arXiv subjects

Anne Mangeney

Publications and source records attributed to Anne Mangeney.

10 recordsLinked to original sources

arXiv2024

Well-posedness and potential-based formulation for the propagation of hydro-acoustic waves and tsunamis

We study a linear model for the propagation of hydro-acoustic waves and tsunami in a stratified free-surface ocean. A formulation was previously obtained by linearizing the compressible Euler equations. The new formulation is obtained by studying the functional spaces and operators associated to the model. The mathematical study of this new formulation is easier and the discretization is also more efficient than for the previous formulation. We prove that both formulations are well posed and show that the solution to the first formulation can be obtained from the solution to the second. Finally, the formulations are discretized using a spectral element method, and we simulate tsunamis generation from submarine earthquakes and landslides.

math.AP↗

arXiv2021

Benchmarking Exercises for Granular Flows

For the 2007 International Forum on Landslide Disaster Management framework, our team performed several numerical simulations on both theoretical and natural cases of granular flows. The objective was to figure out the ability and the limits of our numerical model in terms of reproduction and prediction. Our benchmarking exercises show that for almost all the cases, the model we use is able to reproduce observations at the field scale. Calibrated friction angles are almost similar to that used in other models and the shape of the final deposits is in good agreement with observation. However, as it is tricky to compare the dynamics of natural cases, these exercises do not allow us to highlight the good ability to reproduce the behavior of natural landslides. Nevertheless, by comparing with analytical solution, we show that our model presents very low numerical dissipation due to the discretization and to the numerical scheme used. Finally, in terms of mitigation and prediction, the different friction angles used for each cases figure out the limits of using such model as long as constitutive equations for granular media are not known.

physics.geo-ph↗

arXiv2021

Experimental assessment of the effective friction at the base of granular chute flows on smooth incline

We report on direct measurements of the basal force components for granular material flowing down a smooth incline. We investigate granular flows for a large range of inclination angles from teta=13.4° to 83.6° and various gate opening of the chute. We find that the effective basal friction coefficient, muB, obtained from the ratio of the longitudinal force to the normal one exhibits a systematic increase with increasing slope angle and a significant weakening with increasing particle hold-up H (the depth-integrated particle volume fraction). At low angles, the basal friction is slightly less than or equal to tan(teta). The deviation from tan(teta) can be interpreted as a contribution from the side-wall to the overall friction. At larger angles, the basal friction muB saturates at an asymptotic value that is dependent on the gate opening of the chute. Importantly, our data confirm the outcomes of recent discrete numerical simulations. First, for steady and fully developed flows as well as for moderately accelerated ones, the variation of the basal friction can be captured through a unique dimensionless number, the Froude number Fr, defined as Fr=U/(gHcos(teta))^1/2, where U is the mean flow velocity. Second, the mean velocity scales with the particle hold-up H with a power exponent close to 1/4, contrasting with the Bagnold scaling (U~H^3/2).

cond-mat.soft↗

arXiv2021

Acoustic emissions of nearly steady and uniform granular flows: a proxy for flow dynamics and velocity fluctuations

The seismic waves emitted during granular flows are generated by different sources: high frequencies by inter-particle shocks and low frequencies by global motion and large scale deformation. To unravel these different mechanisms, an experimental study has been performed on the seismic waves emitted by dry quasi steady granular flows. The emitted seismic waves were recorded using shock accelerometers and the flow dynamics were captured with a fast camera. The mechanical characteristics of the particle shocks were analyzed, along with the duration between shocks and the correlations in the particle motion. The high-frequency seismic waves (1-50 kHz) were found to originate from particle shocks and waves trapped in the flowing layer. The low-frequency waves (20-60 Hz) were generated by the oscillations of the particles along their trajectories, i.e. from cycles of dilation/compression during the shear. The profiles of granular temperature (i.e. the square of particle velocity fluctuations) and average velocity were measured and related to the average properties of the flow as well as to the slope angle and flow thickness. These profiles were then used in a simple steady granular flow model to predict the radiated seismic energy and the energetic efficiency, i.e. the fraction of the flow potential energy converted to seismic energy. Scaling laws relating the seismic power, the shear strain rate and the inertial number were derived. In particular, the emitted seismic power is proportional to the granular temperature, which is also related to the mean flow velocity.

cond-mat.soft↗

arXiv2020

A weakly non-hydrostatic shallow model for dry granular flows

A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $μ(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope.

physics.flu-dyn↗

arXiv2020

Multilayer models for shallow two-phase debris flows with dilatancy effects

We present here a multilayer model for shallow grain-fluid mixtures with dilatancy effects. It can be seen as a generalization of the depth-averaged model presented in Bouchut et al. (2016), that includes dilatancy effects by considering a two-layer model, a mixture grain-fluid layer and an upper fluid layer, to allow the exchange of fluid between them. In the present work the approximation of the mixture layer is improved including normal variations of the velocities and concentrations of the two phases thanks to the multilayer approach. In the model presented here dilatancy effects induce in particular a non-hydrostatic pressure for both phases related to the excess pore fluid pressure. We identified here one of the main numerical difficulty of solving two-phase shallow debris flows models: the strongly non-linear behaviour and abrupt changes of the excess pore fluid pressure when starting from non-equilibrium conditions. We propose a simplified approach to approximate the excess pore fluid pressure in the simple case of uniform flows. Our method makes it possible to introduce two or three layers in the normal directions with a reasonable approximation. Analytical solutions for uniform grain-fluid flows over inclined planes, with and without side wall friction, are calculated and compared to the proposed model. In the numerical results, we observe that the proposed model with a two layer description of the mixture accurately represents the velocity measured at the surface of the mixture in the laboratory experiments. This is obviously poorly represented by the depth-averaged velocity in single-layer models. Our numerical results show a significant impact of the parameters involved in dilatancy law, in particular on the calculation of the time evolution of the excess pore fluid pressure.

physics.flu-dyn↗

arXiv2017

Numerical approximation of the 3d hydrostatic Navier-Stokes system with free surface

In this paper we propose a stable and robust strategy to approximate the 3d incompressible hydrostatic Euler and Navier-Stokes systems with free surface. Compared to shallow water approximation of the Navier-Stokes system, the idea is to use a Galerkin type approximation of the velocity field with piecewise constant basis functions in order to obtain an accurate description of the vertical profile of the horizontal velocity. Such a strategy has several advantages. It allows - to rewrite the Navier-Stokes equations under the form of a system of conservation lawswith source terms, - the easy handling of the free surface, which does not require moving meshes, - the possibility to take advantage of robust and accurate numerical techniques developed in extensive amount for Shallow Water type systems. Compared to previous works of some of the authors, the three dimensional case is studied in this paper. We show that the model admits a kinetic interpretation including the vertical exchanges terms, and we use this result to formulate a robust finite volume scheme for its numerical approximation. All the aspects of the discrete scheme (fluxes, boundary conditions,. . . ) are completely described and the stability properties of the proposed numerical scheme (well-balancing, positivity of the water depth,. . . ) are discussed. We validate the model and the discrete scheme with some numerical academic examples (3d non stationary analytical solutions) and illustratethe capability of the discrete model to reproduce realistic tsunami waves.

math.NA↗

arXiv2015

A multilayer shallow model for dry granular flows with the $μ(I)$ rheology: Application to granular collapse on erodible beds

In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $μ(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical treatment of the free surface of the modelled flows, (ii) exact conservation of mass and (iii) the ability to compute 3D profiles of the velocities in the directions along and normal to the slope. The derivation of the model follows [14] and introduces a dimensional analysis based on the shallow flow hypothesis. The proposed first order multilayer model fully satisfies a dissipative energy equation. A comparison with an analytical solution with a non-constant normal profile of the downslope velocity demonstrates the accuracy of the numerical model. Finally, by comparing the numerical results with experimental data, we show that the proposed multilayer model with the $μ(I)$-rheology reproduces qualitatively the effect of the erodible bed on granular flow dynamics and deposits, such as the increase of runout distance with increasing thickness of the erodible bed. We show that the use of a constant friction coefficient in the multilayer model leads to the opposite behaviour. This multilayer model captures the different normal profiles of the downslope velocity during the different phases of the flow (acceleration, stopping, etc.) including the presence of static and flowing zones within the granular column.

math-ph↗

arXiv2014

An energy-consistent depth-averaged Euler system: derivation and properties

In this paper, we present an original derivation process of a non-hydrostatic shallow water-type model which aims at approximating the incompressible Euler and Navier-Stokes systems with free surface. The closure relations are obtained by aminimal energy constraint instead of an asymptotic expansion. The model slightly differs from thewell-known Green-Naghdi model and is confronted with stationary andanalytical solutions of the Euler system corresponding to rotationalflows. At the end of the paper, we givetime-dependent analytical solutions for the Euler system that are alsoanalytical solutions for the proposed model but that are not solutionsof the Green-Naghdi model. We also give and compare analytical solutions of thetwo non-hydrostatic shallow water models.

math.NA↗

arXiv2005

Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile

Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition.

cond-mat.other↗