1,720,967 research outputs found
Dam break in rectangular channels with different upstream-downstream widths
No full textThe classic Stoker dam-break problem (Stoker, 1957) is revisited in cases of different channel widths upstream and downstream of the dam. The channel is supposed to have a rectangular cross section and a horizontal and frictionless bottom. The system of the shallow water equations is enriched, using the width as a space-dependent variable, together with the depth and the unit discharge, which conversely depend on both space and time. Such a formulation allows a quasi-analytical treatment of the system, whose solution is similar to that of the classic Stoker solution when the downstream/upstream depth ratio is sufficiently large, except that a further stationary contact wave exists at the dam position. When the downstream/upstream depth ratio is small, the solution is richer than the Stoker solution because the critical state occurs at the dam position and the solution itself becomes resonant at the same position, where two eigenvalues are null and the strict hyperbolicity of the system is lost. The limits that identify the flow regime for channel contraction and channel expansion are discussed after showing that the nondimensional parameters governing the problem are the downstream/upstream width ratio and the downstream/upstream initial depth ratio. After the introduction of the previous analytical framework, a numerical analysis is also performed to evaluate a numerical method that is conceived to suitably capture rarefactions, shock waves and contact waves. A second-order method is adopted, employing a Dumbser-Osher-Toro Riemann solver equipped with a nonlinear path. Such an original nonlinear path is shown to perform better than the classic linear path when contact waves of large amplitude must be captured, being able to obtain specific energy conservation and mass conservation at the singularity. The codes, written in MATLAB (MathWorks Inc.) language, are made available in Mendeley Data repository
A one-dimensional augmented Shallow Water Equations system for channels of arbitrary cross-section
No full textThis work provides a new formulation of the one-dimensional augmented Shallow Water Equations system for open channels and rivers with arbitrarily shaped cross sections, suitable for numerical integration when discontinuous geometry is encountered. The additional variable considered can be the bottom elevation, a reference width, a shape coefficient, or a vector containing these or other geometric parameters. The appropriate numerical method, which is well suited to coupling with the mathematical one, is a path-conservative method, capable of reconstructing the behaviour of physical and geometrical variables at the cell boundaries, where the discrete solution of hyperbolic systems of equations is discontinuous. A nonlinear path suitable for the shallow water context is adopted. The resulting model is shown to be well-balanced and accurate to the second order and is further validated against analytical solutions related to channels with power-law cross sections, specifically for dam break patterns over a variable-width channel and the run-up dynamics of long water waves over sloping bays
Crollo diga in corrispondenza di brusche variazioni di larghezza
No full textSi affronta il classico problema di Stoker, rivisitandolo per analizzare il comportamento del sistema fisico
quando nella sezione dello sbarramento esista un brusco restringimento o allargamento dell’alveo, supposto
per semplicità rettangolare e piatto
Dam break in power-law cross-section channels with different upstream/downstream widths
No full textThe dam break problem is studied in a channel characterised by a power-law cross-section, with different widths upstream and downstream of the dam. This research is the extension of a previous study by Valiani and Caleffi (2019), designed for rectangular cross-sections, to different and more complex geometries. A 1D a-SWE (one dimensional augmented Shallow Water Equation) system is developed, which has been shown to capture the full range of possible solutions.
To address abrupt changes in the section, the classic SWE system is augmented with a third equation consisting of the time-invariance of the width scale. The idea of the augmented system was introduced by LeFloch and Thanh (2011) for the unit-width SWE, using the bed elevation as an additional variable, and by Valiani and Caleffi (2019) for rectangular narrowing/widening cross-sections, using the channel width as an additional variable.
The numerical model is a Finite Volume Method, second-order accurate in space and time, using a path conservative scheme to evaluate the numerical flux at the cell interfaces. A nonlinear path is adopted, which is shown to be optimal for capturing both the sharp contact wave at the dam and the moving shock(s) downstream of the dam.
The comparison of the numerical results with the analytical results for different solution patterns of the solution supports the confidence in the reliability of the model
Modeling blood flow in viscoelastic vessels: the 1D augmented fluid–structure interaction system
No full textNowadays mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological processes in different medical sectors. The theory behind blood flow modeling is closely related to the study of incompressible flow through compliant thin-walled tubes, starting from the incompressible Navier–Stokes equations. Furthermore, the mechanical interaction between blood flow and vessels wall must be properly described by the model. Recent works showed the benefits of characterizing the rheology of the vessel wall through a viscoelastic law. Taking into account the viscous contribution of the wall material and not simply the elastic one leads to a more realistic representation of the vessel behavior, which manifests not only an instantaneous elastic strain but also a viscous damping effect on pulse pressure waves, coupled to energy losses. In this context, the aim of this work is to propose an easily extensible one-dimensional mathematical model able to accurately capture fluid–structure interactions. The originality of the model lies in the introduction of a viscoelastic tube law in PDE form, valid for both arterial and venous networks, leading to an augmented fluid–structure interaction system. In contrast to well established mathematical models, the proposed one is natively hyperbolic. The model is solved with an efficient and robust second-order numerical scheme; the time integration is based on an Implicit–Explicit Runge–Kutta scheme conceived for applications to hyperbolic systems with stiff relaxation terms. The validation of the proposed model is performed on several different test cases. Results obtained in Riemann problems, adopting a simple elastic tube law for the characterization of the vessel wall, are compared with available exact solutions. To validate the contribution given by the viscoelastic term, the Method of Manufactured Solutions has been applied. Specific tests have been designed to verify the well-balancing with respect to fluid-at-rest condition and the accuracy-preserving property of the scheme. Finally, a specific test case with an inlet pulse pressure wave has been designed to assess the effects of viscoelasticity with respect to a simple elastic behavior of the vessel wall. The complete code, written in MATLAB (MathWorks Inc.) language, with the implemented test cases, is made available in Mendeley Data repository
Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant–Exner morphodynamic model
No full textWithin the framework of the de Saint Venant equations coupled with the Exner equation for morphodynamic evolution, this work presents a new efficient implementation of the Dumbser-Osher-Toro (DOT) scheme for non-conservative problems. The DOT path-conservative scheme is a robust upwind method based on a complete Riemann solver, but it has the drawback of requiring expensive numerical computations. Indeed, to compute the non-linear time evolution in each time step, the DOT scheme requires numerical computation of the flux matrix eigenstructure (the totality of eigenvalues and eigenvectors) several times at each cell edge. In this work, an analytical and compact formulation of the eigenstructure for the de Saint Venant-Exner (dSVE) model is introduced and tested in terms of numerical efficiency and stability. Using the original DOT and PRICE-C (a very efficient FORCE-type method) as reference methods, we present a convergence analysis (error against CPU time) to study the performance of the DOT method with our new analytical implementation of eigenstructure calculations (A-DOT). In particular, the numerical performance of the three methods is tested in three test cases: a movable bed Riemann problem with analytical solution; a problem with smooth analytical solution; a test in which the water flow is characterised by subcritical and supercritical regions. For a given target error, the A-DOT method is always the most efficient choice. Finally, two experimental data sets and different transport formulae are considered to test the A-DOT model in more practical case studies
Modellazione del flusso sanguigno in reti di vasi viscoelastici
No full textSi descrive la modellazione delle giunzioni tra vasi sanguigni viscoelastici e delle condizioni al contorno. Il confronto di riferimento avviene tra un vaso sanguigno con giunzione e il corrispondente caso di vaso continuo. La trattazione è applicabile sia ad arterie che a vene. Si presenta la simulazione di una rete circolatoria arteriosa e si evidenzia il cappio di isteresi tipico del comportamento viscoelastico
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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