1,720,965 research outputs found
Energy-conserving spectral element schemes based on Lagrangian dynamics: Investigating discrete energy conservation
No full textPhysical systems in the continuous domain are often solved using computer-aided software because of their complexity. Preserving the physical quantities from the continuous domain in the discrete domain is therefore of utmost importance. There is however a broad range of techniques that can accomplish the translation between the continuous and discrete domain, e.g. finite difference, volume and element techniques, fourth order Runge-Kutta or Störmer-Verlet to name a few. Accompanied with the aforementioned come strengths and weaknesses but have the common thread to try maintaining the physical behaviour of the continuous system closely. The mimetic spectral element technique is used to develop an energy-conserving spectral element scheme through a Lagrangian formulation. This new formulation of the mimetic spectral element technique allows for solving time-dependent problems and the simple harmonic oscillator serves as the sample problem in this thesis. The solution has been derived from Lagrangian mechanics in a variety of ways. Discrete Lagrangian formulations have been investigated at rst and their respective equations of motions have been tested against the exact solution of the simple harmonic oscillator. This method achieved marching in time and no damping of the solution, yet energy was only bounded and not exactly conserved. The mimetic spectral element formulation of the Lagrangian formulation showed diculties when using variational analysis, i.e. boundary treatment in the future. Arbitrary domain mapping was among the possible solutions, but this formulation was found to be unreliable and unsuccessful. It was found that a more robust formulation, i.e. the spectral marching method, was most suitable. Throughout this thesis the focus was put on the conservation of energy using a Lagrangian formulation. Except the spectral scheme using arbitrary domain mapping, all schemes kept the energy of the system bounded, but no energy was conserved up to machine precision. Using arbitrary domain mapping, the energy seemed to grow over time.Aerospace Engineerin
Advancing the Mimetic Spectral Element Method: Towards Continuum Mechanics Applications
No full textMimetic discretisation techniques are a growing field in computational physics research. Among these techniques, the recently developed mimetic spectral element method allows for exact discretisation of metric independent relations. This has been proven numerically in various mixed formulations, for instance the mixed velocity-vorticity-pressure formulation for Stokes flow, where mass conservation was point-wise strongly satisfied by the solution in the computational domain. Another example is the mixed stress-displacement formulation for the linear elasticity equations, where the balance law of linear momentum was point-wise strongly satisfied as well. A recent extension to a hybrid method leads to additional attractive features, such as the ability to decompose a large part of the computation of the solution into smaller problems. The aim of the research is to find a formulation for linear elasticity that is hybridisable while strongly satisfying conservation of linear and angular momentum as well, where the combination of linear momentum conservation and symmetry of the stress tensor is equivalent to angular momentum conservation. The proposed formulation has a mixed basis of both primal and algebraic dual nodal and edge basis functions. It fulfils the requirements as it is shown to be hybridisable, to satisfy point-wise linear momentum, and the discrete representation of the stress tensor is point-wise symmetric, hence angular momentum conservation is point-wise satisfied as well. The thesis furthermore functions as an overview of the method applied to elliptic problems, showing the results for previous formulations, and as a starting point for the next steps towards applying the method to fluids. A first step is proposed on extending the new formulation to a Stokes flow formulation with the stress as primary unknown, aimed at satisfying both linear and angular momentum conservation as well as mass conservation.Aerospace Engineerin
Mimetic Discretization of the High Frequency Helmholtz Equation using Hermite Interpolating Polynomials
No full textNumerical modelling of high frequency waves is a complex and challenging area. Although the underlying equation seems simple, −∆φ − k2φ = f, the numerical challenges are not. This time harmonic wave equation is known as the Helmholtz equation. The main challenge to be studied is the pollution error, which is the difference between the actual and numerical wavenumber. Due to this error, the solution of most numerical methods deteriorates rapidly when increasing the wavenumber. So far, either problem specific solutions have been found or solutions which require knowledge of the solution itself. In this thesis a numerical method is developed to approach this challenge. A mimetic discretization of the Helmholtz equation using C1-continuous Hermite interpolating polynomials is developed to model the Helmholtz equation in 2 dimensions. Mimetic theory is briefly introduced after which the Hermite polynomials are defined and analysed for their interpolating properties. A least-squares variational problem is defined and discretized using 49 basis function at its lowest order. The model is verified using a single sinusoidal wave after whichplane wave problems are solved and analysed for their wavenumber-dependence. A diffraction and interference problem is set-up and compared to analytical solutions. The proposed method shows no significant advantages over the use of C0-continuous Lagrange polynomials in terms of effectiveness. Both methods show deterioration at the same wave numbers and equal polynomial order. The Hermite polynomials require less unknowns to reach the same accuracy. In short, a p-accurate solution is found using Hermite polynomialsat the cost of a p − 1 model using Lagrange polynomials. This benefit in efficiency does not outweigh the additional effort and boundary information necessary to construct the problem. However, the variety of coefficients offer an opportunity for further research to find relations to the numerical wavenumber in the search of a wavenumber conserving discretization.Aerospace Engineerin
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Mimetic Discretizations with B-Splines: On the Construction of a Discrete Hodge Star Operator
No full textThis thesis introduces a higher-order numerical method for elliptic boundary value problems. The discretization method belongs to the class of mimetic discretizations, which translate as many of properties of the continuous problem to the discrete system, aiming to improve accuracy and reliability. The novelty lies in the application of B-splines as basis functions in a dual grid approach. B-splines or basis splines are piecewise polynomials with a certain degree of continuity between the polynomial pieces. Therefore, splines offer an attractive compromise between piecewise linear functions, commonly seen in finite element analysis, and the Lagrange polynomials from spectral element methods.Aerospace Engineering | Aerodynamics and Wind Energ
Path-consistent schemes for interacting boundary layers: A discontinuous Galerkin approach
No full textThis study is aimed at modelling of the unsteady interacting boundary layer around wind turbine rotor blades. It is shown that nonconservative mechanisms are present in this system, affecting the definition and approximation of solutions to the problem. The objective is to overcome the inconsistency of classical (dissipative) schemes, and find a suitable approximation method. A path-consistent discontinuous Galerkin method is proposed to correctly model the dynamics of this system. In the future, the current implementation is to be joined with the existing part of the RotorFlow simulation code. This will enable the incorporation of unsteady aerodynamic phenomena in the early design stage of new and large wind turbine rotors, which is currently unfeasible due to the high computational cost.Aerospace Engineering | Aerodynamics and Wind Energ
Slow and Fast Hydrogen De agration: A validation study
No full textAmidst the growing demand for energy, many nations are considering the expanded role of nuclear power in their energy portfolios. However, in case of severe accidents, large amounts of hydrogen gas can be released in the nuclear containment. Hydrogen-air mixture forms a very ammable gas which on subsequent ignition can lead to ame propagation in the nuclear containment. This may produce oscillating pressure waves or high over pressures that may damage the safety equipment and even a_ect the structural integrity of the nuclear reactor containment. Hence, there is a need for tools that can perform safety analysis of the nuclear reactors in case of severe accidents. In this respect, Computational Fluid Dynamics (CFD) codes have been widely used in the past to predict such ow and combustion phenomena. However, before any CFD code can be used for safety analysis, it requires thorough validation to corroborate the accuracy of its predicted results. This stems the motivation of the current thesis work.Aerospace Engineering | Aerodynamics and Wind Energ
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