A Riemann solver for single-phase and two-phase shallow flow models based on relaxation. Relations with Roe and VFRoe solvers

We present a Riemann solver derived by a relaxation technique for classical single-phase shallow flow equations and for a two-phase shallow flow model describing a mixture of solid granular material and fluid. Our primary interest is the numerical approximation of this two-phase solid/fluid model, whose complexity poses numerical difficulties that cannot be efficiently addressed by existing solvers. In particular, we are concerned with ensuring a robust treatment of dry bed states. The relaxation system used by the proposed solver is formulated by introducing auxiliary variables that replace the momenta in the spatial gradients of the original model systems. The resulting relaxation solver is related to Roe solver in that its Riemann solution for the flow height and relaxation variables is formally computed as Roe’s Riemann solution. The relaxation solver has the advantage of a certain degree of freedom in the specification of the wave structure through the choice of the relaxation parameters. This flexibility can be exploited to handle robustly vacuum states, which is a well known difficulty of standard Roe’s method, while maintaining Roe’s low diffusivity. For the single-phase model positivity of flow height is rigorously preserved. For the two-phase model positivity of volume fractions in general is not ensured, and a suitable restriction on the CFL number might be needed. Nonetheless, numerical experiments suggest that the proposed two-phase flow solver efficiently models wet/dry fronts and vacuum formation for a large range of flow conditions.As a corollary of our study, we show that for single-phase shallow flow equations the relaxation solver is formally equivalent to the VFRoe solver with conservative variables of Gallouët and Masella [T. Gallouët, J.-M. Masella, Un schéma de Godunov approché C.R. Acad. Sci. Paris, Série I, 323 (1996) 77–84]. The relaxation interpretation allows establishing positivity conditions for this VFRoe method.     

Natrium-Triphenylcyanoborat — Cäsignost — ein Reagens zur Rubidiumtrennung

Zusammenfassung Rubidium kann quantitativ mit Cäsignost, Natriumtriphenylcyanoborat, in Abwesenheit von Cäsium gefällt werden. Ammoniak, Kalium sowie Spaltprodukte werden nicht mitgefällt. Bei Zugabe von inertem Salz (NaCl) wird die Fällung stark beschleunigt.

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Rubidium separation by sodium triphenyl cyanoborate (Cäsignost)

Summary Rubidium can be quantitatively precipitated with Cäsignost Na[(C₆H₅)₃ B(CN)] in absence of cesium. Ammonia, potassium and fission products do not interfere with the precipitation. The addition of an inert salt (NaCl) accelerates the precipitation more than twice.

     

Quantitative discrimination of water and hydrocarbons in porous media by magnetization prepared centric-scan SPRITE

MRI has considerable potential as a non-destructive probe of porous media, offering the possibility of rapid quantification of local oil and water content. This potential has not yet, however, been completely realized. In this paper, we explore a general magnetization preparation approach to the discrimination of water and oil in a model, representative, porous medium. These measurements have, as a common element, a centric scan pure phase encode readout based on the SPRITE methodology. Magnetization preparation permits facile T1, T2 and diffusion coefficient mapping as the basis for oil and water discrimination. Diffusion coefficient mapping proved to be the most robust approach to discrimination of oil and water. These methods are illustrated through static experiments and a dynamic immiscible fluid displacement experiment.     

Sensory analysis in the food industry as a tool for marketing decisions

In the food industry, sensory analysis can be useful to direct marketing decisions concerning not only products, for example product positioning with respect to competitors, but also market segmentation, customer relationship management, advertising strategies and price policies. In this paper we show how interesting information useful for marketing management can be obtained by combining the results from cub models and algorithmic data mining techniques (specifically, variable importance measurements from Random Forest). A case study on sensory evaluation of different varieties of Italian espresso is presented.     

Spatially resolved measurement of rock core porosity

Density weighted, centric scan, Conical SPRITE MRI techniques are applied in the current work for local porosity measurements in fluid saturated porous media. The methodology is tested on a series of sandstone core samples. These samples vary in both porosity and degree of local heterogeneity due to bedding plane structure. The MRI porosity measurement is in good agreement with traditional gravimetric measurements of porosity. Spatially resolved porosity measurements reveal significant porosity variation in some samples. This novel MRI technique should have applications to the characterization of local porosity in a wide variety of porous media.     

Approximation of the hydrostatic Navier–Stokes system for density stratified flows by a multilayer model: Kinetic interpretation and numerical solution

We present a multilayer Saint-Venant system for the numerical simulation of free surface density-stratified flows over variable topography. The proposed model formally approximates the hydrostatic Navier–Stokes equations with a density that varies depending on the spatial and temporal distribution of a transported quantity such as temperature or salinity. The derivation of the multilayer model is obtained by a Galerkin-type vertical discretization of the Navier–Stokes system with piecewise constant basis functions. In contrast with classical multilayer models in the literature that assume immiscible fluids, we allow here for mass exchange between layers. We show that the multilayer system admits a kinetic interpretation, and we use this result to formulate a robust finite volume scheme for its numerical approximation. Several numerical experiments are presented, including simulations of wind-driven stratified flows.