<p>Study of physical phenomena by means of mathematical models is common in various branches of engineering and science. In biomechanics, modelling often involves studying human motion by treating the body as a mechanical system made of interconnected rigid links. Robotics deals with similar cases as robots are often designed to imitate human behavior. Modelling human movements is a complicated task and, therefore, requires several simplifications and assumptions. Available computational resources often dictate the nature and the complexity of the models. In spite of all these factors, several meaningful results are still obtained from the simulations.</p><p>One common problem form encountered in real life is the movement between known initial and final states in a pre-specified time. This presents a problem of dynamic redundancy as several different trajectories are possible to achieve the target state. Movements are mathematically described by differential equations. So modelling a movement involves solving these differential equations, along with optimization to find a cost effective trajectory and forces or moments required for this purpose.</p><p>In this study, an algorithm developed in Matlab is used to study dynamics of several common human movements. The main underlying idea is based upon temporal finite element discretization, together with optimization. The algorithm can deal with mechanical formulations of varying degrees of complexity and allows precise definitions of initial and target states and constraints. Optimization is carried out using different cost functions related to both kinematic and kinetic variables.</p><p>Simulations show that generally different optimization criteria give different results. To arrive on a definite conclusion on which criterion is superior over others it is necessary to include more detailed features in the models and incorporate more advanced anatomical and physiological knowledge. Nevertheless, the algorithm and the simplified models present a platform that can be built upon to study more complex and reliable models.</p>

Study of physical phenomena by means of mathematical models is common in various branches of engineering and science. In biomechanics, modelling often involves studying human motion by treating the body as a mechanical system made of interconnected rigid links. Robotics deals with similar cases as robots are often designed to imitate human behavior. Modelling human movements is a complicated task and, therefore, requires several simplifications and assumptions. Available computational resources often dictate the nature and the complexity of the models. In spite of all these factors, several meaningful results are still obtained from the simulations. One common problem form encountered in real life is the movement between known initial and final states in a pre-specified time. This presents a problem of dynamic redundancy as several different trajectories are possible to achieve the target state. Movements are mathematically described by differential equations. So modelling a movement involves solving these differential equations, along with optimization to find a cost effective trajectory and forces or moments required for this purpose. In this study, an algorithm developed in Matlab is used to study dynamics of several common human movements. The main underlying idea is based upon temporal finite element discretization, together with optimization. The algorithm can deal with mechanical formulations of varying degrees of complexity and allows precise definitions of initial and target states and constraints. Optimization is carried out using different cost functions related to both kinematic and kinetic variables. Simulations show that generally different optimization criteria give different results. To arrive on a definite conclusion on which criterion is superior over others it is necessary to include more detailed features in the models and incorporate more advanced anatomical and physiological knowledge. Nevertheless, the algorithm and the simplified models present a platform that can be built upon to study more complex and reliable models. / QC 20101110

Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

Liquid jet atomisation has a wide variety of application in areas such as injectors in automobile and launch vehicle combustors, spray painting, ink jet printing etc. Understanding physical mechanisms involved in the primary regime of atomisation in combustors is extremely challenging due to the lack of experimental techniques that can reliably provide measurements of gas and liquid velocity fields in this region. Experimental studies have so far been mostly restricted to conditions at atmospheric conditions rather than technically relevant operating pressures. We present a computational fluid dynamics based modelling approach that can capture the evolution of the flow field in the dense primary atomization region of the spray as part of the present thesis work. A fully compressible 3D flow solver is coupled with an interface tracking solver based on level set method. A generalised mathematical formulation for thermodynamic models is implemented in flow solver enabling easy switching between various equations of states. Solvers are parallelised to run on large number of processors and are shown to have good scalability. A modification to the level set method which greatly reduces mass conservation inaccuracies when compared with existing state-of-art baseline schemes has been developed during this work. The Ghost uid Method is used for applying matching conditions at the Interface. The liquid and gas phases are modelled using the perfect gas and Tait equations of state respectively. Several validation studies have been carried out to ensure quantitative accuracy of the solver implemented. Results from canonical Rayleigh Taylor instability simulations shows good agreement with reported results in literature. Finally, results for unsteady evolution of a water-air jet at a liquid to gas density ratio of 10 are shown. Physical mechanisms causing the initial droplet formation are discussed in detail. Droplet feedback is identified as one of the important mechanisms in triggering liquid core instabilities. Comparisons between droplet size distributions obtained from computations are carried out. Vorticity dynamics is used to understand hole and ligament formation from liquid core. Effect of numerical droplets on the simulation results is also looked at in detail.

Os custos econômicos e perdas potenciais de vidas humanas resultantes de falhas em sistemas de drenagem de águas pluviais podem ser enormes, aumentando a necessidade da busca de melhores métodos de dimensionamento destes. Os métodos baseados na precipitação de projeto são os mais usados para a estimativa do hidrograma de projeto em bacias urbanas, devido às facilidades que os mesmos apresentam em relação aos outros métodos. Entretanto, estes métodos têm suas limitações e incertezas, que podem influenciar as características do hidrograma de projeto resultante, incertezas que são, em consequência, transferidas ao dimensionamento hidráulico das obras propostas. No presente trabalho, foram avaliados os efeitos da discretização espacial da bacia, da discretização temporal e da posição do pico do hietograma de projeto, sobre as principais características do hidrograma de projeto. Esses efeitos foram ainda avaliados no dimensionamento hidráulico do sistema de macrodrenagem dos bairros de Mavalane “A” e Maxaquene “A”, localizados na cidade de Maputo em Moçambique. Para avaliar os referidos efeitos, a bacia foi discretizada em 1, 5, 7 e 12 sub-bacias. O intervalo de tempo do hietograma de projeto foi discretizado em 1, 2, 3, 4 e 5 minutos, sendo calculados para cada discretização e intervalo de tempo, hietogramas com pico no início, 25%, 50%, 75% e final do evento com duração correspondente a 90 minutos e 24 horas. Os hietogramas foram transformados em vazão no programa IPHS1, a qual foi propagada no sistema de macrodrenagem usando o modelo EPA SWMM 5.0, sendo obtidos os hidrogramas de projeto resultantes. O exutório da bacia e o trecho C19 localizado na região central da bacia foram escolhidos para análise dos resultados. Os resultados obtidos mostram uma influência importante dos efeitos avaliados nas características do hidrograma de projeto: vazão de pico, tempo de pico e volume parcial e, consequentemente, no dimensionamento da rede de macrodrenagem, sendo o efeito da discretização da bacia o mais influente, seguido dos efeitos da posição do pico da chuva e intervalo de tempo. / The economic costs and potential losses of human lives due to failure in stormwater drainage systems can be significant, calling for an improvement in methods used for its design. The design storm approach, also known as “single-event design-storm” is widespread used in formulating design hydrograph from historical rainfall data in urban watersheds, due to its relative advantages when compared to other methods. Therefore, this approach has its uncertainties which can affect the resulted design hydrograph, and consequently affect the hydraulic design of proposed structures. In this study is presented an assessment of the adopted values in design criteria, during the estimation of design hydrograph used in hydraulic design of stormwater drainage systems. In particular, are assessed the effects of spatial discretization of the watershed, the temporal discretization and peak position of the design hyetograph, in the main features of the resulted design hydrograph. The same effects are then assessed in the hydraulic design of the major stormwater drainage system of Mavalane “A” and Maxaquene “A” neighborhoods, located in Maputo city in Mozambique. To assess these effects, the watershed was discretized into 1, 5, 7 and 12 sub-watersheds. The time step of the design hyetograph was discretized into 1, 2, 3, 4 and 5 minutes, and then computed for each discretization and time step, hyetographs with peak positioned in the beginning, 25%, 50%, 75% and the end of the duration of 90 minutes and 24 hours. The hyetographs were converted into runoff in IPHS1, wish was dynamically routed in the drainage system, using EPA SWMM 5.0. The watershed outlet and conduit C19 were used to analyze the results. The results show an important influence of the assessed effects on the design hydrograph features: hydrograph peak, time to peak and partial volume and, consequently, on the hydraulic design of the major stormwater drainage system, being the effect of spatial discretization of the watershed, the most important, followed by hyetograph peak position and time step.

A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.

A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.