A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

A method of fundamental solutions for theaxisymmetric backward heat equation

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Theoretical investigations of intercellular communication in the microcirculation: Conducted responses, myoendothelial projections and endothelium derived hyperpolarizing factor

The contractile state of microcirculatory vessels is a major determinant of the blood pressure of the whole systemic circulation. Continuous bi-directional communication exists between the endothelial cells (ECs) and smooth muscle cells (SMCs) that regulates calcium (Ca2+) dynamics in these cells. This study presents theoretical approaches to understand some of the important and currently unresolved microcirculatory phenomena. ^ Agonist induced events at local sites have been shown to spread long distances in the microcirculation. We have developed a multicellular computational model by integrating detailed single EC and SMC models with gap junction and nitric oxide (NO) coupling to understand the mechanisms behind this effect. Simulations suggest that spreading vasodilation mainly occurs through Ca 2+ independent passive conduction of hyperpolarization in RMAs. Model predicts a superior role for intercellular diffusion of inositol (1,4,5)-trisphosphate (IP3) than Ca2+ in modulating the spreading response. ^ Endothelial derived signals are initiated even during vasoconstriction of stimulated SMCs by the movement of Ca2+ and/or IP3 into the EC which provide hyperpolarizing feedback to SMCs to counter the ongoing constriction. Myoendothelial projections (MPs) present in the ECs have been recently proposed to play a role in myoendothelial feedback. We have developed two models using compartmental and 2D finite element methods to examine the role of these MPs by adding a sub compartment in the EC to simulate MP with localization of intermediate conductance calcium activated potassium channels (IKCa) and IP3 receptors (IP 3R). Both models predicted IP3 mediated high Ca2+ gradients in the MP after SMC stimulation with limited global spread. This Ca 2+ transient generated a hyperpolarizing feedback of ∼ 2–3mV. ^ Endothelium derived hyperpolarizing factor (EDHF) is the dominant form of endothelial control of SMC constriction in the microcirculation. A number of factors have been proposed for the role of EDHF but no single pathway is agreed upon. We have examined the potential of myoendothelial gap junctions (MEGJs) and potassium (K+) accumulation as EDHF using two models (compartmental and 2D finite element). An extra compartment is added in SMC to simulate micro domains (MD) which have NaKα2 isoform sodium potassium pumps. Simulations predict that MEGJ coupling is much stronger in producing EDHF than alone K+ accumulation. On the contrary, K+ accumulation can alter other important parameters (EC V m, IKCa current) and inhibit its own release as well as EDHF conduction via MEGJs. The models developed in this study are essential building blocks for future models and provide important insights to the current understanding of myoendothelial feedback and EDHF.^

Assessment of primary energy conversions of oscillating water columns. I. Hydrodynamic analysis

This is an investigation on the development of a numerical assessment method for the hydrodynamic performance of an oscillating water column (OWC) wave energy converter. In the research work, a systematic study has been carried out on how the hydrodynamic problem can be solved and represented reliably, focusing on the phenomena of the interactions of the wave-structure and the wave-internal water surface. These phenomena are extensively examined numerically to show how the hydrodynamic parameters can be reliably obtained and used for the OWC performance assessment. In studying the dynamic system, a two-body system is used for the OWC wave energy converter. The first body is the device itself, and the second body is an imaginary “piston,” which replaces part of the water at the internal water surface in the water column. One advantage of the two-body system for an OWC wave energy converter is its physical representations, and therefore, the relevant mathematical expressions and the numerical simulation can be straightforward. That is, the main hydrodynamic parameters can be assessed using the boundary element method of the potential flow in frequency domain, and the relevant parameters are transformed directly from frequency domain to time domain for the two-body system. However, as it is shown in the research, an appropriate representation of the “imaginary” piston is very important, especially when the relevant parameters have to be transformed from frequency-domain to time domain for a further analysis. The examples given in the research have shown that the correct parameters transformed from frequency domain to time domain can be a vital factor for a successful numerical simulation.

Precast Prestressed Concrete Panel Subdecks in Skewed Bridges, Interim Report, 1990

Precast prestressed concrete panels have been used in bridge deck construction in Iowa and many other states. To investigate the performance of these panels at abutment or pier diaphragm locations for bridges with various skew angles, a research program involving both analytical and experimental aspects, is being conducted. This interim report presents the status of the research with respect to four tasks. Task 1 which involves a literature review and two surveys is essentially complete. Task 2 which involved field investigations of three Iowa bridges containing precast panel subdecks has been completed. Based on the findings of these investigations, future inspections are recommended to evaluate potential panel deterioration due to possible corrosion of the prestressed strands. Task 3 is the experimental program which has been established to monitor the behavior of five configurations of full scale composite deck slabs. Three dimensional test and instrumentation frameworks have been constructed to load and monitor the slab specimens. The first slab configuration representing an interior panel condition is being tested and preliminary results are presented for one of these tests in this interim report. Task 4 involves the analytical investigation of the experimental specimens. Finite element methods are being applied to analytically predict the behavior of the test specimens. The first test configuration of the interior panel condition has been analyzed for the same loads used in the laboratory, and the results are presented herein. Very good correlation between the analytical and experimental results has occurred.

Cone penetration testing to assess slope stability in the 1979 Nice landslide area (Ligurian Margin, SE France)

In the landslide-prone area near the Nice international airport, southeastern France, an interdisciplinary approach is applied to develop realistic lithological/geometrical profiles and geotechnical/strength sub-seafloor models. Such models are indispensable for slope stability assessments using limit equilibrium or finite element methods. Regression analyses, based on the undrained shear strength (su) of intact gassy sediments are used to generate a sub-seafloor strength model based on 37 short dynamic and eight long static piezocone penetration tests, and laboratory experiments on one Calypso piston and 10 gravity cores. Significant strength variations were detected when comparing measurements from the shelf and the shelf break, with a significant drop in su to 5.5 kPa being interpreted as a weak zone at a depth between 6.5 and 8.5 m below seafloor (mbsf). Here, a 10% reduction of the in situ total unit weight compared to the surrounding sediments is found to coincide with coarse-grained layers that turn into a weak zone and detachment plane for former and present-day gravitational, retrogressive slide events, as seen in 2D chirp profiles. The combination of high-resolution chirp profiles and comprehensive geotechnical information allows us to compute enhanced 2D finite element slope stability analysis with undrained sediment response compared to previous 2D numerical and 3D limit equilibrium assessments. Those models suggest that significant portions (detachment planes at 20 m or even 55 mbsf) of the Quaternary delta and slope apron deposits may be mobilized. Given that factors of safety are equal or less than 1 when further considering the effect of free gas, a high risk for a landslide event of considerable size off Nice international airport is identified

Integração analítica das matrizes de influência da formulação elástica anisotrópica plana do método dos elementos de contorno

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2015.

Validación de la simulación numérica del flujo bifásico hidrodinámico en sistemas de lecho fluido

Este trabajo tiene como objetivo la mejora en la validación de la simulación numérica del flujo bifásico característico del transporte de lecho fluido, mediante la formulación y desarrollo de un modelo numérico combinado Volúmenes Finitos - Elementos Finitos. Para ello se simula numéricamente el flujo de mezcla sólido-gas en una Cámara de Lecho Fluido, bajo implementación en código COMSOL, cuyos resultados son mejores comparativamente a un modelo basado en el método de Elementos Discretos implementado en código abierto MFIX. El problema fundamental de la modelización matemática del fenómeno de lecho fluido es la irregularidad del dominio, el acoplamiento de las variables en espacio y tiempo y, la no linealidad. En esta investigación se reformula apropiadamente las ecuaciones conservativas del fenómeno, tales que permitan obtener un problema variacional equivalente y solucionable numéricamente. Entonces; se define una ecuación de estado en función de la presión hidrodinámica y la fracción volumétrica de sólidos, quedando desacoplado el sistema en tres sub-problemas, garantizando así la existencia de solución del problema general. Una vez aproximados numéricamente ambos modelos, se comparan los resultados de donde se observa que el modelo materia del presente artículo, verifica de forma más eficaz las condiciones de mezcla óptima, reflejada en la calidad del burbujeo y velocidad de mezcla.

Error estimation and adaptive mesh refinement for aerodynamic flows

This lecture course covers the theory of so-called duality-based a posteriori error estimation of DG finite element methods. In particular, we formulate consistent and adjoint consistent DG methods for the numerical approximation of both the compressible Euler and Navier-Stokes equations; in the latter case, the viscous terms are discretized based on employing an interior penalty method. By exploiting a duality argument, adjoint-based a posteriori error indicators will be established. Moreover, application of these computable bounds within automatic adaptive finite element algorithms will be developed. Here, a variety of isotropic and anisotropic adaptive strategies, as well as $hp$-mesh refinement will be investigated.

Induced Damping on Vibrating Circular Plates Submerged in still Fluid

When a structure vibrates immersed in a fluid it is known that the dynamic properties of the system are modified. The surrounding fluid will, in general, contribute to the inertia, the rigidity and the damping coefficient of the coupled fluid-structure system. For light structures, like spacecraft antennas, even when the fluid is air the contribution to the dynamic properties can be important. For not so light structures the ratio of the equivalent fluid/structure mass and rigidity can be very small and the fluid contribution could be neglected. For the ratio of equivalent fluid/structure damping both terms are of the same order and therefore the fluid contribution must be studied. The working life of the spacecraft structure would be on space and so without any surrounding fluid. The response of a spacecraft structure on its operational life would be attenuated by the structural damping alone but when the structure is dynamically tested on the earth the dynamic modal test is performed with the fluid surrounding it. The results thus are contaminated by the effects of the fluid. If the damping added by the fluid is of the same order as the structural damping the response of the structure in space can be quite different to the response predicted on earth. It is therefore desirable to have a method able to determine the amount of damping induced by the fluid and that should be subtracted of the total damping measured on the modal vibration test. In this work, a method for the determination of the effect of the surrounding fluid on the dynamic characteristics of a circular plate has been developed. The plate is assumed to vibrate harmonically with the vacuum modes and the generalized forces matrix due to the fluid is thus computed. For a compressible fluid this matrix is formed by complex numbers including terms of inertia, rigidity and damping. The matrix due to the fluid loading is determined by a boundary element method (BEM). The BEM used is of circular rings on the plate surface so the number of elements to obtain an accurate result is very low. The natural frequencies of the system are computed by an iteration procedure one by one and also the damping fluid contribution. Comparisons of the present method with various experimental data and other theories show the efficiency and accuracy of the method for any support condition of the plate.

Otimização evolucionária para problemas de transferência de calor em PCI usando MEC

Dissertação (mestrado)—Universidade de Brasília, Faculdade UnB Gama, Programa de Pós-graduação em Integridade de Materiais da Engenharia, 2015.