Development of a lattice Boltzmann method for two‐layered shallow‐water flow

Rocca, Michele La; Adduce, Claudia; Lombardi, Valentina; Sciortino, Giampiero; Hinkelmann, Reinhard

doi:10.1002/fld.2742

Cited by 46 publications

(30 citation statements)

References 35 publications

(157 reference statements)

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“…lock-exchange flows, have drawn much attention (see e.g. Shin, Dalziel & Linden 2004;Marino, Thomas & Linden 2005;Cantero et al 2007;La Rocca et al 2008, 2012aAdduce, Sciortino & Proietti 2012). Gravity currents propagating down an inclined boundary have been considered less but are also commonly encountered in geophysical environments and engineering applications, such as powder-snow avalanches (Hopfinger 1983) and spillage of hazardous materials (Fannelop 1994).…”

Section: Introductionmentioning

confidence: 99%

Experiments on gravity currents propagating on different bottom slopes

Dai

2013

J. Fluid Mech.

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Experiments for gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range 0 • θ 9 • are reported. While the flow patterns for gravity currents on θ = 6 • , 9 • are qualitatively different from those on θ = 0 • , similarities are observed in the acceleration phase for the flow patterns between θ = 2 • and θ = 6 • , 9 • and in the deceleration phase, the patterns for gravity currents on θ = 2 • are found similar to those on θ = 0 • . Previously, it was known that the front location history in the deceleration phase obeys a power-relationship, which is essentially an asymptotic form of the solution to thermal theory. We showed that this power-relationship applies only in the early stage of the deceleration phase, and when gravity currents propagate into the later stage of the deceleration phase, viscous effects become more important and the front location data deviate from this relationship. When the power-relationship applies, it is found that at θ = 9 • , u f (x f + x 0 ) 1/2 /B 0 1/2 ≈ 2.88 +0.19 −0.17 , which changes to 2.86 +0.13 −0.13 at θ = 6 • , 2.54 +0.08 −0.07 at θ = 2 • , and 1.51 +0.07 −0.07 on a horizontal boundary, where u f is the front velocity, (x f + x 0 ) is the front location measured from the virtual origin, and B 0 is the released buoyancy. Our results indicate that in the slope angle range 6 • θ 9 • , the asymptotic relationship between the front velocity and front location in the deceleration phase is not sensitive to the variation of slope angle. In the late deceleration phase when the front location data deviate from the power-relationship, we found that the flow patterns for θ = 6 • , 9 • are dramatically different from those for θ = 0 • , 2 • . For high slope angles, i.e. θ = 6 • , 9 • , the edge of the gravity current head experiences a large upheaval and enrolment by ambient fluid towards the end of the deceleration phase, while for low slope angles, i.e. θ = 0 • , 2 • , the gravity current head maintains a more streamlined shape without violent mixing with ambient fluid throughout the course of gravity current propagation. Our findings indicate two plausible routes to the finale of a gravity current event.

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Section: Introductionmentioning

confidence: 99%

Experiments on gravity currents propagating on different bottom slopes

Dai

2013

J. Fluid Mech.

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“…The development of gravity currents is typically an unsteady phenomenon, i.e., current kinematics and the inner density distribution are time varying, therefore the lockexchange setup is a simple and convenient way to investigating the flow features of these particular currents. Numerical modeling has also been used to investigate the evolution and impact of gravity currents [2,10,13,23,27,[33][34][35]44,47,59]. Although the motion of these currents is invariably three-dimensional, laboratory experiments and numerical results indicate that the large-scale features may be reasonably well described through a two-dimensional approach [27].…”

Section: Introductionmentioning

confidence: 99%

“…Several laboratory studies have been based on image analysis techniques to investigate the dynamics of gravity currents [2,25,33,34,36,54] the last two with the very same apparatus herein used). Recent advances in measurement techniques have enabled velocity and density measurements within gravity currents.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the head of gravity currents

et al. 2013

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The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying the density of the saline mixture in the lock and the bed roughness. Experiments were conducted in a Perspex flume, of horizontal bed and rectangular cross section, and recorded with a CCD camera. An image analysis technique was applied to visualize and characterize the current allowing thus the understanding of its general dynamics and, more specifically, of the current head dynamics. The temporal evolution of both head length and mass shows repeated stretching and breaking cycles: during the stretching phase, the head length and mass grow until reaching a limit, then the head becomes unstable and breaks. In the instants of break, the head aspect ratio shows a limit of 0.2 and the mass of 123Environ Fluid Mech the head is of the order of the initial mass in the lock. The average period of the herein called breaking events is seen to increase with bed roughness and the spatial periodicity of these events is seen to be approximately constant between runs. The rate of growth of the mass at the head is taken as a measure to assess entrainment and it is observed to occur at all stages of the current development. Entrainment rate at the head decreases in time suggesting this as a phenomenon ruled by local buoyancy and the similarity between runs shows independence from the initial reduced gravity and bed roughness.

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“…Examples of these cases are rapidly varied flows (RVF) in which the gradient of flow depth varies significantly over a short distance. For standard LBM, techniques to address numerical diffusivity have been considered by La Rocca et al (2012), amongst others. Such techniques will be examined for the new generalized scheme in a later paper.…”

Section: Numerical Diffusivity In Lbmmentioning

confidence: 99%

“…Frandsen (2008) discussed the suitability of a one-dimensional (1D) LBM with BGK scheme to simulate the behaviour of free-surface nonlinear waves in shallow water, with the assumption that the waves do not overturn (sub-critical flow conditions). In 2012 the numerical diffusivity of LBM for simulation of the two-layered, shallow-water flow was investigated (La Rocca, Adduce, Lombardi, Sciortino, & Hinkelmann, 2012). In that work two separate sets of LBM equations were used, one for each layer and the coupling terms between the two sets defined as external forces, acting on one layer by the other.…”

Section: Introductionmentioning

confidence: 99%

Generalized transformation of the lattice Boltzmann method for shallow water flows

Hedjripour

Callaghan

Baldock

2016

Journal of Hydraulic Research

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A one-dimensional lattice Boltzmann model is developed to solve the shallow water equations for steady and unsteady flows within both the subcritical and supercritical regimes. Previous work is extended through a generalized Galilean transformation applied to the standard scheme. The transformation yields a general asymmetric lattice Boltzmann model scheme which can successfully model a wide range of both subcritical and supercritical flow regimes, and enables implementation of the asymmetric model for practical purposes. In current work, a new set of equilibrium functions, boundary conditions and the external force weights are derived for the generalized transformed scheme. A new stability region is also defined, allowing selection of a lattice speed that maintains numerical stability for a wider range of sub-and supercritical flows and combinations of those flow conditions, compared to the previous scheme with fixed asymmetry. The model is validated against a range of benchmark cases in open-channel hydraulics that demonstrate the applicability of the new model.

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Development of a lattice Boltzmann method for two‐layered shallow‐water flow

Cited by 46 publications

References 35 publications

Experiments on gravity currents propagating on different bottom slopes

Experiments on gravity currents propagating on different bottom slopes

Dynamics of the head of gravity currents

Generalized transformation of the lattice Boltzmann method for shallow water flows

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