2,905 research outputs found
On the Efficiency of Staggered C-Grid Discretization for the Inviscid Shallow Water Equations from the Perspective of Nonstandard Calculus
No full textThis paper provides a rationale for the commonly observed numerical efficiency of staggered C-grid discretizations for solving the inviscid shallow water equations. In particular, using the key concepts of nonstandard calculus, we aim to show that the grid staggering of the primitive variables (surface elevation and normal velocity components) is capable of dealing with flow discontinuities. After a brief introduction of hyperreals through the notion of infinitesimal increments, a nonstandard rendition of the governing equations is derived that essentially turns into a finite procedure and permits a convenient way of modeling the hydraulic jumps in open channel flow. A central result of this paper is that the discrete formulations thus obtained are distinguished by the topological structures of the solution fields and subsequently provide a natural framework for the staggered discretization of the governing equations. Another key of the present study is to demonstrate that the discretization naturally regularizes the solution of the inviscid flow passing through the hydraulic jump without the need of non-physical dissipation. The underlying justification is provided by analytically studying the distributions of the flow variables across an infinitesimal thin hydraulic jump along with the use of hyperreal Heaviside step functions. This main finding is shown to be useful to comprehend the importance of the application of staggered finite difference schemes to accurately predict rapidly varying free-surface flows. A numerical experiment is provided to confirm this result.Environmental Fluid Mechanic
The role of the Rankine-Hugoniot relations in staggered finite difference schemes for the shallow water equations
No full textThe purpose of this work is to point out the relevance of the Rankine-Hugoniot jump relations regarding the numerical solution of the inviscid shallow water equations. To arrive at physically relevant solutions in rapidly varied flow, it is of crucial importance that continuity of mass flux and momentum flux across a steady discontinuity is fulfilled at the discrete level. By adopting this viewpoint, finite difference schemes can be studied that may be well suited to solve shallow water flow problems involving discontinuities, while they are not based on a characteristic decomposition of the governed hyperbolic equations. Three schemes on staggered grids with either the water level or the water depth at the cell centre and the flow velocity or the depth-integrated velocity at the cell interface are examined. They differ in (1) the character of the transport velocity to bias the discretization of the advective acceleration term in the upwind direction, and (2) the determination of the water depth at the cell face with which the depth-integrated velocity must be linked to the flow velocity. A detailed analysis is provided and aimed at highlighting the necessity of fulfilling the Rankine-Hugoniot jump conditions for preventing the odd-even decoupling problem. The accuracy and robustness of three selected schemes is assessed by means of convergence tests, three idealized 1D test problems with exact solutions and a 1D laboratory experiment of the breaking, runup and rundown of a solitary wave on a sloping beach. Numerical results reveal that schemes satisfying exactly the jump conditions display improved performance over schemes which do not share this property. Also, these results support strong evidence on the link between not fulfilling the jump conditions and the appearance of odd-even oscillations.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Environmental Fluid Mechanic
Physics-Capturing Discretizations for Spectral Wind-Wave Models
No full textThis paper discusses the discretization methods that have been commonly employed to solve the wave action balance equation, and that have gained a renewed interest with the widespread use of unstructured grids for third-generation spectral wind-wave models. These methods are the first-order upwind finite difference and first-order vertex-centered upwind finite volume schemes for the transport of wave action in geographical space. The discussion addresses the derivation of these schemes from a different perspective. A mathematical framework for mimetic discretizations based on discrete calculus is utilized herein. A key feature of this algebraic approach is that the process of exact discretization is segregated from the process of interpolation, the latter typically involved in constitutive relations. This can help gain insight into the performance characteristics of the discretization method. On this basis, we conclude that the upwind finite difference scheme captures the wave action flux conservation exactly, which is a plus for wave shoaling. In addition, we provide a justification for the intrinsic low accuracy of the vertex-centred upwind finite volume scheme, due to the physically inaccurate but common flux constitutive relation, and we propose an improvement to overcome this drawback. Finally, by way of a comparative demonstration, a few test cases is introduced to establish the ability of the considered methods to capture the relevant physics on unstructured triangular meshes.Environmental Fluid Mechanic
Accuracy aspects of conventional discretization methods for scalar transport with nonzero divergence velocity field arising from the energy balance equation
No full textWe are concerned with the numerical solution of a linear transport problem with nonzero divergence velocity field that originates from the spectral energy balance equation describing the evolution of wind waves and swells in coastal seas. The discretization error of the commonly used first-order upwind finite difference and first-order vertex-centered upwind finite volume schemes in one space dimension is analyzed. Smoothness of nondivergent velocity field plays a crucial role in this. No such analysis has been attempted to date for such problems. The two schemes studied differ in the manner in which they treat the scalar flux numerically. The finite difference variant is shock captured, whereas the vertex-centered finite volume approximation employs an arithmetic mean of the velocity and appears not to be flux conservative. The methods are subsequently extended to two dimensions on triangular meshes. Numerical experiments are provided to verify the convergence analysis. The main finding is that the finite difference scheme displays optimal rates of convergence and offers higher accuracy over the finite volume scheme, regardless the regularity of the velocity field. The latter scheme notably yields convergence rates of 0.5 and 0 in L2-norm and L∞-norm, respectively, when the velocity field is not smooth. A test case illustrating wave shoaling and refraction over submerged shoals is also presented and demonstrates the practical importance of flux conservation.Environmental Fluid Mechanic
Computation of free surface waves in coastal waters with SWASH on unstructured grids
No full textThis paper aims to present the extension of the non-hydrostatic wave-flow model SWASH with the covolume method to build discretization schemes on unstructured triangular grids. Central to this method that is free of spurious pressure modes, is the use of dual pairs of meshes that are mutually orthogonal, such as the Delaunay-Voronoi mesh systems. The approximants sought are the components of the flow velocity vector normal to the cell faces of the primal mesh. In addition to the covolume approach, a novel upwind difference scheme for the horizontal advection terms in the momentum equation is proposed. This scheme obeys the Rankine-Hugoniot jump relations and prevents the odd-even decoupling of the velocity field accordingly. Moreover, cases with flow discontinuities, such as steady bores and broken waves, are properly treated. In spite of the low-order accuracy of the proposed method, unstructured meshes easily allow for local refinement in a way that retains the desired accuracy. The unstructured-grid version of SWASH is applicable to a wide range of 2DH wave-flow problems to investigate the nonlinear dynamics of free surface waves over varying bathymetries. Its efficiency and robustness is tested on a number of these problems employing unstructured triangular meshes.Environmental Fluid Mechanic
Modelling wave transformation across a fringing reef using SWASH
No full textThis paper presents the application of the open source non-hydrostatic wave-flow model SWASH to wave propagation over a fringing reef, and the results are discussed and compared with observations obtained from a laboratory experiment subjected to various incident wave conditions. This study focus not only on wave breaking, bottom friction, and wave-induced setup and runup, but also on the generation and propagation of infragravity waves beyond the reef crest. Present simulations demonstrate the overall predictive capabilities of the model for a typical coral reef with steep slopes and extended reef flats.Hydraulic EngineeringCivil Engineering and Geoscience
CAPRI versus AGLINK-COSIMO: Two partial equilibrium models - Two baseline approaches
No full textThe agricultural modelling world has generated several models aiming at the analysis of the response of the sector to certain changes in exogenous mainly policy variables. Among those, the CAPRI modelling system developed by a consortium centred on the University of Bonn and the AGLINK-COSIMO model, a joint product of the OECD and the FAO, are well known and accepted as comprehensive tools. This analysis focuses on a qualitative comparison of both models and particularly on the process of setting up the baseline. The baseline is a medium-term projection of agricultural markets reflecting current policies and those already decided upon. This projection in turn serves as the base for comparisons when analyzing scenarios. It is shown that CAPRI uses generic and automatic procedures whenever possible for conducting the database and the baseline, while AGLINK-COSIMO puts more emphasis on expert knowledge in this process. Both approaches are shown to have certain advantages while the conclusion that a combination of them would potentially improve both models will be drawn from this analysis.CAPRI, AGLINK-COSIMO, Baseline process, Agricultural and Food Policy,
After the Addendum: Author Rights Management and/as Library Service
No full textThis report presents the findings from a qualitative study of Rice University faculty attitudes and practices around author rights conducted by Marcel LaFlamme, a graduate student in the Department of Anthropology, during his tenure as a Fondren Fellow. This project was supervised by Shannon Kipphut-Smith, Fondren Library’s scholarly communications liaison
Ruskin traduzido: Sesame and Lilies por Proust e Catalán
No full textTese (doutorado) - Universidade Federal de Santa Catarina, Centro de Comunicação e Expressão, Programa de Pós-Graduação em Literatura, Florianópolis, 2009.Este trabalho parte da análise das traduções da obra Sesame and Lilies, de John Ruskin, para o francês e para o castelhano para fazer um exame de questões ligadas ao gênero ensaístico, à tradução de ensaios e à autoria. Para isso, analisarei a tradução de Marcel Proust para o francês e seu paratexto e a tradução para o castelhano feita por Miguel Catalán e o respectivo paratexto.This study analises the translations of Sesame and Lilies, by John Ruskin, into French and Spanish in order to examine issues related to the essay as a literary genre, to the translation of essays and to authorship. This exam will be carried out by analising the translation into French by Marcel Proust and its paratext and the translation into Spanish by Miguel Catalán, accompanied by its paratext
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