20 research outputs found
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
IFCP Riemann solver: Application to tsunami modelling using GPUs
In this work, we present a simplified two-layer model of Savage-Hutter type to simulate tsunamis
generated by landslides (see (Fern´andez et al. 2008)). A layer composed of fluidized granular material is
assumed to flow within an upper layer composed of an inviscid fluid (e.g. water). The sediment layer ismodelled
by a Savage-Hutter type model where buoyancy effects have been considered. The system is discretized using
IFCP finite volume scheme. The first order IFCP scheme was introduced in (Fern´andez et al. 2011) and it is
constructed by using a suitable decomposition of a Roe matrix by means of a parabolic viscosity matrix, that
captures information of the intermediate fields (Intermediate Field Capturing Parabola). Its extension to high
order and two-dimensional domains is straightforward. To conclude, some numerical examples are presente
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.RamĂrez-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 AĂ‘OS DESPUÉS. Editorial Universitat Politècnica de València. 1798-1819. https://doi.org/10.4995/LC2015.2015.899OCS1798181
A semi-implicit approach for sediment transport models with gravitational effects
International audienceIn this work an efficient semi-implicit method, which is based on the theta method, for sediment bedload transport models with gravitational effects under subcritical regimes is proposed. Several families of models with gravitational effects are presented and rewritten under a general formulation that allows us to apply the semi-implicit method. In the numerical tests we focus on the application of a generalization of the Ashida-Michiue model, which includes the gradient of both the bedload and the fluid surface. Analytical steady states solutions (both lake at rest and non vanishing velocity) are deduced an approximated with the proposed scheme. In all the presented tests, the computational efforts are notably reduced thanks to the proposed method without loosing the accuracy in the results
A two-phase solid-fluid model for dense granular flows including dilatancy effects: comparison with submarine granular collapse experiments
We simulate here the collapse of granular columns immersed in a viscous fluid based on a simplified version of the model developed by [2]. The simulation quite well reproduces the dynamics and deposit of the granular mass as well as the excess pore fluid pressure measured in the laboratory experiments of [10] owing that dilatancy effects and pore pressure feedback are accounted for. In particular, the difference in the behaviour of initially loose and dense columns is reproduced numerically
Coupling superposed 1D and 2D shallow-water models: Source terms in finite volume schemes
International audienc
Non-hydrostatic layer-averaged Euler system with layerwise linear horizontal velocity
A new hierarchy of non-hydrostatic layer-averaged models for the non-stationary Euler equations is presented in this work, with improved dispersion relations. They are a generalisation of the layeraveraged models introduced in [9], named LDNH models, where the vertical profile of the horizontal velocity is layerwise constant. This assumption implies that solutions of LDNH can be seen as a first order Galerkin approximation of Euler equations. This work focuses on particular weak solutions where the horizontal velocity is layerwise linear on z and possibly discontinuous across layer interfaces. Several closure relations of the layer-averaged system with non-hydrostatic pressure are presented. The resulting models are named LIN-NH p models, with p = 0, 1, 2. Parameter p indicates the degree of the vertical velocity profile considered in the approximation of the vertical momentum equation. All the introduced models satisfy a dissipative energy balance. Finally, an analysis and a comparison of the dispersive properties of each model are carried out. We show that Models LIN-NH 1 and LIN-NH 2 provide a better dispersion relation, group velocity and shoaling than LDNH models