1,720,981 research outputs found
A new model of granular flows over general topography with erosion and deposition
No full text[[abstract]]A fundamental issue for describing gravity-driven flows over general topography is the search for an "optimal" coordinate. Bouchut and Westdickenberg [1] proposed an arbitrary coordinate system (BW) for general topography. The unified coordinate (UC) system (e.g., [2], [3]), which was developed for computational fluid dynamics, combines the advantages of both Eulerian and Lagrangian systems, so that the coordinates can instantaneously move with some singular surface within the flows. By utilizing the benefit of the BW coordinates and UC system, a new model of gravity-driven flows over general topography is derived, in which the erosion and deposition processes at the bed are considered. The depth-integrated mass and momentum equations are presented in the time-dependent and terrain-following coordinate system, which coincides with the interface distinguishing between the static and flowing layers. A shock-capturing numerical scheme is implemented to solve the derived equation system. Simulation results present the new features of this model and reveal a new physical insight of the erosion/deposition processes.[[note]]SC
Volume-weighted mixture theory for granular materials
No full text[[abstract]]In the present work we treat granular materials as mixtures composed of a solid and a surrounding void continuum, proposing then a continuum thermodynamic theory for it. In contrast to the common mass-weighted balance equations of mass, momentum, energy and entropy for mixtures, the volume-weighted balance equations and the associated jump conditions of the corresponding physical quantities are derived in terms of volume-weighted field quantities here. The evolution equations of volume fractions, volume-weighted velocity, energy, and entropy are presented and explained in detail. By virtue of the second law of thermodynamics, three dissipative mechanisms are considered which are specialized for a simple set of linear constitutive equations. The derived theory is applied to the analysis of reversible and irreversible compaction of cohesionless granular particles when a vertical oscillation is exerted on the system. In this analysis, a hypothesis for the existence of a characteristic depth within the granular material in its closely compacted state is proposed to model the reversible compaction.[[note]]SC
A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone
No full text[[abstract]]In this paper a detailed approach is proposed for the behavior of two-dimensional cohesionless granular materials moving down a confined inclined plane chute into the horizontal run-out zone, where the upslope propagating bore is treated as a growing deposition heap. It deals with the theoretical-numerical and experimental treatments. The depth-averaged field equations of balance of mass and linear momentum are described in moving coordinates for general topography as prescribed by Tai and Kuo [Acta Mech. 199, 71 (2008)]. A most simplistic approach to the erosion/deposition parameterization is proposed and the spatial coordinate coincides with the arc length of the variable basal surface. These equations describe the temporal evolution of the depth and velocity of the granular mass, especially the locations and shapes of the growing deposition heaps beneath the flowing layer. Experiments were carried out with different material supply rates and in two types of chutes, which differed by the bottom surface of the chute. In these experiments the sequential motions of the granular mass were recorded by a high-speed digital camera. The outlines of the deposition heap and flowing layers were obtained by successive images differences. Comparison of the experimental findings with the computational results proved to lead to good correspondence between experiment and theory. Even the development of the detailed geometry of the deposition heap is satisfactorily reproduced. (C) 2008 American Institute of Physics. [DOI: 10.1063/1.3033490][[note]]SC
MODELING SHALLOW GRAVITY-DRIVEN SOLID-FLUID MIXTURES OVER ARBITRARY TOPOGRAPHY
No full text[[abstract]]The purpose of this paper is to derive modeling equations for debris flows on real terrain. Thus, we use curvilinear coordinates adapted to the topography as introduced, e.g., by Bouchut and Westdicken berg [F. Bouchutand M. Westdickenberg, Commun. Math. Sci., 2(3), 359-389, 2004], and develop depth-averaged models of gravity-driven saturated mixtures of solid grains and pore fluid on an arbitrary rigid basal surface. First, by only specifying the interaction force and ordering approximations in terms of an aspect ratio between atypical length perpendicular to the topography, and atypical length parallel to the topography, we derive the governing equations for the shallow flow of a binary mixture, driven by gravitational force. In doing so, the non-uniformity through the avalanche depth of the constituent velocities and of the solid volume fraction is accounted for by coefficients of Boussinesq type. Then, the material behaviour peculiarities of both constituents properly enter the theory. One constituent is a granular solid. For its stresses we propose three models, one of them of Mohr-Coulomb type. The other constituent is a Newtonian/non-Newtonian fluid with small viscosity, obeying a viscous bottom friction condition. The final governing equations for the shallow flow of the mixture, incorporating the constitutive assumptions, are deduced, and the limiting equilibrium is then investigated.[[note]]SC
A hierarchy of avalanche models on arbitrary topography
No full text[[abstract]]We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca et al. (Math. Mod. Meth. Appl. Sci. 19, 127-171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage-Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surfaces.[[note]]SC
Description of local dilatancy and local rotation of granular assemblies by microstretch modeling
No full text[[abstract]]This study investigates the microstretch continuum modeling of granular assemblies while accounting for both the dilatant and rotational degrees of freedom of a macroelement. By introducing the solid volume fraction and the gyration radius of a granular system, the balance equations of the microstretch continuum are transformed into a new formulation of evolution equations comprising six variables: the solid volume fraction, the gyration radius, the velocity field, the averaged angular velocity, the rate of gyration radius, and the internal energy. The bulk microinertia density, the averaged angular velocity, and the microgyration tensor at a macroscopic point are obtained in terms of discrete physical quantities. The bulk part and the rotational part of the microgyration tensor are proposed as the two indices to measure the local dilatancy and local rotation of granular assemblies. It is demonstrated in the numerical simulation that the two indices can be used to identify the shear band evolution in a granular system under a biaxial compression. (C) 2009 Elsevier Ltd. All rights reserved.[[note]]SC
NON-CARTESIAN, TOPOGRAPHY-BASED AVALANCHE EQUATIONS AND APPROXIMATIONS OF GRAVITY DRIVEN FLOWS OF IDEAL AND VISCOUS FLUIDS
No full text[[abstract]]When dealing with geophysical flows across three-dimensional topography or other thin layer flows, for the physical modelling and for computational reasons, it is more convenient to use curvilinear coordinates adapted to the basal solid surface, instead of the Cartesian coordinates. Using such curvilinear coordinates, e. g. introduced by Bouchut and Westdickenberg,(3) and the corresponding contravariant components of vector and tensor fields, we derive in full generality the governing equations for the avalanche mass. These are next used to deduce (i) the thin layer equations for arbitrary topography, when the flowing mass is an ideal fluid, and (ii) the thin layer equations corresponding to arbitrary topography and to a viscous fluid that experiences bottom friction, modelled by a viscous sliding law.[[note]]SC
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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