a very efficient computation of the long-time behaviour of the flow. We use small-scale periodic discrete particle simulations to calibrate (close) our continuum framework, and validate the simple one-dimensional (1-D) model with full-scale 3-D discrete particle simulations. The comparison shows that there are conditions under which the model works surprisingly well given the strong approximations made; for example, instantaneous vertical segregation.

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Section: Time-dependent Numerical Solutionmentioning

confidence: 99%

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

et al. 2019

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“…The details of the numerical method used can be found in appendix 3.A. The method is implemented in the hpGEM software package [82,83], which provides a framework for DGFEM simulations. Due to the wetting and drying treatment and the small but finite gradients of the height in the front, the accuracy of the method is reduced to first order.…”

Section: Time-dependent Numerical Solutionmentioning

confidence: 99%

On segregation in bidisperse granular flows

Denissen¹

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We consider a monodisperse dry granular material flowing down a rough inclined channel with downslope contracting sidewalls: theoretically and numerically. Utilising the depth-averaged shallow granular theory together with an empirical, but discrete particle simulations validated constitutive friction law, an extended novel one-dimensional (depth-and width-averaged) granular hydraulic theory is presented. For steady flows, besides describing the subcritical flow state, the one-dimensional model also predicts two other steady states, for a range of upstream prescribed flow conditions and channel openings. These states are supercritical flows with weak oblique shocks (smooth when widthaveraged) and flows with a steady jump in the contraction region. Both, super-and subcritical flow states were verified by numerically solving the depth-averaged two-dimensional shallow granular model. Despite the strong inhomogeneities in the linear contraction region, the one-and two-dimensional solutions (averaged across the channel) incomparably match well.

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Discrete and continuous hamiltonian systems for wave modelling

Cited by 2 publications

References 84 publications

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

Bulbous head formation in bidisperse shallow granular flow over an inclined plane

On segregation in bidisperse granular flows

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