23 research outputs found
2D granular flows with the rheology and side walls friction: a well balanced multilayer discretization
We present here numerical modelling of granular flows with the
rheology in confined channels. The contribution is twofold: (i) a model to
approximate the Navier-Stokes equations with the rheology through an
asymptotic analysis. Under the hypothesis of a one-dimensional flow, this model
takes into account side walls friction; (ii) a multilayer discretization
following Fern\'andez-Nieto et al. (J. Fluid Mech., vol. 798, 2016, pp.
643-681). In this new numerical scheme, we propose an appropriate treatment of
the rheological terms through a hydrostatic reconstruction which allows this
scheme to be well-balanced and therefore to deal with dry areas. Based on
academic tests, we first evaluate the influence of the width of the channel on
the normal profiles of the downslope velocity thanks to the multilayer approach
that is intrinsically able to describe changes from Bagnold to S-shaped (and
vice versa) velocity profiles. We also check the well balance property of the
proposed numerical scheme. We show that approximating side walls friction using
single-layer models may lead to strong errors. Secondly, we compare the
numerical results with experimental data on granular collapses. We show that
the proposed scheme allows us to qualitatively reproduce the deposit in the
case of a rigid bed (i. e. dry area) and that the error made by replacing the
dry area by a small layer of material may be large if this layer is not thin
enough. The proposed model is also able to reproduce the time evolution of the
free surface and of the flow/no-flow interface. In addition, it reproduces the
effect of erosion for granular flows over initially static material lying on
the bed. This is possible when using a variable friction coefficient
but not with a constant friction coefficient
A two-layer shallow water model for bedload sediment transport: convergence to Saint-Venant-Exner model
A two-layer shallow water type model is proposed to describe bedload sediment
transport. The upper layer is filled by water and the lower one by sediment.
The key point falls on the definition of the friction laws between the two
layers, which are a generalization of those introduced in Fern\'andez-Nieto et
al. (ESAIM: M2AN, 51:115-145, 2017). This definition allows to apply properly
the two-layer shallow water model for the case of intense and slow bedload
sediment transport. Moreover, we prove that the two-layer model converges to a
Saint-Venant-Exner system (SVE) including gravitational effects when the ratio
between the hydrodynamic and morphodynamic time scales is small. The SVE with
gravitational effects is a degenerated nonlinear parabolic system. This means
that its numerical approximation is very expensive from a computational point
of view, see for example T. Morales de Luna et al. (J. Sci. Comp., 48(1):
258-273, 2011). In this work, gravitational effects are introduced into the
two-layer system without such extra computational cost. Finally, we also
consider a generalization of the model that includes a non-hydrostatic pressure
correction for the fluid layer and the boundary condition at the sediment
surface. Numerical tests show that the model provides promising results and
behave well in low transport rate regimes as well as in many other situations
Formal deduction of the Saint-Venant-Exner model including arbitrarily sloping sediment beds and associated energy
In this work we present a deduction of the Saint-Venant-Exner model through
an asymptotic analysis of the Navier-Stokes equations. A multi-scale analysis
is performed in order to take into account that the velocity of the sediment
layer is smaller than the one of the fluid layer. This leads us to consider a
shallow water type system for the fluid layer and a lubrication Reynolds
equation for the sediment one. This deduction provides some improvements with
respect to the classical Saint-Venant-Exner model: (i) the deduced model has an
associated energy. Moreover, it allows us to explain why classical models do
not have an associated energy and how to modify them in order to recover a
model with this property. (ii) The model incorporates naturally a necessary
modification that must be taken into account in order to be applied to
arbitrarily sloping beds. Furthermore, we show that this modification is
different of the ones considered classically, and that it coincides with a
classical one only if the solution has a constant free surface. (iii) The
deduced solid transport discharge naturally depends on the thickness of the
moving sediment layer, what allows to ensure sediment mass conservation.
Moreover, we include a simplified version of the model for the case of
quasi-stationary regimes. Some of these simplified models correspond to the
generalization of classical ones such as Meyer-PeterM\"uller and
Ashida-Michiue models. Three numerical tests are presented to study the
evolution of a dune for several definition of the repose angle, to see the
influence of the proposed definition of the effective shear stress in
comparison with the classical one, and by comparing with experimental data.Comment: 44 pages, sumbitted to Advances in Water Resources 17 july 201
A two-phase shallow debris flow model with energy balance
This paper proposes a thin layer depth-averaged two-phase model provided by a dissipative energy balance to describe avalanches of solid-fluid mixtures. This model is derived from a 3D two-phase model based on the equations proposed by Jackson [The Dynamics of Fluidized Particles. Cambridges Monographs on Mechanics (2000)] which takes into account the force of buoyancy and the forces of interaction between the solid and fluid phases. Jackson’s model is based on mass and momentum conservation within the two phases, i.e. two vector and two scalar equations. This system has five unknowns: the solid volume fraction, the solid and fluid pressures and the solid and fluid velocities, i.e. three scalars and two vectors. As a result, an additional equation is necessary to close the system. Surprisingly, this issue is inadequately accounted for in the models that have been developed on the basis of Jackson’s work. In particular, Pitman and Le [Philos. Trans. R. Soc. A 363 (2005) 799–819] replaced this closure simply by imposing an extra boundary condition. If the pressure is assumed to be hydrostatic, this condition can be considered as a closure condition. However, the corresponding model cannot account for a dissipative energy balance. We propose here a closure equation to complete Jackson’s model, imposing incompressibility of the solid phase. We prove that the resulting whole 3D model is compatible with a dissipative energy balance. From this model, we deduce a 2D depth-averaged model and we also prove that the energy balance associated with this model is dissipative. Finally, we propose a numerical scheme to approximate the depth-averaged model. We present several numerical tests for the 1D case that are compared to the results of the model proposed by Pitman and Le
Formal deduction of the Saint-Venant-Exner model including arbitrarily sloping sediment beds and associated energy
In this work we present a deduction of the Saint-Venant-Exner model through
an asymptotic analysis of the Navier-Stokes equations. A multi-scale analysis is
performed in order to take into account that the velocity of the sediment layer is
smaller than the one of the
uid layer. This leads us to consider a shallow water
type system for the
uid layer and a lubrication Reynolds equation for the sediment
one. This deduction provides some improvements with respect to the classical Saint-
Venant-Exner model: (i) the deduced model has an associated energy. Moreover,
it allows us to explain why classical models do not have an associated energy and
how to modify them in order to recover a model with this property. (ii) The model
incorporates naturally a necessary modi cation that must be taken into account in
order to be applied to arbitrarily sloping beds. Furthermore, we show that this
modi cation is di erent of the ones considered classically, and that it coincides with
a classical one only if the solution has a constant free surface. (iii) The deduced
solid transport discharge naturally depends on the thickness of the moving sediment
layer, what allows to ensure sediment mass conservation. Moreover, we include a
simpli ed version of the model for the case of quasi-stationary regimes. Some of these
simpli ed models correspond to the generalization of classical ones such as Meyer-
Peter&M uller and Ashida-Michiue models. Three numerical tests are presented to
study the evolution of a dune for several de nition of the repose angle, to see the
in
uence of the proposed de nition of the e ective shear stress in comparison with
the classical one, and by comparing with experimental data
A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel-Bulkley model
40 pages. 12 figures.International audienceWe are interested in the derivation of an integrated Herschel-Bulkley model for shallow flows, as well as in the design of a numerical algorithm to solve the resulting equations. The goal is to simulate the evolution of thin sheet of viscoplastic materials on inclined planes and, in particular, to be able to compute the evolution from dynamic to stationary states. The model involves a variational inequality and it is valid from null to moderate slopes. The proposed numerical scheme is well balanced and involves a coupling between a duality technique (to treat plasticity), a fixed point method (to handle the power law) and a finite volume discretization. Several numerical tests are done, including a comparison with an analytical solution, to confirm the well balanced property and the ability to cope with the various rheological regimes associated with the Herschel-Bulkley constitutive law
The mur neutralisant as an active thermal system: Saint Gobain tests (1931) versus CFD simulation (2015)
[EN] At the same time as the initial development of air conditioning systems for indoor climate control in buildings were
occurring in USA, Le Corbusier and Lyon made truly innovative proposals for different projects he was working on in
Europe. These served to generate homogenous thermal environments and focused on the combined effect of his mur
neutralisant and respiration exacte. The clearest example of their shortcomings is the City of Refuge in Paris (1930-33).
Given the technological and economic mistrust towards these proposals, as it was impossible to execute these according to
the original plan these were not pursued. CFD simulations carried out by our research team confirm that the mur
neutralisant and respiration exacte for the City of Refuge in Paris would have functioned together if they had been executed
following the original plans. The main aim of this paper is to confirm the validity of the mur neutralisant as an active thermal
system for buildings. Firstly, the results of the tests carried out by the engineers of Saint Gobain are compared to the results
of the CFD simulations. Based on the comparison of the results from the physical models tested in Saint Gobain laboratories
and CFD energy model simulations, a possible calibration is proposed for CFD which might prompt the establishment of
other operation hypotheses.Ramírez-Balas, C.; Sendra, J.; Suárez, R.; Fernández-Nieto, E.; Narbona-Reina, G. (2016). The mur neutralisant as an active thermal system: Saint Gobain tests (1931) versus CFD simulation (2015). En LE CORBUSIER. 50 AÑOS DESPUÉS. Editorial Universitat Politècnica de València. 1798-1819. https://doi.org/10.4995/LC2015.2015.899OCS1798181
the WAF method for non-homogeneous SWE with pollutant
This paper deals with the extension of the WAF method to discretize Shallow Water Equations with pollutants. We consider two different versions of the WAF method, by approximating the intermediate waves using the flux of HLL or the direct approach of HLLC solver. It is seen that both versions can be written under the same form with different definitions for the approximation of the velocity waves. We also propose an extension of the method to non-homogeneous systems. In the case of homogeneous systems it is seen that we can rewrite the third component of the numerical flux in terms of an intermediate wave speed approximation. We conclude that – in order to have the same relation for non-homogeneous systems – the approximation of the intermediate wave speed must be modified. The proposed extension of the WAF method preserves all stationary solutions, up to second order accuracy, and water at rest in an exact way, even with arbitrary pollutant concentration. Finally, we perform several numerical tests, by comparing it with HLLC solver, reference solutions and analytical solutions
Nurses' perceptions of aids and obstacles to the provision of optimal end of life care in ICU
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