An Optimal Order Interior Penalty Discontinuous Galerkin Discretization of the Compressible Navier-Stokes Equations

In this article we propose a new symmetric version of the interior penalty discontinuous Galerkin finite element method for the numerical approximation of the compressible Navier-Stokes equations. Here, particular emphasis is devoted to the construction of an optimal numerical method for the evaluation of certain target functionals of practical interest, such as the lift and drag coefficients of a body immersed in a viscous fluid. With this in mind, the key ingredients in the construction of the method include: (i) An adjoint consistent imposition of the boundary conditions; (ii) An adjoint consistent reformulation of the underlying target functional of practical interest; (iii) Design of appropriate interior-penalty stabilization terms. Numerical experiments presented within this article clearly indicate the optimality of the proposed method when the error is measured in terms of both the L_2-norm, as well as for certain target functionals. Computational comparisons with other discontinuous Galerkin schemes proposed in the literature, including the second scheme of Bassi & Rebay, cf. [11], the standard SIPG method outlined in [25], and an NIPG variant of the new scheme will be undertaken.

Algoritmos de otimização e o problema inverso aplicados à identificação de danos estruturais com o uso do MEF

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 2015.

A Caputo fractional derivative of a function with respect to another function

In this paper we consider a Caputo type fractional derivative with respect to another function. Some properties, like the semigroup law, a relationship between the fractional derivative and the fractional integral, Taylor’s Theorem, Fermat’s Theorem, etc., are studied. Also, a numerical method to deal with such operators, consisting in approximating the fractional derivative by a sum that depends on the first-order derivative, is presented. Relying on examples, we show the efficiency and applicability of the method. Finally, an application of the fractional derivative, by considering a Population Growth Model, and showing that we can model more accurately the process using different kernels for the fractional operator is provided.

Influência de feixes de condutores em linhas de transmissão UAT CA

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2015.

Um método numérico para a solução de problemas em física quântica de poucos corpos

Neste artigo é apresentado um método numérico que pode ser utilizado por alunos de graduação para a solução de problemas em física quântica de poucos corpos. O método é aplicado a dois problemas de dois corpos geralmente vistos pelos estudantes: o átomo de hidrogênio e o dêuteron. O método porém, pode ser estendido para três ou mais partículas.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Finite difference calculations of permeability in large domains in a wide porosity range.

Determining effective hydraulic, thermal, mechanical and electrical properties of porous materials by means of classical physical experiments is often time-consuming and expensive. Thus, accurate numerical calculations of material properties are of increasing interest in geophysical, manufacturing, bio-mechanical and environmental applications, among other fields. Characteristic material properties (e.g. intrinsic permeability, thermal conductivity and elastic moduli) depend on morphological details on the porescale such as shape and size of pores and pore throats or cracks. To obtain reliable predictions of these properties it is necessary to perform numerical analyses of sufficiently large unit cells. Such representative volume elements require optimized numerical simulation techniques. Current state-of-the-art simulation tools to calculate effective permeabilities of porous materials are based on various methods, e.g. lattice Boltzmann, finite volumes or explicit jump Stokes methods. All approaches still have limitations in the maximum size of the simulation domain. In response to these deficits of the well-established methods we propose an efficient and reliable numerical method which allows to calculate intrinsic permeabilities directly from voxel-based data obtained from 3D imaging techniques like X-ray microtomography. We present a modelling framework based on a parallel finite differences solver, allowing the calculation of large domains with relative low computing requirements (i.e. desktop computers). The presented method is validated in a diverse selection of materials, obtaining accurate results for a large range of porosities, wider than the ranges previously reported. Ongoing work includes the estimation of other effective properties of porous media.

In Situ Characterization of Optical Absorption by Carbonaceous Aerosols: Calibration and Measurement

Light absorption by aerosols has a great impact on climate change. A Photoacoustic spectrometer (PA) coupled with aerosol-based classification techniques represents an in situ method that can quantify the light absorption by aerosols in a real time, yet significant differences have been reported using this method versus filter based methods or the so-called difference method based upon light extinction and light scattering measurements. This dissertation focuses on developing calibration techniques for instruments used in measuring the light absorption cross section, including both particle diameter measurements by the differential mobility analyzer (DMA) and light absorption measurements by PA. Appropriate reference materials were explored for the calibration/validation of both measurements. The light absorption of carbonaceous aerosols was also investigated to provide fundamental understanding to the absorption mechanism. The first topic of interest in this dissertation is the development of calibration nanoparticles. In this study, bionanoparticles were confirmed to be a promising reference material for particle diameter as well as ion-mobility. Experimentally, bionanoparticles demonstrated outstanding homogeneity in mobility compared to currently used calibration particles. A numerical method was developed to calculate the true distribution and to explain the broadening of measured distribution. The high stability of bionanoparticles was also confirmed. For PA measurement, three aerosol with spherical or near spherical shapes were investigated as possible candidates for a reference standard: C60, copper and silver. Comparisons were made between experimental photoacoustic absorption data with Mie theory calculations. This resulted in the identification of C60 particles with a mobility diameter of 150 nm to 400 nm as an absorbing standard at wavelengths of 405 nm and 660 nm. Copper particles with a mobility diameter of 80 nm to 300 nm are also shown to be a promising reference candidate at wavelength of 405 nm. The second topic of this dissertation focuses on the investigation of light absorption by carbonaceous particles using PA. Optical absorption spectra of size and mass selected laboratory generated aerosols consisting of black carbon (BC), BC with non-absorbing coating (ammonium sulfate and sodium chloride) and BC with a weakly absorbing coating (brown carbon derived from humic acid) were measured across the visible to near-IR (500 nm to 840 nm). The manner in which BC mixed with each coating material was investigated. The absorption enhancement of BC was determined to be wavelength dependent. Optical absorption spectra were also taken for size and mass selected smoldering smoke produced from six types of commonly seen wood in a laboratory scale apparatus.

Vortex Shedding Dynamics in Long Aspect-Ratio Aerodynamics Bodies

The focus of the current dissertation is to study qualitatively the underlying physics of vortex-shedding and wake dynamics in long aspect-ratio aerodynamics in incompressible viscous flow through the use of the KLE method. We carried out a long series of numerical experiments in the cases of flow around the cylinder at low Reynolds numbers. The study of flow at low Reynolds numbers provides an insight in the fluid physics and also plays a critical role when applying to stalled turbine rotors. Many of the conclusions about the qualitative nature of the physical mechanisms characterizing vortex formation, shedding and further interaction analyzed here at low Re could be extended to other Re regimes and help to understand the separation of the boundary layers in airfoils and other aerodynamic surfaces. In the long run, it aims to provide a better understanding of the complex multi-physics problems involving fluid-structure-control interaction through improved mathematical computational models of the multi-physics process. Besides the scientific conclusions produced, the research work on streamlined and bluff-body condition will also serve as a valuable guide for the future design of blade aerodynamics and the placement of wind turbines and hydrakinetic turbines, increasing the efficiency in the use of expensive workforce, supplies, and infrastructure. After the introductory section describing the main fields of application of wind power and hydrokinetic turbines, we describe the main features and theoretical background of the numerical method used here. Then, we present the analysis of the numerical experimentation results for the oscillatory regime right before the onset of vortex shedding for circular cylinders. We verified the wake length of the closed near-wake behind the cylinder and analysed the decay of the wake at the wake formation region, and then studied the St-Re relationship at the Reynolds numbers before the wake sheds compared to the experimental data. We found a theoretical model that describes the time evolution of the amplitude of fluctuations in the vorticity field on the twin vortex wake, which accurately matches the numerical results in terms of the frequency of the oscillation and rate of decay. We also proposed a model based on an analog circuit that is able to interpret the concerning flow by reducing the number of degrees of freedom. It follows the idea of the non-linear oscillator and resembles the dynamics mechanism of the closed near-wake with a common configured sine wave oscillator. This low-dimensional circuital model may also help to understand the underlying physical mechanisms, related to vorticity transport, that give origin to those oscillations.

A measure of conductivity for lattice fermions at finite density

We study the linear response to an external electric field of a system of fermions in a lattice at zero temperature. This allows to measure numerically the Euclidean conductivity which turns out to be compatible with an analytical calculation for free fermions. The numerical method is generalizable to systems with dynamical interactions where no analytical approach is possible.

A finite element framework for the interplay between delamination and buckling of rubber-like bi-material systems and stretchable electronics

In this study, a finite element (FE) framework for the analysis of the interplay between buckling and delamination of thin layers bonded to soft substrates is proposed. The current framework incorporates the following modeling features: (i) geometrically nonlinear solid shell elements, (ii) geometrically nonlinear cohesive interface elements, and (iii) hyperelastic material constitutive response for the bodies that compose the system. A fully implicit Newton–Raphson solution strategy is adopted to deal with the complex simultaneous presence of geometrical and material nonlinearities through the derivation of the consistent FE formulation. Applications to a rubber-like bi-material system under finite bending and to patterned stiff islands resting on soft substrate for stretchable solar cells subjected to tensile loading are proposed. The results obtained are in good agreement with benchmark results available in the literature, confirming the accuracy and the capabilities of the proposed numerical method for the analysis of complex three-dimensional fracture mechanics problems under finite deformations.

Different Parameters Variation Analysis of a PV Cell

The paper states an introduction, description and implementation of a PV cell under the variation of parameters. Analysis and observation of a different parameters variation of a PV cell are discussed here. To obtain the model for the purpose of analyzing an equivalent circuit with the consisting parameters a photo current source, a series resistor, a shunt resistor and a diode is used. The fundamental equation of PV cell is used to study the model and to analyze and best fit observation data. The model can be used in measuring and understanding the behaviour of photovoltaic cells for certain changes in PV cell parameters. A numerical method is used to analyze the parameters sensitivity of the model to achieve the expected result and to understand the deviation of changes in different parameters situation at various conditions respectively. The ideal parameters are used to study the models behaviour. It is also compared the behaviour of current-voltage and power-voltage by comparing with produced maximum power point though it is a challenge to optimize the output with real time simulation. The whole working process is also discussed and an experimental work is also done to get the closure and insight about the produced model and to decide upon the validity of the discussed model.

Active control of sound radiated by vibrating surfaces on a McLaren supercar

Sound radiators based on forced vibrations of plates are becoming widely employed, mainly for active sound enhancement and noise cancelling systems, both in music and automotive environment. Active sound enhancement solutions based on electromagnetic shakers hence find increasing interest. Mostly diffused applications deal with active noise control (ANC) and active vibration control systems for improving the acoustic experience inside or outside the vehicle. This requires investigating vibrational and, consequently, vibro-acoustic characteristics of vehicles. Therefore, simulation and processing methods capable of reducing the calculation time and providing high-accuracy results, are strongly demanded. In this work, an ideal case study on rectangular plates in fully clamped conditions preceded a real case analysis on vehicle panels. The sound radiation generated by a vibrating flat or shallow surface can be calculated by means of Rayleigh’s integral. The analytical solution of the problem is here calculated implementing the equations in MATLAB. Then, the results are compared with a numerical model developed in COMSOL Multiphysics, employing Finite Element Method (FEM). A very good matching between analytical and numerical solutions is shown, thus the cross validation of the two methods is achieved. The shift to the real case study, on a McLaren super car, led to the development of a mixed analytical-numerical method. Optimum results were obtained with mini shakers excitement, showing good matching of the recorded SPL with the calculated one over all the selected frequency band. In addition, a set of directivity measurements of the hood were realized, to start studying the spatiality of sound, which is fundamental to active noise control systems.

Numerical simulations of Lamb waves in plates using a semi-analytical finite element method

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2011

Numerical simulation of two-chamber plasma sources using finite element method

Numerical simulation of plasma sources is very important. Such models allows to vary different plasma parameters with high degree of accuracy. Moreover, they allow to conduct measurements not disturbing system balance.Recently, the scientific and practical interest increased in so-called two-chamber plasma sources. In one of them (small or discharge chamber) an external power source is embedded. In that chamber plasma forms. In another (large or diffusion chamber) plasma exists due to the transport of particles and energy through the boundary between chambers.In this particular work two-chamber plasma sources with argon and oxygen as active mediums were onstructed. This models give interesting results in electric field profiles and, as a consequence, in density profiles of charged particles.