Дисертації з теми "Higher Order Method"
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1
KUSAKARI, Keiichirou. "Higher-Order Path Orders Based on Computability." Institute of Electronics, Information and Communication Engineers, 2004. http://hdl.handle.net/2237/14973.
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Eng, Ju-Ling. "Higher order finite-difference time-domain method." Connect to resource, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1165607826.
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3
Zhu, Xuemei. "A higher-order panel method for third-harmonic diffraction problems." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/43339.
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Sykes, James Henry Carleton University Dissertation Engineering Mechanical and Aerospace. "A higher order panel method for linearized unsteady subsonic aerodynamics." Ottawa, 1994.
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5
Ben, Romdhane Mohamed. "Higher-Degree Immersed Finite Elements for Second-Order Elliptic Interface Problems." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/39258.
Повний текст джерелаАнотація:
A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have been developed to solve these kinds of problems and handle the non-smooth behavior of the input data and/or the solution across the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems.
In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior penalty (IP) for solving two-dimensional second-order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. An analysis of the constructed IFE spaces and their dimensions is presented. Shape functions of Lagrange and hierarchical types are constructed for these spaces, and a proof for the existence is established. The interpolation errors in the proposed piecewise quadratic spaces yield optimal O(h³) and O(h²) convergence rates, respectively, in the L² and broken H¹ norms under mesh refinement. Furthermore, numerical results are presented to validate our theory and show the optimality of our quadratic IFE method.
Our approach in this thesis is, first, to establish a theory for the simplified case of a linear interface. After that, we extend the framework to quadratic interfaces. We, then, describe a general procedure for handling arbitrary interfaces occurring in real physical practical applications and present computational examples showing the optimality of the proposed method. Furthermore, we investigate a general procedure for extending our quadratic IFE spaces to p-th degree and construct hierarchical shape functions for p=3.Ph. D.
6
Li, Ming-Sang. "Higher order laminated composite plate analysis by hybrid finite element method." Thesis, Massachusetts Institute of Technology, 1989. http://hdl.handle.net/1721.1/40145.
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Maniar, Hiren Dayalal. "A three dimensional higher order panel method based on B-splines." Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11127.
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8
Bonhaus, Daryl Lawrence. "A Higher Order Accurate Finite Element Method for Viscous Compressible Flows." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/29458.
Повний текст джерелаАнотація:
The Streamline Upwind/Petrov-Galerkin (SU/PG) method is applied to higher-order
finite-element discretizations of the Euler equations in one dimension and the Navier-Stokes
equations in two dimensions. The unknown flow quantities are discretized on
meshes of triangular elements using triangular Bezier patches. The nonlinear residual
equations are solved using an approximate Newton method with a pseudotime term. The
resulting linear system is solved using the Generalized Minimum Residual algorithm with
block diagonal preconditioning.
The exact solutions of Ringleb flow and Couette flow are used to quantitatively
establish the spatial convergence rate of each discretization. Examples of inviscid flows
including subsonic flow past a parabolic bump on a wall and subsonic and transonic flows
past a NACA 0012 airfoil and laminar flows including flow past a a flat plate and flow past
a NACA 0012 airfoil are included to qualitatively evaluate the accuracy of the discretiza-tions.
The scheme achieves higher order accuracy without modification. Based on the test
cases presented, significant improvement of the solution can be expected using the higher-order
schemes with little or no increase in computational requirements. The nonlinear sys-tem
also converges at a higher rate as the order of accuracy is increased for the same num-ber
of degrees of freedom; however, the linear system becomes more difficult to solve.
Several avenues of future research based on the results of the study are identified, includ-ing
improvement of the SU/PG formulation, development of more general grid generation
strategies for higher order elements, the addition of a turbulence model to extend the
method to high Reynolds number flows, and extension of the method to three-dimensional
flows. An appendix is included in which the method is applied to inviscid flows in three
dimensions. The three-dimensional results are preliminary but consistent with the findings
based on the two-dimensional scheme.Ph. D.
9
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1205350171405-81971.
Повний текст джерелаАнотація:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this workIn der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben
10
Stöcker, Christina. "Level set methods for higher order evolution laws." Doctoral thesis, Forschungszentrum caesar, 2007. https://tud.qucosa.de/id/qucosa%3A24054.
Повний текст джерелаАнотація:
A numerical treatment of non-linear higher-order geometric evolution equations with the level set and the finite element method is presented. The isotropic, weak anisotropic and strong anisotropic situation is discussed. Most of the equations considered in this work arise from the field of thin film growth. A short introduction to the subject is given. Four different models are discussed: mean curvature flow, surface diffusion, a kinetic model, which combines the effects of mean curvature flow and surface diffusion and includes a further kinetic component, and an adatom model, which incorporates in addition free adatoms. As an introduction to the numerical schemes, first the isotropic and weak anisotropic situation is considered. Then strong anisotropies (non-convex anisotropies) are used to simulate the phenomena of faceting and coarsening. The experimentally observed effect of corner and edge roundings is reached in the simulation through the regularization of the strong anisotropy with a higher-order curvature term. The curvature regularization leads to an increase by two in the order of the equations, which results in highly non-linear equations of up to 6th order. For the numerical solution, the equations are transformed into systems of second order equations, which are solved with a Schur complement approach. The adatom model constitutes a diffusion equation on a moving surface. An operator splitting approach is used for the numerical solution. In difference to other works, which restrict to the isotropic situation, also the anisotropic situation is discussed and solved numerically. Furthermore, a treatment of geometric evolution equations on implicitly given curved surfaces with the level set method is given. In particular, the numerical solution of surface diffusion on curved surfaces is presented. The equations are discretized in space by standard linear finite elements. For the time discretization a semi-implicit discretization scheme is employed. The derivation of the numerical schemes is presented in detail, and numerous computational results are given for the 2D and 3D situation. To keep computational costs low, the finite element grid is adaptively refined near the moving curves and surfaces resp. A redistancing algorithm based on a local Hopf-Lax formula is used. The algorithm has been extended by the authors to the 3D case. A detailed description of the algorithm in 3D is presented in this work.In der Arbeit geht es um die numerische Behandlung nicht-linearer geometrischer Evolutionsgleichungen höherer Ordnung mit Levelset- und Finite-Elemente-Verfahren. Der isotrope, schwach anisotrope und stark anisotrope Fall wird diskutiert. Die meisten in dieser Arbeit betrachteten Gleichungen entstammen dem Gebiet des Dünnschicht-Wachstums. Eine kurze Einführung in dieses Gebiet wird gegeben. Es werden vier verschiedene Modelle diskutiert: mittlerer Krümmungsfluss, Oberflächendiffusion, ein kinetisches Modell, welches die Effekte des mittleren Krümmungsflusses und der Oberflächendiffusion kombiniert und zusätzlich eine kinetische Komponente beinhaltet, und ein Adatom-Modell, welches außerdem freie Adatome berücksichtigt. Als Einführung in die numerischen Schemata, wird zuerst der isotrope und schwach anisotrope Fall betrachtet. Anschließend werden starke Anisotropien (nicht-konvexe Anisotropien) benutzt, um Facettierungs- und Vergröberungsphänomene zu simulieren. Der in Experimenten beobachtete Effekt der Ecken- und Kanten-Abrundung wird in der Simulation durch die Regularisierung der starken Anisotropie durch einen Krümmungsterm höherer Ordnung erreicht. Die Krümmungsregularisierung führt zu einer Erhöhung der Ordnung der Gleichung um zwei, was hochgradig nicht-lineare Gleichungen von bis zu sechster Ordnung ergibt. Für die numerische Lösung werden die Gleichungen auf Systeme zweiter Ordnungsgleichungen transformiert, welche mit einem Schurkomplement-Ansatz gelöst werden. Das Adatom-Modell bildet eine Diffusionsgleichung auf einer bewegten Fläche. Zur numerischen Lösung wird ein Operatorsplitting-Ansatz verwendet. Im Unterschied zu anderen Arbeiten, die sich auf den isotropen Fall beschränken, wird auch der anisotrope Fall diskutiert und numerisch gelöst. Außerdem werden geometrische Evolutionsgleichungen auf implizit gegebenen gekrümmten Flächen mit Levelset-Verfahren behandelt. Insbesondere wird die numerische Lösung von Oberflächendiffusion auf gekrümmten Flächen dargestellt. Die Gleichungen werden im Ort mit linearen Standard-Finiten-Elementen diskretisiert. Als Zeitdiskretisierung wird ein semi-implizites Diskretisierungsschema verwendet. Die Herleitung der numerischen Schemata wird detailliert dargestellt, und zahlreiche numerische Ergebnisse für den 2D und 3D Fall sind gegeben. Um den Rechenaufwand gering zu halten, wird das Finite-Elemente-Gitter adaptiv an den bewegten Kurven bzw. den bewegten Flächen verfeinert. Es wird ein Redistancing-Algorithmus basierend auf einer lokalen Hopf-Lax Formel benutzt. Der Algorithmus wurde von den Autoren auf den 3D Fall erweitert. In dieser Arbeit wird der Algorithmus für den 3D Fall detailliert beschrieben.
11
鍾偉昌 and Wai-cheong Chung. "Geometrically nonlinear analysis of plates using higher order finite elements." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207601.
Повний текст джерела
12
Chung, Wai-cheong. "Geometrically nonlinear analysis of plates using higher order finite elements /." [Hong Kong : University of Hong Kong], 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12225022.
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13
Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.
Повний текст джерелаАнотація:
We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the method by random variables with the same moments conditional on the linear term. We use a version of perturbation method and a technique from optimal transport theory to find a coupling which gives a good approximation in Lp sense. This new method is a Runge-Kutta method or so-called derivative-free method. We have implemented this new method in MATLAB. The performance of the method has been studied for degenerate matrices. We have given the details of proof for order h3/2 and the outline of the proof for order h2.
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SAKAI, Masahiko, and Keiichirou KUSAKARI. "On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems." IEICE, 2005. http://hdl.handle.net/2237/9579.
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15
Alon, Yair. "Analysis of thick composite plates using higher order three dimensional finite elements." Thesis, Monterey, California : Naval Postgraduate School, 1990. http://handle.dtic.mil/100.2/ADA243188.
Повний текст джерелаАнотація:
Thesis (M.S. in Aeronautical Engineering and Aeronautics and Astronautics Engineers Degree)--Naval Postgraduate School, December 1990.Thesis Advisor(s): Kolar, Ramesh. Second Reader: Lindsey, G. H. "December 1990." Description based on title screen as viewed on March 30, 2010. DTIC Descriptor(s): Thickness, stability, composite materials, laminates, theory, elastic properties, orientation(direction), composite structures, three dimensional, solutions(general), integration, plates, anisotropy, isotropism, convergence, thinness, behavior, nonlinear analysis, static tests, formulas(mathematics), lagrangian functions, fibers DTIC Identifier(s): Laminates, plates, structural response, composite structures, finite element analysis, nonlinear analysis, stress strain relations, theses, displacement, buckling, interpolation. Author(s) subject terms: Finite element, nonlinear analysis, plate bending thick plates, laminated composites, buckling, constant arc length three dimensional element Includes bibliographical references (p. 87-88). Also available in print.
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Ismatullah. "Analysis of space-borne antennas by higher-order method of moments and inverse equivalent current methods." kostenfrei, 2010. https://mediatum2.ub.tum.de/node?id=977261.
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Wei, Dong. "A univariate decomposition method for higher-order reliability analysis and design optimization." Diss., University of Iowa, 2006. http://ir.uiowa.edu/etd/55.
Повний текст джерела
18
Danmeier, Donald Gregory 1969. "A higher-order method for large-amplitude simulations of bodies in waves." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/9708.
Повний текст джерелаАнотація:
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1999.Includes bibliographical references (leaves 133-139).
In this thesis, we simulate large-amplitude motion of three-dimensional bodies in waves using a higher-order boundary element method. A 'geometry-independent' approach is adopted in which the representation of the body surface is separated from the discretization of the hydrodynamic solution. Traditional formulations of the wave-body problem assume small-amplitude waves and body motions, and perturbation expansion about the mean position of the body and free surface leads to a completely linearized system. In the present thesis, the body boundary condition is imposed exactly, but disturbances at the free-surface are assumed to be small enough to justify linearization. Previous applications of this so-called body-exact problem have concentrated on the analysis of heave and pitch motion of ships with forward speed. This study focuses on marine applications where a large-amplitude response is induced by small-amplitude incident waves. The time-varying nature of the body-exact formulation makes its numerical solution computationally intensive. Therefore, a new 'higher-order' panel method has been developed to overcome inefficiencies associated with the conventional constant-strength planar-panel approach. Unlike most higher-order schemes, the present method separates the discretization of the hydrodynamic solution from the representation of the body surface by applying a 8-spline description of the potential over a generic parameterization of the geometry. This allows for accurate (or even analytic) representation of the surface while retaining the desirable characteristics of higher-order methods, most. notably improved efficiency and the ability to evaluate gradients of the potential needed for nonlinear analyses. Robustness and efficiency of the present method are demonstrated by its application to three problems in which the large-amplitude response of the body is important. In the first example, we examine the hydrodynamic loads on an underwater vehicle during a near surface maneuver. The vertical drift force is found by integrating the quadratic Bernoulli pressure, and its variation with respect to submergence is shown to complicate the control of the vessel. Next, multi-body interactions are examined in the cont.ext of the drift motion of a floating body in the vicinity of a fixed structure. Here, the presence of the structure is shown to repel the floating body against the direction of incident wave propagation for certain conditions. In the final application, we examine instabilities of floating bodies to illustrate the importance of accounting for finite-amplitude motions. Period doubling and exponentially large motions in the numerical simulations are related to parametric forcing captured by the body-exact formulation.
by Donald Gregory Danmeier.
Ph.D.
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Fung, Jimmy Jr. "Parameter Identification of Nonlinear Systems Using Perturbation Methods and Higher-Order Statistics." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36921.
Повний текст джерелаАнотація:
A parametric identification procedure is proposed that combines
the method of multiple scales and higher-order statistics to
efficiently and accurately model nonlinear
systems. A theoretical background for the method of
multiple scales and higher-order
statistics is given.
Validation of the procedure is performed
through applying it to numerical simulations of two
nonlinear systems. The results show how the procedure can
successfully characterize the system damping and nonlinearities and
determine the corresponding parameters.
The procedure is then applied to experimental measurements from
two structural systems, a
cantilevered beam and a three-beam frame. The results show that
quadratic damping should be accounted for in both systems.
Moreover, for the three-beam frame, the parametric excitation is
much more important than the direct excitation.
To show the flexibility of the
procedure, numerical simulations of ship motion under parametric
excitation are used to determine nonlinear parameters govening the
relation between pitch, heave, and roll motions. The results show
a high level of agreement between the numerical simulation and the
mathematical model with the identified parameters.Master of Science
20
VARELLO, ALBERTO. "Advanced higher-order one-dimensional models for fluid-structure interaction analysis." Doctoral thesis, Politecnico di Torino, 2013. http://hdl.handle.net/11583/2517517.
Повний текст джерелаАнотація:
The aim of this work is the development of a refined reduced order model suitable for numerical applications in solid and fluid mechanics with a remarkable reduction in computational cost. Nowadays, numerical reduced order models are widely exploited in many areas, such as aerospace, mechanical and biomechanical engineering for structural analysis, fluid dynamic analysis and coupled (aeroelastic) fluid-structure interaction analysis.
One-dimensional (1D) structural models, commonly known as beams, are for instance used in many applications to analyze the structural behavior of slender bodies, such as columns, arches, blades, aircraft wings, bridges, skyscrapers, rotor and wind turbine blades. One-dimensional structural elements are simpler and computationally more efficient than 2D (plate/shell) and 3D (solid) elements. This feature makes beam theories still very attractive for the static, dynamic response, free vibration and aeroelastic analyses, despite the approximations which they introduce in the simulation.
Recently, 1D models are intensively exploited for the simulation of the human cardiovascular system under either physiological or pathological conditions. As it is easily comprehensible, fluid flows in pipes, channel, capillaries or even arteries are particularly suitable for the application of one-dimensional models also to fluid dynamics. Typically, one-dimensional models for fluid dynamics and fluid-structure interaction (FSI) problems are again remarkably more efficient than three-dimensional methods in terms of computational cost.
A key point for reduced order models is the capability in simulating in an accurate way the investigated physical problem. For instance, in last decades the growing use of advanced composite and sandwich materials in thin-walled beam-like structures has revealed that 1D theories have to be refined in order to predict the behavior of such complex structures with high fidelity. For this purpose, a higher-order one-dimensional method is introduced in this work and its capabilities are highlighted and discussed. The present work is subdivided into three fundamental parts corresponding to the physical fields the proposed refined model is applied to.
Firstly, a structural part presents the formulation of a displacement-based higher-order one-dimensional model for the analysis of beam-like structures. Classical beam theories (Euler-Bernoulli and Timoshenko) have intrinsic limitations which preclude their applications for the analysis of a wide class of engineering problems. The Carrera Unified Formulation (CUF) is employed to introduce a hierarchical modeling with a variable order of expansion for the displacement unknowns over the beam cross-section. The finite element method (FEM) is used to handle arbitrary geometries and loading conditions. The influence of higher-order effects over the cross-section deformation, not detectable by classical and low-order beam theories, on the static, free vibration and time-dependent response of several structures with arbitrary cross-section geometries and made of arbitrary materials is remarked through the numerical results presented.
Secondly, an aeroelastic part describes the extension of the refined structural model to the static aeroelastic analysis of lifting surfaces made of metallic and composite materials. A coupled aeroelastic computational model based on the Vortex Lattice aerodynamic Method and the finite element method (FEM) is formulated. A refined aeroelastic approach is also presented by replacing the Vortex Lattice aerodynamic Method with the more powerful 3D Panel Method. Comparison with results obtained by existing plate/shell aeroelastic models shows that the present 1D model could result less expensive from the computational point of view with respect to shell cases with same accuracy. The effect of the cross-section deformation on the aeroelastic static response and on the critical wing divergence velocity is evaluated for different wing configurations. The beneficial effects of aeroelastic tailoring in the case of wings made of composite anisotropic materials are also confirmed by using the present model.
Finally, a third part concerning the use of the refined one-dimensional CUF model for fluid dynamic problems is presented. The basic partial differential equations (PDEs) of fluid mechanics (Navier-Stokes and Stokes equations) are faced and 1D refined models with variable velocity-pressure accuracy are presented on the basis of the one-dimensional Carrera Unified Formulation and the finite element method. The application of these higher-order models to describe the three-dimensional fluid flow evolution on a computational domain is formulated for the Stokes problem. The present approach reveals its capabilities in predicting accurately, with a reduced computational cost with respect to more consuming two-dimensional or three-dimensional methods, nonclassical and complex fluid flows. Moreover, the numerical results show the promising potentiality of such an approach to the future extension of fluid-structure CUF-CUF models, i.e. the coupling of CUF models used for both structural and fluid dynamic analyses.
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Bernasconi, Daniel Joseph. "A higher-order potential flow method for thick bodies, thin surfaces and wakes." Thesis, University of Southampton, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.484982.
Повний текст джерелаАнотація:
Ahigher-order method is developed that models continuous source and doublet singularity distributions over three-dimensional curved surfaces. The singular on-surface influence coefficients are treated by a robust desingularisation algorithm, whereas off-surface coefficients are calculated by means of an efficient subdivision and variable cubature scheme. Whilst higher-order methods have previously been developed fo! thick bodies and Dirichlet boundary conditions, this method is also capable of modelling continuous geometry and singularity surfaces over thin bodies and wakes that require Neumann boundary conditions. The Continuous Surface Method (CSM) has a number of advantages over conventional constant panel methods (CPMs). Firstly, as curved geometries are represented exactly, changing the order of the solution does not modify the physical shape of the configuration. Furthermore, as singularity solutions are continuous, the significant grid-dependency of CPMs does not arise. Finally, the continuous singularity distributions allow velocities to be evaluated accurately across the entire surface without interpolation: this enables the calculation of continuous pressure distributions and the construction ofstreamlines and wakes flowing very close to surfaces, without any problems of divergence. Numerical results comparing the CSM to a CPM have shown that for equal run times, the CSM obtains greater accuracy in pressure distributions than a CPM, and produces much smoother velocity fields. However the CSM was not able to improve upon the efficiency ofthe CPM in determining total aerodynamic forces. A wake relaxation scheme in which wakes are modelled as curved B-spline patches is developed, and is convergent for simple geometries. For.a more complex example of wakes shed from two closely overlapping sails, the wake relaxation converges to within around 0.5% of total aerodynamic load, but the low panel resolutions employed in the CSM are insufficient to model the detail of . the wake roll-up effectively. Three alternative schemes to address this problem are evaluated.
22
Dubcová, Lenka. "Novel self-adaptive higher-order finite elements methods for Maxwell's equations of electromagnetics." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2008. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
Повний текст джерела
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Forgues, Francois. "Higher-Order Moment Models for Multiphase Flows Coupled to a Background Gas." Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/39098.
Повний текст джерелаАнотація:
Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of sizes and velocities at each location in space. Lagrangian methods can be too expensive and many Eulerian methods, though often computationally more affordable, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. For example, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking. The predictive capabilities of modern techniques from the kinetic theory of gases to the treatment of disperse multiphase flows are investigated. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are considered and their abilities to predict particle-stream
crossing are assessed. Furthermore, a new polydisperse model has been proposed for treatment of flows that display a range of particles sizes. The proposed model is an extension of the well-known maximum-entropy ten-moment model from rarefied gas dynamics with an addition for the treatment of a range of particle diameters. This
model allows for anisotropic variance of particle velocities in phase space and directly treats correlations between particle diameter and velocity. The derivation and mathematical structure, of the proposed models are presented. A fine-volume discretization solution procedure for the resulting moment equations is described and
used for performing numerical experiments. Results for flow problems that are designed to demonstrate the fundamental behaviour of each model are presented. It is shown that the new models offer clear advantages in terms of accuracy as compared to traditional Eulerian models for multiphase flows.
24
SAKAI, Masahiko, Yoshitsugu WATANABE, and Toshiki SAKABE. "An Extension of the Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems." IEICE, 2001. http://hdl.handle.net/2237/9578.
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Prinsloo, Rian Hendrik. "A practical implementation of the higher-order transverse-integrated nodal diffusion method / Rian Hendrik Prinsloo." Thesis, North-West University, 2012. http://hdl.handle.net/10394/9533.
Повний текст джерелаАнотація:
Transverse-integrated nodal di usion methods currently represent the standard
in full core neutronic simulation. The primary shortcoming of this
approach is the utilization of the quadratic transverse leakage approximation.
This approach, although proven to work well for typical LWR
problems, is not consistent with the formulation of nodal methods and
can cause accuracy and convergence problems. In this work, an improved,
consistent quadratic leakage approximation is formulated, which derives
from the class of higher-order nodal methods developed some years ago.
In this thesis a number of iteration schemes are developed around this
consistent quadratic leakage approximation which yields accurate node
average results in much improved calculational times. The most promising
of these iteration schemes results from utilizing the consistent leakage
approximation as a correction method to the standard quadratic leakage
approximation. Numerical results are demonstrated on a set of benchmark
problems and further applied to realistic reactor problems for particularly
the SAFARI-1 reactor operating at Necsa, South Africa. The nal optimal
solution strategy is packaged into a standalone module which may be
simply coupled to existing nodal di usion codes, illustrated via coupling of
the module to the OSCAR-4 code system developed at Necsa and utilized
for the calculational support of a number of operating research reactors
around the world.Thesis(PhD (Reactor Science))--North-West University, Potchefstroom Campus, 2013
26
Altintan, Derya. "An Extension To The Variational Iteration Method For Systems And Higher-order Differential Equations." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613864/index.pdf.
Повний текст джерелаАнотація:
It is obvious that differential equations can be used to model real-life problems. Although it is possible to obtain analytical solutions of some of them, it is in general
difficult to find closed form solutions of differential equations. Finding thus approximate solutions has been the subject of many researchers from different areas.
In this thesis, we propose a new approach to Variational Iteration Method (VIM) to obtain the solutions of systems of first-order differential equations. The main
contribution of the thesis to VIM is that proposed approach uses restricted variations only for the nonlinear terms and builds up a matrix-valued Lagrange multiplier that leads to the extension of the method (EVIM).
Close relation between the matrix-valued Lagrange multipliers and fundamental solutions of the differential equations highlights the relation between the extended version of the variational iteration method and the classical variation of parameters formula.
It has been proved that the exact solution of the initial value problems for (nonhomogenous) linear differential equations can be obtained by such a generalisation using
only a single variational step.
Since higher-order equations can be reduced to first-order systems, the proposed approach is capable of solving such equations tooindeed, without such a reduction, variational iteration method is also extended to higher-order scalar equations. Further, the close connection with the associated first-order systems is presented. Such extension of the method to higher-order equations is then applied to solve boundary value problems: linear and nonlinear ones. Although the corresponding Lagrange multiplier resembles the Green&rsquo
s function, without the need of the latter, the extended approach to the variational iteration method is systematically applied to solve boundary value problems, surely in the nonlinear case as well. In order to show the applicability of the method, we have applied the EVIM to various real-life problems: the classical Sturm-Liouville eigenvalue problems, Brusselator reaction-diffusion, and chemical master equations. Results show that the method is simple, but powerful and effective.
27
Temimi, Helmi. "A Discontinuous Galerkin Method for Higher-Order Differential Equations Applied to the Wave Equation." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/26454.
Повний текст джерелаАнотація:
We propose a new discontinuous finite element method for higher-order initial value problems where the finite element solution exhibits an optimal convergence rate in the L2- norm. We further show that the q-degree discontinuous solution of a differential equation of order m and its first (m-1)-derivatives are strongly superconvergent at the end of each step. We also establish that the q-degree discontinuous solution is superconvergent at the roots of (q+1-m)-degree Jacobi polynomial on each step.
Furthermore, we use these results to construct asymptotically correct a posteriori error estimates. Moreover, we design a new discontinuous Galerkin method to solve the wave equation by using a method of lines approach to separate the space and time where we first apply the classical finite element method using p-degree polynomials in space to obtain a system of second-order ordinary differential equations which is solved by our new discontinuous Galerkin method. We provide an error analysis for this new method to show that, on each space-time cell, the discontinuous Galerkin finite element solution is superconvergent at the tensor product of the shifted roots of the Lobatto polynomials in space and the Jacobi polynomial in time. Then, we show that the global L2 error in space and time is convergent. Furthermore, we are able to construct asymptotically correct a posteriori error estimates for both spatial and temporal components of errors. We validate our theory by presenting several computational results for one, two and three dimensions.Ph. D.
28
AYYALASOMAYAJULA, HARITHA. "HIGHER-ORDER ACCURATE SOLUTION FOR FLOW THROUGH A TURBINE LINEAR CASCADE." University of Cincinnati / OhioLINK, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1054757181.
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Srinivas, L. "FIR System Identification Using Higher Order Cumulants -A Generalized Approach." Thesis, Indian Institute of Science, 1994. http://hdl.handle.net/2005/637.
Повний текст джерелаАнотація:
The thesis presents algorithms based on a linear algebraic solution for the identification of the parameters of the FIR system using only higher order statistics when only the output of the system corrupted by additive Gaussian noise is observed.
All the traditional parametric methods of estimating the parameters of the system have been based on the 2nd order statistics of the output of the system. These methods suffer from the deficiency that they do not preserve the phase response of the system and hence cannot identify non-minimum phase systems. To circumvent this problem, higher order statistics which preserve the phase characteristics of a process and hence are able to identify a non-minimum phase system and also are insensitive to additive Gaussian noise have been used in recent years.
Existing algorithms for the identification of the FIR parameters based on the higher order cumulants use the autocorrelation sequence as well and give erroneous results in the presence of additive colored Gaussian noise. This problem can be overcome by obtaining algorithms which do not utilize the 2nd order statistics.
An existing relationship between the 2nd order and any Ith order cumulants is generalized to a relationship between any two arbitrary k, Ith order cumulants. This new relationship is used to obtain new algorithms for FIR system identification which use only cumulants of order > 2 and with no other restriction than the Gaussian nature of the additive noise sequence. Simulation studies are presented to demonstrate the failure of the existing algorithms when the imposed constraints on the 2nd order statistics of the additive noise are violated while the proposed algorithms perform very well and give consistent results.
Recently, a new algebraic approach for parameter estimation method denoted the Linear Combination of Slices (LCS) method was proposed and was based on expressing the FIR parameters as a linear combination of the cumulant slices. The rank deficient cumulant matrix S formed in the LCS method can be expressed as a product of matrices which have a certain structure. The orthogonality property of the subspace orthogonal to S and the range space of S has been exploited to obtain a new class of algorithms for the estimation of the parameters of a FIR system. Numerical simulation studies have been carried out to demonstrate the good behaviour of the proposed algorithms.
Analytical expressions for the covariance of the estimates of the FIR parameters of the different algorithms presented in the thesis have been obtained and numerical comparison has been done for specific cases.
Numerical examples to demonstrate the application of the proposed algorithms for channel equalization in data communication and as an initial solution to the cumulant matching nonlinear optimization methods have been presented.
30
Quattrochi, Douglas J. (Douglas John). "Hypersonic heat transfer and anisotropic visualization with a higher order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/35567.
Повний текст джерелаАнотація:
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (leaves 83-89).
Higher order discretizations of the Navier-Stokes equations promise greater accuracy than conventional computational aerodynamics methods. In particular, the discontinuous Galerkin (DG) finite element method has O(hP+l) design accuracy and allows for subcell resolution of shocks. This work furthers the DG finite element method in two ways. First, it demonstrates the results of DG when used to predict heat transfer to a cylinder in a hypersonic flow. The strong shock is captured with a Laplacian artificial viscosity term. On average, the results are in agreement with an existing hypersonic benchmark. Second, this work improves the visualization of the higher order polynomial solutions generated by DG with an adaptive display algorithm. The new algorithm results in more efficient displays of higher order solutions, including the hypersonic flow solutions generated here.
by Douglas J. Quattrochi.
S.M.
31
Marais, Neilen. "Higher order hierarchal curvilinear triangular vector elements for the finite element method in computational electromagnetics." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53447.
Повний текст джерелаАнотація:
Thesis (MScEng)--Stellenbosch University, 2003.ENGLISH ABSTRACT: The Finite Element Method (FEM) as applied to Computational Electromagnetics (CEM), can be used to solve a large class of Electromagnetics problems with high accuracy, and good computational efficiency. Computational efficiency can be improved by using element basis functions of higher order. If, however, the chosen element type is not able to accurately discretise the computational domain, the converse might be true. This paper investigates the application of elements with curved sides, and higher order basis functions, to computational domains with curved boundaries. It is shown that these elements greatly improve the computational efficiency of the FEM applied to such domains, as compared to using elements with straight sides, and/or low order bases.
AFRIKAANSE OPSOMMING: Die Eindige Element Metode (EEM) kan breedvoerig op Numeriese Elektromagnetika toegepas word, met uitstekende akkuraatheid en 'n hoë doeltreffendheids vlak. Numeriese doeltreffendheid kan verbeter word deur van hoër orde element basisfunksies gebruik te maak. Indien die element egter nie die numeriese domein effektief kan diskretiseer nie, mag die omgekeerde geld. Hierdie tesis ondersoek die toepassing van elemente met geboë sye, en hoër orde basisfunksies, op numeriese domeine met geboë grense. Daar word getoon dat sulke elemente 'n noemenswaardinge verbetering in die numeriese doeltreffendheid van die EEM meebring, vergeleke met reguit- en/of laer-orde elemente.
32
Ruggeri, Felipe. "A higher order time domain panel method for linear and weakly non linear seakeeping problems." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3135/tde-09122016-074844/.
Повний текст джерелаАнотація:
This thesis addresses the development of a weakly non-linear Higher Order Time Domain Rankine Panel Method (TDRPM) for the linear and weakly non-linear seakeeping analysis of floating offshore structures, including wave-current interaction effects. A higher order boundary elements method is adopted based on the body geometry description using Non-uniform Rational B-splines (NURBS) formulation, which can be generated by many standard Computed Aided Design (CAD) softwares widely available, and the several computed quantities (velocity potential, free surface elevation and others) are described using a B-spline formulation of arbitrary degree. The problem is formulated considering wave-current-body interactions up to second order effects, these ones considering the terms obtained by interaction of zero/first order quantities. In order to provide numerical stability, the Initial Boundary Value Problem (IBVP) is formulated in terms of the velocity potential and the local acceleration potential, the later used to predict the hydrodynamic pressure accurately. The zeroth order problem is solved using the double-body linearization instead of the Neumman-Kelvin one in order to allow bluff bodies simulation, leading to very complex expressions regarding the m-terms computation. The method adopts the Rankine sources as Green\'s function, which are integrated using Gauss quadrature in the entire domain, but for the self-influence terms that are integrated using a desingularized procedure. The numerical method is verified initially considering simplified geometries (sphere and circular cylinder) for both, first and second-order computations, with and without current effects. The derivatives of the velocity potential are verified by comparing the numerical m-terms to the analytical solutions for a hemisphere under uniform flow. The mean and double frequency drift forces are computed for fixed and floating structures and the quantities involved in these computations (wave runup, velocity field) are also compared to literature results, including the free floating response of a sphere under current effects. Two practical cases are also studied, namely the wave-induced second order responses of a semi-submersible platform and the wavedrift-damping effect evaluated through the equilibrium angle of a turret moored FPSO. For the former, some specific model tests were designed and conducted in a wave-basin.Essa tese aborda o desenvolvimento de um método de Rankine de ordem alta no domínio do tempo (TDRPM) para o estudo de problemas lineares e fracamente não lineares, incluindo o efeito de corrente, envolvendo sistemas flutuantes. O método de ordem alta desenvolvido considera a geometria do corpo como descrita pelo padrão Non-uniform Rational Basis Spline (NURBS), que está disponível em diverso0s softwares de Computed Aided Design (CAD) disponíveis, sendo as diversas funções (potencial de velocidades, elevação da superfície-livre e outros) descritos usando B-splines de grau arbitrário. O problema é formulado considerando interações onda-corrente-estrutura para efeitos de até segunda ordem, os de ordem superior sendo calculados considerando as interações somente dos termos de ordem inferior. Para garantir a estabilidade numérica, o problema de contorno com valor inicial é formulado0 com relação ao potencial de velocidade e de parcela local do potencial de acelerações, este para garantir cálculos precisos da pressão dinâmica. O problema de ordem zero é resolvido usando a linearização de corpo-duplo ao invés da linearização de Neumman-Kelvin para permitir a análise de corpos rombudos, o que requer o cálculo de termos-m de grande complexidade. O método adota fontes de Rankine como funções de Green, que são integradas através de quadratura de Gauss-Legendre no domínio todo, exceto com relação aos termos de auto-influência que adotasm um procedimento de dessingularização. O método numérico é inicialmente verificado considerando corpos de geometria simplificada (esfera e cilindro), considerando efeitos de primeira e segunda ordens, com e sem corrente. As derivadas do potencial de velocidade são verificadas comparando os termos-m obtidos numericamente com soluções analíticas disponíveis para a esfera em fluído infinito. As forças de deriva média e dupla-frequência são calculadas para estruturas fixas e flutuantes, sendo as funções calculadas (elevação da superfície, campo de velocidade) comparadas com resultados disponíveis na literatura, incluindo o movimento da esfera flutuante sob a ação de corrente e ondas. São também estudados dois casos de aplicação prática, a resposta de segunda ordem de uma plataforma semi-submersível e o efeito de wave-drift damping para o ângulo de equilíbrio de uma plataforma FPSO ancorada através de sistema turred. No caso da semi-submersível, os ensaios foram projetados e realizados em tanque de provas.
33
Davis, Jake Daniel. "A Higher-Order Method Implemented in an Unstructured Panel Code to Model Linearized Supersonic Flows." DigitalCommons@CalPoly, 2019. https://digitalcommons.calpoly.edu/theses/1968.
Повний текст джерелаАнотація:
Since their conception in the 1960s, panel codes have remained a critical tool in the design and development of air vehicles. With continued advancement in computational technologies, today's codes are able to solve flow fields around arbitrary bodies more quickly and with higher fidelity than those that preceded them. Panel codes prove most useful during the conceptual design phase of an air vehicle, allowing engineers to iterate designs, and generate full solutions of the flow field around a vehicle in a matter of seconds to minutes instead of hours to days using traditional CFD methods. There have been relatively few panel codes with the capacity to solve supersonic flow fields, and there has been little recently published work done to improve upon them.
This work implements supersonic potential flow methods into Cal Poly’s open source panel code, CPanel. CPanel was originally developed to solve steady, subsonic flows utilizing constant strength source and doublet panels to define the geometry, and an unstructured geometry discretization; it was later extended to include viscous vortex particle wakes and transient modeling. In this thesis, a higher-order method is implemented in CPanel for use in solving linearized supersonic flows, where a higher-order method is one that utilizes at least one singularity element whose order is higher than constant. CPanel results are verified against analytical solutions, such as the Taylor-Maccoll solution for supersonic conical flows and 2D shock-expansion theory, and the PANAIR and MARCAP supersonic panel codes. Results correlate well with the analytical solutions, and show strong agreement with the other codes.
34
Underwood, Tyler Carroll. "Performance Comparison of Higher-Order Euler Solvers by the Conservation Element and Solution Element Method." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1399017583.
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35
Bilyeu, David L. "A HIGHER-ORDER CONSERVATION ELEMENT SOLUTION ELEMENT METHOD FOR SOLVING HYPERBOLIC DIFFERENTIAL EQUATIONS ON UNSTRUCTURED MESHES." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1396877409.
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36
KUSAKARI, Keiichirou, Masahiko SAKAI, and Toshiki SAKABE. "Primitive Inductive Theorems Bridge Implicit Induction Methods and Inductive Theorems in Higher-Order Rewriting." IEICE, 2005. http://hdl.handle.net/2237/9580.
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37
Nyamayaro, Takura T. A. "On the design and implementation of a hybrid numerical method for singularly perturbed two-point boundary value problems." University of the Western Cape, 2014. http://hdl.handle.net/11394/4326.
Повний текст джерелаАнотація:
>Magister Scientiae - MScWith the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these solvers are tailor-made for specific classes of problems. Therefore, more of such must be developed to accompany the growing need for mathematical models that help in the understanding of the contemporary world. This thesis treats two point boundary value singularly perturbed problems. The solution to this type of problem undergoes steep changes in narrow regions (called boundary or internal layer regions) thus rendering the classical numerical procedures inappropriate. To this end, robust numerical methods such as finite difference methods, in particular fitted mesh and fitted operator methods have extensively been used. While the former consists of transforming the continuous problem into a discrete one on a non-uniform mesh, the latter involves a special discretisation of the problem on a uniform mesh and are known to be more accurate. Both classes of methods are suitably designed to accommodate the rapid change(s) in the solution. Quite often, finite difference methods on piece-wise uniform meshes (of Shishkin-type) are adopted. However, methods based on such non-uniform meshes, though layer-resolving, are not easily extendable to higher dimensions. This work aims at investigating the possibility of capitalising on the advantages of both fitted mesh and fitted operator methods. Theoretical results are confirmed by extensive numerical simulations.
38
Ahmed, Naveed, and Gunar Matthies. "Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39044.
Повний текст джерелаАнотація:
We present the analysis for the higher order continuous Galerkin−Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin−Petrov and discontinuous Galerkin time discretization schemes will be given.
39
Namarathne, Dinithi L. "Measuring intensity dependent optical nonlineartities without sample damage using higher order vortex beams." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/129569/9/Dinithi_Namarathne_Thesis.pdf.
Повний текст джерелаАнотація:
This study developed a beam shaping based method to avoid nonlinear sample damage in high intense pulse laser applications. This is achieved by developing a complete theoretical and experimental framework for Z-scan experiments to utilise higher order vortex beams instead of common Gaussian beam. An image processing based extension was introduced to Z-scan experiments, which can be utilised to achieve results of different Z-scan modes from a single experimental dataset efficiently. The results of this study will have a positive impact on utilising different beam profiles to achieve profile specific advantages in nonlinear applications.
40
Carreno, Coll Victor Alberto. "Transition assertions : a higher-order logic based method for the specification and verification of real-time systems." Thesis, University of Cambridge, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627145.
Повний текст джерела
41
Roessler, Edmund B. (Edmind Brian) 1963. "A Bezier based higher order panel method for steady flow analysis of lifting and non-lifting bodies." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/91337.
Повний текст джерела
42
Barter, Garrett E. (Garrett Ehud) 1979. "Shock capturing with PDE-based artificial viscosity for an adaptive, higher-order discontinuous Galerkin finite element method." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/44931.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 135-143).
The accurate simulation of supersonic and hypersonic flows is well suited to higher-order (p > 1), adaptive computational fluid dynamics (CFD). Since these cases involve flow velocities greater than the speed of sound, an appropriate shock capturing for higher-order, adaptive methods is necessary. Artificial viscosity can be combined with a higher-order discontinuous Galerkin finite element discretization to resolve a shock layer within a single cell. However, when a nonsmooth artificial viscosity model is employed with an otherwise higher-order approximation, element-to-element variations induce oscillations in state gradients and pollute the downstream flow. To alleviate these difficulties, this work proposes a new, higher-order, state based artificial viscosity with an associated governing partial differential equation (PDE). In the governing PDE, the shock sensor acts as a forcing term, driving the artificial viscosity to a non-zero value where it is necessary. The decay rate of the higher-order solution modes and edge-based jumps are both shown to be reliable shock indicators. This new approach leads to a smooth, higher-order representation of the artificial viscosity that evolves in time with the solution. For applications involving the Navier-Stokes equations, an artificial dissipation operator that preserves total enthalpy is introduced. The combination of higher-order, PDE-based artificial viscosity and enthalpy-preserving dissipation operator is shown to overcome the disadvantages of the non-smooth artificial viscosity. The PDE-based artificial viscosity can be used in conjunction with an automated grid adaptation framework that minimizes the error of an output functional. Higher-order solutions are shown to reach strict engineering tolerances with fewer degrees of freedom.
(cont.) The benefit in computational efficiency for higher-order solutions is less dramatic in the vicinity of the shock where errors scale with O(h/p). This includes the near-field pressure signals necessary for sonic boom prediction. When applied to heat transfer prediction on unstructured meshes in hypersonic flows, the PDE-based artificial viscosity is less susceptible to errors introduced by poor shock-grid alignment. Surface heating can also drive the output-based grid adaptation framework to arrive at the same heat transfer distribution as a well-designed structured mesh.
by Garrett Ehud Barter.
Ph.D.
43
Garbin, Turpaud Fernando, and Pachas Ángel Alfredo Lévano. "Higher-order non-local finite element bending analysis of functionally graded." Bachelor's thesis, Universidad Peruana de Ciencias Aplicadas (UPC), 2019. http://hdl.handle.net/10757/626024.
Повний текст джерелаАнотація:
La teoría de vigas de Timoshenko TBT y una teoría de alto orden IFSDT son formuladas utilizando las ecuaciones constitutivas no locales de Eringen. Se utilizaron ecuaciones constitutivas en 3D en el modelo IFSDT. Se utilizó una variación del material con el uso de materiales funcionalmente graduados a lo largo del peralte de una viga de sección rectangular. El principio de trabajos virtuales utilizado y ejemplos numéricos fueron presentados para comparar ambas teorías de vigas.Timoshenko Beam Theory (TBT) and an Improved First Shear Deformation Theory (IFSDT) are reformulated using Eringen’s non-local constitutive equations. The use of 3D constitutive equation is presented in IFSDT. A material variation is made by the introduction of FGM power law in the elasticity modulus through the height of a rectangular section beam. The virtual work statement and numerical results are presented in order to compare both beam theories.
Tesis
44
Jewell, Jeffrey Steven. "Higher-order Runge--Kutta type schemes based on the Method of Characteristics for hyperbolic equations with crossing characteristics." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1028.
Повний текст джерелаАнотація:
The Method of Characteristics (MoC) is a well-known procedure used to find the numerical solution of systems of hyperbolic partial differential equations (PDEs). The main idea of the MoC is to integrate a system of ordinary differential equations (ODEs) along the characteristic curves admitted by the PDEs. In principle, this can be done by any appropriate numerical method for ODEs. In this thesis, we will examine the MoC applied to systems of hyperbolic PDEs with straight-line and crossing characteristics. So far, only first- and second-order accurate explicit MoC schemes for these types of systems have been reported. As such, the purpose of this thesis is to develop MoC schemes which are of an order greater than two.
The order of the global truncation error of an MoC scheme goes hand-in-hand with the order of the ODE solver used. The MoC schemes which have already been developed use the first-order Simple Euler (SE) and second-order Modified Euler (ME) methods as the ODE solvers. The SE and ME methods belong to a larger family of numerical methods for ODEs known as the Runge--Kutta (RK) methods. First, we will attempt to develop third- and fourth-order MoC schemes by using the classical third- and fourth-order RK methods as the ODE solver. We will show that the resulting MoC schemes can be strongly unstable, meaning that the error in the numerical solution becomes unbounded rather quickly.
We then turn our attention to the so-called pseudo-RK (pRK) methods for ODEs. The pRK methods are at the intersection of RK and multistep methods, and a variety of third- and fourth-order schemes can be constructed. We show that when certain pRK schemes are used in the MoC, at most a weak instability, or no instability at all, is present, and thus the resulting methods are suitable for long-time computations. Finally, we present some numerical results confirming that the MoC using third- and fourth-order pRK schemes have the desired accuracy.
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Sarkar, Samrat. "Blur adaptation with source and observer methods." Thesis, Queensland University of Technology, 2017. https://eprints.qut.edu.au/103277/1/Samrat_Sarkar_Thesis.pdf.
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Blur adaptation is the improvement of visual and perceptual performance with time following viewing of a blurred target. It is possible to generate blurred images with two different methods – source and observer methods. This study compared blur adaption with source and observer methods for combinations of defocus and higher-order aberrations. Participants adapted to a blurred natural scene for 1 minute and performed a visual acuity task with tumbling Es. Negligible blur adaption was noticed for both source and observer methods. A longer adapting period might be necessary to achieve significant improvement in visual acuity following blur adaptation.
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Titterington, Lynda Carol. "Case studies in pathophysiology: a study of an online interactive learning environment to develop higher order thinking and argumentation." The Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1196183110.
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Pohl, Alexander [Verfasser]. "Simulation of Diffraction Based on the Uncertainty Relation : an Efficient Simulation Method Combining Higher Order Diffractions and Reflections / Alexander Pohl." Berlin : epubli GmbH, 2014. http://d-nb.info/1058698656/34.
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Schwartz, Uwe [Verfasser], and Gernot [Akademischer Betreuer] Längst. "Functional Chromatin Extraction: A method to study DNA accessibility in higher-order structures of chromatin / Uwe Schwartz ; Betreuer: Gernot Längst." Regensburg : Universitätsbibliothek Regensburg, 2021. http://d-nb.info/1238897096/34.
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Barrera, Cruz Jorge Luis. "A Hierarchical Interface-enriched Finite Element Method for the Simulation of Problems with Complex Morphologies." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430838711.
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Heimann, Felix [Verfasser], and Peter [Akademischer Betreuer] Bastian. "An Unfitted Higher-Order Discontinuous Galerkin Method for Incompressible Two-Phase Flow with Moving Contact Lines / Felix Heimann ; Betreuer: Peter Bastian." Heidelberg : Universitätsbibliothek Heidelberg, 2013. http://d-nb.info/117738101X/34.
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