2D granular flows with the μ(I)\mu(I) rheology and side walls friction: a well balanced multilayer discretization

We present here numerical modelling of granular flows with the $\mu(I)$ rheology in confined channels. The contribution is twofold: (i) a model to approximate the Navier-Stokes equations with the $\mu(I)$ 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 $\mu(I)$ but not with a constant friction coefficient

Derivation of a multilayer approach to model suspended sediment transport: application to hyperpycnal and hypopycnal plumes

We propose a multi-layer approach to simulate hyperpycnal and hypopycnal plumes in flows with free surface. The model allows to compute the vertical profile of the horizontal and the vertical components of the velocity of the fluid flow. The model can describe as well the vertical profile of the sediment concentration and the velocity components of each one of the sediment species that form the turbidity current. To do so, it takes into account the settling velocity of the particles and their interaction with the fluid. This allows to better describe the phenomena than a single layer approach. It is in better agreement with the physics of the problem and gives promising results. The numerical simulation is carried out by rewriting the multi-layer approach in a compact formulation, which corresponds to a system with non-conservative products, and using path-conservative numerical scheme. Numerical results are presented in order to show the potential of the model

Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in which the number of vertical layers and their distribution are allowed to change in different regions of the computational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a significant efficiency improvement for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justified, the resulting discretization does not introduce any major spurious feature and allows again to reduce substantially the computational cost in areas with complex bathymetry. As an example of the potential of the proposed technique, an application to a sediment transport problem is presented, showing a remarkable improvement with respect to standard discretization approaches

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 $\mu(I)$ 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

Modelo fenomenológico para la predicción del aceite extraído de Moringa oleífera utilizando un equipo de laboratorio Soxhlet

Moringa oleifera is an oilseed crop with poten­tial for biodiesel production. The second step in this process is the extraction of oil. Extraction in hot water, with a Soxhlet apparatus and the ultrasound technique are the most commonly used methods. The aim of the present work was to obtain a phenomenological model for the Moringa oleifera oil extraction process using Soxhlet. Effective diffusivity for Moringa oil through the kernels is obtained, using the kinetics of the extraction process (experimentally determined) and the Fick’s diffusion second law for non-steady state. The value of 0.685·10-12 m2/s fully matched reports on effective diffusion coefficient for other solids. It was also verified from the statistical analysis and a linear fit for experimental data that the model can be used to describe the oil extraction process of Moringa oleifera in the Soxhlet extractor, responding to the diffusive phenomenon (process controlled by internal resistance).Moringa oleífera es un cultivo oleaginoso con potencial para producir biodiesel. La segunda etapa del proceso es la extracción de aceite. Los métodos más utilizados son la extracción en agua caliente, con Soxhlet y la técnica de ultrasonidos. El objetivo del trabajo fue obtener un modelo fenomenológico para el proceso de extracción de aceite de Moringa oleífera en Soxhlet. Utilizando la cinética del proceso extractivo (determinada experimentalmente) y la segunda ley de difusión de Fick en estado no estacionario, se obtuvo la difusividad efectiva del aceite de Moringa a través de los cotiledones. El valor de 0.685·10-12 m2/s, se corresponde con reportes del coeficiente de difusión efectiva para otros sólidos. Se verificó a partir del análisis estadístico y ajuste lineal de los datos experimentales, que el modelo describe el proceso de extracción de aceite de Moringa oleífera en Soxhlet, respondiendo al fenómeno difusivo (proceso controlado por la resistencia interna)

A deep learning approach for the recognition of urban ground pavements in historical sites

Urban management is a topic of great interest for local administrators, particularly because it is strongly connected to smart city issues and can have a great impact on making cities more sustainable. In particular, thinking about the management of the physical accessibility of cities, the possibility of automating data collection in urban areas is of great interest. Focusing then on historical centres and urban areas of cities and historical sites, it can be noted that their ground surfaces are generally characterised by the use of a multitude of different pavements. To strengthen the management of such urban areas, a comprehensive mapping of the different pavements can be very useful. In this paper, the survey of a historical city (Sabbioneta, in northern Italy) carried out with a Mobile Mapping System (MMS) was used as a starting point. The approach here presented exploit Deep Learning (DL) to classify the different pavings. Firstly, the points belonging to the ground surfaces of the point cloud were selected and the point cloud was rasterised. Then the raster images were used to perform a material classification using the Deep Learning approach, implementing U-Net coupled with ResNet 18. Five different classes of materials were identified, namely sampietrini, bricks, cobblestone, stone, asphalt. The average accuracy of the result is 94%.Xunta de Galicia | Ref. ED481B-2019-061Xunta de Galicia | Ref. ED431C 2020/01Ministerio de Ciencia e Innovación | Ref. PID2019-105221RB-C43Ministerio de Ciencia e Innovación | Ref. RYC2020-029193-

A dark energy multiverse

We present cosmic solutions corresponding to universes filled with dark and phantom energy, all having a negative cosmological constant. All such solutions contain infinite singularities, successively and equally distributed along time, which can be either big bang/crunchs or big rips singularities. Classicaly these solutions can be regarded as associated with multiverse scenarios, being those corresponding to phantom energy that may describe the current accelerating universe