This thesis introduces a topology optimization approach to design, from scratch, efficient microwave devices, such as antennas and waveguide transitions. The design of these devices is formulated as a general optimization problem that aims to build the whole layout of the device in order to extremize a chosen objective function. The objective function quantifies some required performance and is evaluated using numerical solutions to the 3D~Maxwell's equations by the finite-difference time-domain (FDTD) method. The design variables are the local conductivity at each Yee~edge in a given design domain, and a gradient-based optimization method is used to solve the optimization problem. In all design problems, objective function gradients are computed based on solutions to adjoint-field problems, which are also FDTD discretization of Maxwell's equations but solved with different source excitations. For any number of design variables, the computation of the objective function gradient requires one solution to the original field problem and one solution to the associated adjoint-field problem. The optimization problem is solved iteratively using the globally convergent Method of Moving Asymptotes (GCMMA). By the proposed approach, various design problems, including tens of thousands of design variables, are formulated and solved in a few hundred iterations. Examples of solved design problems are the design of wideband antennas, dual-band microstrip antennas, wideband directive antennas, and wideband coaxial-to-waveguide transitions. The fact that the proposed approach allows a fine-grained control over the whole layout of such devices results in novel devices with favourable performance. The optimization results are successfully verified with a commercial software package. Moreover, some devices are fabricated and their performance is successfully validated by experiments.

Geothermal energy is an important source of clean and renewable energy. This project deals with the study of deep geothermal power plants for the generation of electricity. The design involves the extraction of heat from the Earth and its conversion into electricity. This is performed by allowing fluid deep into the Earth where it gets heated due to the surrounding rock. The fluid gets vaporized and returns to the surface in a heat pipe. Finally, the energy of the fluid is converted into electricity using turbine or organic rankine cycle (ORC). The main feature of the system is the employment of side channels to increase the amount of thermal energy extracted. A finite difference computer model is developed to solve the heat transport equation. The numerical model was employed to evaluate the performance of the design. The major goal was to optimize the output power as a function of parameters such as thermal diffusivity of the rock, depth of the main well, number and length of lateral channels. The sustainable lifetime of the system for a target output power of 2 MW has been calculated for deep geothermal systems with drilling depths of 8000 and 10000 meters, and a financial analysis has been performed to evaluate the economic feasibility of the system for a practical range of geothermal parameters. Results show promising an outlook for deep geothermal systems for practical applications.

Gas separation with polymer membranes are becoming one of the mainstream separation techniques for a myriad of industrial applications. Membrane technologies are recognized as a viable and economical unit operation compared to more conventional separation processes. The design and material selection of membrane separation processes depends highly on the transport properties of separated gas molecules within the membrane material. Therefore, to use efficient methods for gas membrane characterization is paramount for the proper design of membrane separation processes. A membrane can be typically characterized by three main properties: permeability, solubility and diffusivity. The permeability of a membrane is the product of its diffusivity and solubility, therefore obtaining two of the three parameters is sufficient to fully characterize a membrane. The time-lag method is one of the oldest and most used gas membrane characterization methods. However, it suffers from various limitations that make the method not applicable for many types of membranes. The focus in this study was to develop new gas membrane characterization techniques that are based on extracting the membrane properties from the upstream gas pressure measurements rather than only from the downstream pressure measurements. It is believed that characterizing the membrane based on the upstream pressure measurements would be highly useful in characterizing barrier materials which are usually difficult to characterize using the conventional time-lag method. Moreover, glassy polymers which are widely used in industry exhibit behavior associated with nonlinear sorption isotherms and, therefore, the conventional time-lag method is incapable of obtaining an accurate estimation of glassy polymer properties. As a result, sorption experiments to generate a sorption isotherm are usually required in addition to permeation experiments to fully characterize glassy polymer membranes. To quantify the errors associated with the conventional time-lag assumptions and to fundamentally comprehend the impact of nonlinearities on the time-lag method, a comprehensive numerical investigation has been undertaken using the finite difference method. The investigation has clearly put in evidence the effect of the various Langmuir parameters on the accuracy of the time lag and on the time required to achieve steady state. This investigation also allowed assessing the errors associated with the usual assumptions made on the boundary conditions in determining the time lag. In this study, three novel gas membrane characterization methods were developed and proposed. Two of the proposed methods are concerned with the characterization of membranes that can be represented with a linear sorption isotherm. These two methods are entirely based on the upstream pressure measurements. The third membrane characterization method that is proposed is based on the dynamic monitoring of both upstream and downstream pressure measurements and is applicable to systems that exhibit a nonlinear isotherm sorption behavior. The three proposed methods are promising and further experimental validation is recommended to determine their full range of applicability.

A theory is developed for the analysis of composite systems consisting of steel wide flange sections reinforced with GFRP plates connected to one of the flanges through a layer of adhesive. The theory is based on an extension of the Gjelsvik theory and thus incorporates local and global warping effects but omits shear deformation effects. The theory captures the longitudinal transverse response through a system of three coupled differential equations of equilibrium and the lateral-torsional response through another system of three coupled differential equations. Closed form solutions are developed and a super-convergent finite element is formulated based under the new theory. A comparison to 3D FEA results based on established solid elements in Abaqus demonstrates the validity of the theory when predicting the longitudinal-transverse response, but showcases its shortcomings in predicting the torsional response of the composite system. The comparison sheds valuable insight on means of improving the theory. A more advanced theory is subsequently developed based on enriched kinematics which incorporates shear deformation effects. The shear deformable theory captures the longitudinal-transverse response through a system of four coupled differential equations of equilibrium and the lateral-torsional response through another system of six coupled differential equations. A finite difference approximation is developed for the new theory and a new finite element formulation is subsequently to solve the new system of equations. A comparison to 3D FEA illustrates the validity of the shear deformable theory in predicting the longitudinal-transverse response as well as the lateral-torsional response. Both theories are shown to be computationally efficient and reduce the modelling and running time from several hours per run to a few minutes or seconds while capturing the essential features of the response of the composite system.

The efficiency of the conventional, explicit finite difference time domain (FDTD)method is constrained by the upper limit on the temporal discretization, imposed by the Courant–Friedrich–Lewy (CFL) stability condition. Therefore, there is a growing interest in overcoming this limitation by employing unconditionally stable FDTD methods for which time-step and space-step can be independently chosen. Unconditionally stable Crank Nicolson method has not been widely used in time domain electromagnetics despite its high accuracy and low anisotropy. There has been no work on the Crank Nicolson FDTD (CN–FDTD) method for frequency dependent medium. In this thesis a new three-dimensional frequency dependent CN–FDTD (FD–CN–FDTD) method is proposed. Frequency dependency of single–pole Debye materials is incorporated into the CN–FDTD method by means of an auxiliary differential formulation. In order to provide a convenient and straightforward algorithm, Mur’s first-order absorbing boundary conditions are used in the FD–CN–FDTD method. Numerical tests validate and confirm that the FD–CN–FDTD method is unconditionally stable beyond the CFL limit. The proposed method yields a sparse system of linear equations which can be solved by direct or iterative methods, but numerical experiments demonstrate that for large problems of practical importance iterative solvers are to be used. The FD–CN–FDTD sparse matrix is diagonally dominant when the time-stepis near the CFL limit but the diagonal dominance of the matrix deteriorates with the increase of the time-step, making the solution time longer. Selection of the matrix solver to handle the FD–CN–FDTD sparse system is crucial to fully harness the advantages of using larger time-step, because the computational costs associated with the solver must be kept as low as possible. Two best–known iterative solvers, Bi-Conjugate Gradient Stabilised (BiCGStab) and Generalised Minimal Residual (GMRES), are extensively studied in terms of the number of iteration requirements for convergence, CPU time and memory requirements. BiCGStab outperforms GMRES in every aspect. Many of these findings do not match with the existing literature on frequency–independent CN–FDTD method and the possible reasons for this are pointed out. The proposed method is coded in Fortran and major implementation techniques of the serial code as well as its parallel implementation in Open Multi-Processing (OpenMP) are presented. As an application, a simulation model of the human body is developed in the FD–CN–FDTD method and numerical simulation of the electromagnetic wave propagation inside the human head is shown. Finally, this thesis presents a new method modifying the frequency dependent alternating direction implicit FDTD (FD–ADI–FDTD) method. Although the ADI–FDTD method provides a computationally affordable approximation of the CN–FDTD method, it exhibits a loss of accuracy with respect to the CN-FDTD method which may become severe for some practical applications. The modified FD–ADI–FDTD method can improve the accuracy of the normal FD–ADI–FDTD method without significantly increasing the computational costs.

No contexto do método MAC e baseado em esquemas de diferenças finitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre. Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretiza ção explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável. Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção. Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para fluidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres. Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW. A eficiência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado / In the context of the MAC method and based on finite difference schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface flows. In the stability analysis, the main result shows a precise stability restriction on the Crank-Nicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable. In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure fields; hence new projection methods for free surface flows need to be developed. The developed projection methods result in new methodologies for low Reynolds number free surface flows. It is also shown that the proposed methods can be applied for viscoelastic fluids. New strategies are derived for obtaining second-order accurate projection methods for free surface flows. In addition to the theoretical results on the stability of numerical schemes, implicit techniques and projection methods, computational tests are carried out and the results compared to consolidate the theory. The numerical results are obtained by the FREEFLOW system. The eficiency and robustness of the techniques in this work are demonstrated by solving complex tridimensional problems involving free surface and low Reynolds numbers, including the jet buckling and the extrudate swell problems

Escoamentos viscoelásticos não estacionários com superfícies livres são comuns em muitos processos industriais e diversas técnicas numéricas têm sido empregadas para reproduzir computacionalmente estes processos. A maioria dos modelos empregados utiliza equações diferenciais na definição do tensor de tensões. Porém, para alguns grupos de fluidos complexos, por exemplo, fluidos de Boger, os modelos integrais mostram-se mais capacitados em fornecer uma boa aproximação para os comportamentos não lineares desses fluidos. Este trabalho trata da solução numérica do modelo constitutivo integral KBKZ-PSM para escoamentos transientes bidimensionais com superfícies livres. O método numérico proposto é uma técnica numérica que utiliza diferenças finitas para simular escoamentos com superfícies livres na presença de paredes sólidas. As principais características do método numérico proposto são: solução das equações de conservação de quantidade de movimento e massa utilizando um método semi-implícito; a condição de contorno na superfície livre é acoplada à equação de Poisson, o que garante conservação de massa; a discretização do tempo t é realizada por uma nova técnica numérica; o tensor de Finger é calculado pelo método dos campos de deformação e avançado no tempo pelo método de Euler modificado. Essa nova técnica é verificada em escoamentos cisalhantes e elongacionais. Adicionalmente, uma solução analítica desenvolvida para escoamentos em canais bidimensionais é empregada para verificar e analisar a convergência do método proposto. Com relação a escoamentos com superfícies livres, a convergência é verificada por meio de refinamento de malha nas simulações de um jato incidindo sobre placa rígida e no problema do inchamento do extrudado. Finalmente, o método é aplicado para investigar os problemas jet buckling e inchamento do extrudado de fluidos KBKZ-PSM. / Unsteady viscoelastic free surface flows are common in many industrial processes and a variety of numerical techniques have been employed to simulate these flows. The majority of constitutive models employed are based on differential equations to define the extra stress tensor. However, for some complex fluids, for instance, Boger fluids, integral models are more adequate to approximate the nonlinear behaviour of these fluids. This work deals with the numerical solution of the integral constitutive model KBKZ-PSM for two-dimensional unsteady free surface flows. The proposed numerical method is a numerical technique that employs finite differences to simulate moving free surface flows that interact with solid walls. The main features of the method are: numerical solution of the momentum and mass equations by an implicit method; the pressure condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by the modified Euler method. This new technique is verified by solving shear and uniaxial elongational flows. Moreover, an analytic solution for channel flows is obtained that is used in the verification and convergence analysis of the proposed methodology. For free surface flows, the assessment of convergence lies on the mesh refinement on the simulation of a jet impinging on a flat surface and the extrudade swell problem. Finally, the new method is applied to investigate the jet buckling phenomenon and extrudate swell of KBKZ-PSM fluids.

Tato diplomová práce se zabývá rigorózními simulacemi plazmonických biosenzorů založených na jevu zvýšené optické transmise. První část je věnována popisu fyzikálních jevů a poznatků, které tvoří základ pro studium vlastností plazmonických senzorů, a popisu výpočetní metody konečných prvků v časové oblasti, která je využita v této práci. Vlastní výsledky jsou uvedeny v další části, která se zabývá výzkumem citlivosti, rozlišení a dalších charakteristik zvoleného typu plazmonického sensoru, tvořeného sítí kruhových nanoděr v tenké zlaté vrstvě na substrátě nitridu křemíku, v závislosti na řadě jeho geometrických parametrů. Tyto závislosti jsou sledovány ve třech různých případech, a to senzoru umístěného ve vakuu, ponořeného ve vodě a v případě kdy je na zlatém povrchu umístěna tenká dielektrická vrstva, která reprezentuje přítomnost biomolekul uchycených na povrchu senzoru.

Diplomová práca sa zaoberá rozptylom elektromagnetického žiarenia na biologickej bunke použitím metódy konečných diferencií v časovej oblasti (FDTD), Bornovej aproximácie a Rytovovej aproximácie. Metóda FDTD dáva presné výsledky v širokej škále problémov. Je spravené porovnanie Bornovej aproximácie a Rytovovej aproximácie prostredníctvom FDTD metódy. Ďaľšia časť práce zahrnuje krátky popis koherenciou riadeného holografického mikroskopu CCHM. Záverečná časť sa venuje zobrazeniu rozptýleného poľa získaného z jednotlivých simulácií pomocou simulácie objektového ramena mikroskopu CCHM.

Tato diplomová práce se zabývá tématem výměny tepla v zásobníku tepla typu ”packed bed”. Cílem je popsat přenos tepla v zásobníku tepla obsahující kamínky malých průměrů, skrz který proudí horký vzduch. Toto je modelováno v prostředí MATLAB. Na začátku je krátký úvod do problematiky zahrnující ukládání tepla a jeho možné využití. Dále je uveden krátký přehled o základech přenosu tepla, typech přenosu tepla a termofyzikální vlastnosti systému vzduch-kámen. Ve třetí kapitole je představen zásobník tepla typu ”packed bed” a rozličné modely a dané podmínky jsou vysvětleny. Další kapitola se zabývá s numerickými metodami, převážně s metodou konečných diferencí použitou v této práci. Pátá kapitola se zaměřuje na obecnou optimalizaci daného problému přenosu tepla. Populačně založený metaheuristický optimalizační algoritmus zvaný Genetický algoritmus je popsán. Sestavení modelu je ukázáno v šesté kapitole, stejně jako prezentace výsledků získaných z programu MATLAB. V poslední kapitole je pak diskutován závěr a doporučení.