Truncation error estimation in the Discontinuous Galerkin Spectral Element Method

En esta tesis, el método de estimación de error de truncación conocido como restimation ha sido extendido de esquemas de bajo orden a esquemas de alto orden. La mayoría de los trabajos en la bibliografía utilizan soluciones convergidas en mallas de distinto refinamiento para realizar la estimación. En este trabajo se utiliza una solución en una única malla con distintos órdenes polinómicos. Además, no se requiere que esta solución esté completamente convergida, resultando en el método conocido como quasi-a priori T-estimation. La aproximación quasi-a priori estima el error mientras el residuo del método iterativo no es despreciable. En este trabajo se demuestra que algunas de las hipótesis fundamentales sobre el comportamiento del error, establecidas para métodos de bajo orden, dejan de ser válidas en esquemas de alto orden, haciendo necesaria una revisión completa del comportamiento del error antes de redefinir el algoritmo. Para facilitar esta tarea, en una primera etapa se considera el método conocido como Chebyshev Collocation, limitando la aplicación a geometrías simples. La extensión al método Discontinuouos Galerkin Spectral Element Method presenta dificultades adicionales para la definición precisa y la estimación del error, debidos a la formulación débil, la discretización multidominio y la formulación discontinua. En primer lugar, el análisis se enfoca en leyes de conservación escalares para examinar la precisión de la estimación del error de truncación. Después, la validez del análisis se demuestra para las ecuaciones incompresibles y compresibles de Euler y Navier Stokes. El método de aproximación quasi-a priori r-estimation permite desacoplar las contribuciones superficiales y volumétricas del error de truncación, proveyendo información sobre la anisotropía de las soluciones así como su ratio de convergencia con el orden polinómico. Se demuestra que esta aproximación quasi-a priori produce estimaciones del error de truncación con precisión espectral. ABSTRACT In this thesis, the τ-estimation method to estimate the truncation error is extended from low order to spectral methods. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, only one grid with different polynomial orders is used in this work. Furthermore, a non timeconverged solution is used resulting in the quasi-a priori τ-estimation method. The quasi-a priori approach estimates the error when the residual of the time-iterative method is not negligible. It is shown in this work that some of the fundamental assumptions about error tendency, well established for low order methods, are no longer valid in high order schemes, making necessary a complete revision of the error behavior before redefining the algorithm. To facilitate this task, the Chebyshev Collocation Method is considered as a first step, limiting their application to simple geometries. The extension to the Discontinuous Galerkin Spectral Element Method introduces additional features to the accurate definition and estimation of the error due to the weak formulation, multidomain discretization and the discontinuous formulation. First, the analysis focuses on scalar conservation laws to examine the accuracy of the estimation of the truncation error. Then, the validity of the analysis is shown for the incompressible and compressible Euler and Navier Stokes equations. The developed quasi-a priori τ-estimation method permits one to decouple the interfacial and the interior contributions of the truncation error in the Discontinuous Galerkin Spectral Element Method, and provides information about the anisotropy of the solution, as well as its rate of convergence in polynomial order. It is demonstrated here that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

Loose Coupling Based Reference Scheme for Shop Floor-Control-System/Production-Equipment Integration.

Acoplamiento del sistema informático de control de piso de producción (SFS) con el conjunto de equipos de fabricación (SPE) es una tarea compleja. Tal acoplamiento involucra estándares abiertos y propietarios, tecnologías de información y comunicación, entre otras herramientas y técnicas. Debido a la turbulencia de mercados, ya sea soluciones personalizadas o soluciones basadas en estándares eventualmente requieren un esfuerzo considerable de adaptación. El concepto de acoplamiento débil ha sido identificado en la comunidad de diseño organizacional como soporte para la sobrevivencia de la organización. Su presencia reduce la resistencia de la organización a cambios en el ambiente. En este artículo los resultados obtenidos por la comunidad de diseño organizacional son identificados, traducidos y organizados para apoyar en la solución del problema de integración SFS-SPE. Un modelo clásico de acoplamiento débil, desarrollado por la comunidad de estudios de diseño organizacional, es resumido y trasladado al área de interés. Los aspectos claves son identificados para utilizarse como promotores del acoplamiento débil entre SFS-SPE, y presentados en forma de esquema de referencia. Así mismo, este esquema de referencia es presentado como base para el diseño e implementación de una solución genérica de acoplamiento o marco de trabajo (framework) de acoplamiento, a incluir como etapa de acoplamiento débil entre SFS y SPE. Un ejemplo de validación con varios conjuntos de equipos de fabricación, usando diferentes medios físicos de comunicación, comandos de controlador, lenguajes de programación de equipos y protocolos de comunicación es presentado, mostrando un nivel aceptable de autonomía del SFS. = Coupling shop floor software system (SFS) with the set of production equipment (SPE) becomes a complex task. It involves open and proprietary standards, information and communication technologies among other tools and techniques. Due to market turbulence, either custom solutions or standards based solutions eventually require a considerable effort of adaptation. Loose coupling concept has been identified in the organizational design community as a compensator for organization survival. Its presence reduces organization reaction to environment changes. In this paper the results obtained by the organizational de sign community are identified, translated and organized to support the SFS-SPE integration problem solution. A classical loose coupling model developed by organizational studies community is abstracted and translated to the area of interest. Key aspects are identified to be used as promoters of SFS-SPE loose coupling and presented in a form of a reference scheme. Furthermore, this reference scheme is proposed here as a basis for the design and implementation of a generic coupling solution or coupling framework, that is included as a loose coupling stage between SFS and SPE. A validation example with various sets of manufacturing equipment, using different physical communication media, controller commands, programming languages and wire protocols is presented, showing an acceptable level of autonomy gained by the SFS.

A finite element scheme for shock capturing /

At head of title: "In-house Laboratory Independent Research Program."

Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault

Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

Integrated power scheme simulator for human-system integration studies

We present a simulator of a hydropower company’s view of its scheme, and its broader market and network context, which has been developed to evaluate advanced displays for control room operations. Although simplified, the simulator captures all the main aspects of scheme operations. The simulator allows controlled studies to be performed that test the effectiveness of current vs advanced display concepts under normal vs unexpected operating conditions that can be scripted into the simulator.

Linking finite-element analysis and computer-aided drafting processes

The aim of this research was to investigate the integration of computer-aided drafting and finite-element analysis in a linked computer-aided design procedure and to develop the necessary software. The Be'zier surface patch for surface representation was used to bridge the gap between the rather separate fields of drafting and finite-element analysis because the surfaces are defined by analytical functions which allow systematic and controlled variation of the shape and provide continuous derivatives up to any required degree. The objectives of this research were achieved by establishing : (i) A package which interpretes the engineering drawings of plate and shell structures and prepares the Be'zier net necessary for surface representation. (ii) A general purpose stand-alone meshed-surface modelling package for surface representation of plates and shells using the Be'zier surface patch technique. (iii) A translator which adapts the geometric description of plate and shell structures as given by the meshed-surface modeller to the form needed by the finite-element analysis package. The translator was extended to suit fan impellers by taking advantage of their sectorial symmetry. The linking processes were carried out for simple test structures, simplified and actual fan impellers to verify the flexibility and usefulness of the linking technique adopted. Finite-element results for thin plate and shell structures showed excellent agreement with those obtained by other investigators while results for the simplified and actual fan impellers also showed good agreement with those obtained in an earlier investigation where finite-element analysis input data were manually prepared. Some extensions of this work have also been discussed.

A semi- analytic finite element approach to the stress analysis of circular plate

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Finite Element Modeling of Spiral Frequency Steerable Acoustic Transducers (FSATs) for guided waves based Structural Health Monitoring of plate-like structures

Structural Health Monitoring (SHM) is an emerging area of research associated to improvement of maintainability and the safety of aerospace, civil and mechanical infrastructures by means of monitoring and damage detection. Guided wave structural testing method is an approach for health monitoring of plate-like structures using smart material piezoelectric transducers. Among many kinds of transducers, the ones that have beam steering feature can perform more accurate surface interrogation. A frequency steerable acoustic transducer (FSATs) is capable of beam steering by varying the input frequency and consequently can detect and localize damage in structures. Guided wave inspection is typically performed through phased arrays which feature a large number of piezoelectric transducers, complexity and limitations. To overcome the weight penalty, the complex circuity and maintenance concern associated with wiring a large number of transducers, new FSATs are proposed that present inherent directional capabilities when generating and sensing elastic waves. The first generation of Spiral FSAT has two main limitations. First, waves are excited or sensed in one direction and in the opposite one (180 ̊ ambiguity) and second, just a relatively rude approximation of the desired directivity has been attained. Second generation of Spiral FSAT is proposed to overcome the first generation limitations. The importance of simulation tools becomes higher when a new idea is proposed and starts to be developed. The shaped transducer concept, especially the second generation of spiral FSAT is a novel idea in guided waves based of Structural Health Monitoring systems, hence finding a simulation tool is a necessity to develop various design aspects of this innovative transducer. In this work, the numerical simulation of the 1st and 2nd generations of Spiral FSAT has been conducted to prove the directional capability of excited guided waves through a plate-like structure.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Vibration of ship structures and its control

Noise and vibration in complex ship structures are becoming a prominent issue for ship building industry and ship companies due to the constant demand of building faster ships of lighter weight, and the stringent noise and libration regulation of the industry. In order to retain the full benefit of building faster ships without compromising too much on ride comfort and safety, noise and vibration control needs to be implemented. Due to the complexity of ship structures, the coupling of different wave types and multiple wave propagation paths, active control of global hull modes is difficult to implement and very expensive. Traditional passive control such as adding damping materials is only effective in the high frequency range. However, most severe damage to ship structures is caused by large structural deformation of hull structures and high dynamic stress concentration at low frequencies. The most discomfort and fatigue of passengers and the crew onboard ships is also due to the low frequency noise and vibration. Innovative approaches are therefore, required to attenuate the noise and vibration at low frequencies. This book was developed from several specialized research topics on vibration and vibration control of ship structures, mostly from the author's own PhD work at the University of Western Australia. The book aims to provide a better understanding of vibration characteristics of ribbed plate structures, plate/plate coupled structures and the mechanism governing wave propagation and attenuation in periodic and irregular ribbed structures as well as in complex ship structures. The book is designed to be a reference book for ship builders, vibro-acoustic engineers and researchers. The author also hopes that the book can stimulate more exciting future work in this area of research. It is the author's humble desire that the book can be some use for those who purchase it. This book is divided into eight chapters. Each chapter focuses on providing solution to address a particular issue on vibration problems of ship structures. A brief summary of each chapter is given in the general introduction. All chapters are inter-dependent to each other to form an integration volume on the subject of vibration and vibration control of ship structures and alike. I am in debt to many people in completing this work. In particular, I would like to thank Professor J. Pan, Dr N.H. Farag, Dr K. Sum and many others from the University of Western Australia for useful advices and helps during my times at the University and beyond. I would also like to thank my wife, Miaoling Wang, my children, Anita, Sophia and Angela Lin, for their sacrifice and continuing supports to make this work possible. Financial supports from Australian Research Council, Australian Defense Science and Technology Organization and Strategic Marine Pty Ltd at Western Australia for this work is gratefully acknowledged.

Vibration characteristics of plate elements subjected in-plane loads (axial loads)

Axial deformations resulting from in-plane loads (axial forces) of plate elements impact significantly on their vibration characteristics. Although, numerous methods have been developed to quantify axial forces and hence deformations of individual plate elements with different boundary conditions based on their natural frequencies, these methods are unable to apply to the plate elements in a structural system. This is because the natural frequency is a global parameter for the entire structure. Thus, this paper proposes a comprehensive vibration based procedure to quantify axial deformations of plate elements in a structural framing system. Unique capabilities of the proposed method present through illustrative examples. Keywords- Plate Elements, Dynamic Stiffness Matrix, Finite Element Method, Vibration Characteristics, Axial Deformation

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Simulation of inplane and out of plane AE source in thin plate

In most materials, short stress waves are generated during the process of plastic deformation, phase transformation, crack formation and crack growth. These phenomena are applied in acoustic emission (AE) for the detection of material defects in a wide spectrum of areas, ranging from nondestructive testing for the detection of materials defects to monitoring of microseismical activity. AE technique is also used for defect source identification and for failure detection. AE waves consist of P waves (primary longitudinal waves), S waves (shear/transverse waves) and Rayleigh (surface) waves as well as reflected and diffracted waves. The propagation of AE waves in various modes has made the determination of source location difficult. In order to use acoustic emission technique for accurate identification of source, an understanding of wave propagation of the AE signals at various locations in a plate structure is essential. Furthermore, an understanding of wave propagation can also assist in sensor location for optimum detection of AE signals along with the characteristics of the source. In real life, as the AE signals radiate from the source it will result in stress waves. Unless the type of stress wave is known, it is very difficult to locate the source when using the classical propagation velocity equations. This paper describes the simulation of AE waves to identify the source location and its characteristics in steel plate as well as the wave modes. The finite element analysis (FEA) is used for the numerical simulation of wave propagation in thin plate. By knowing the type of wave generated, it is possible to apply the appropriate wave equations to determine the location of the source. For a single plate structure, the results show that the simulation algorithm is effective to simulate different stress waves.