Doctor of Philosophy

dissertationComputational simulation has become an indispensable tool in the study of both basic mechanisms and pathophysiology of all forms of cardiac electrical activity. Because the heart is comprised of approximately 4 billion electrically active cells, it is not possible to geometrically model or computationally simulate each individual cell. As a result computational models of the heart are, of necessity, abstractions that approximate electrical behavior at the cell, tissue, and whole body level. The goal of this PhD dissertation was to evaluate several aspects of these abstractions by exploring a set of modeling approaches in the field of cardiac electrophysiology and to develop means to evaluate both the amplitude of these errors from a purely technical perspective as well as the impacts of those errors in terms of physiological parameters. The first project used subject specific models and experiments with acute myocardial ischemia to show that one common simplification used to model myocardial ischemia-the simplest form of the border zone between healthy and ischemic tissue-was not supported by the experimental results. We propose a alternative approximation of the border zone that better simulates the experimental results. The second study examined the impact of simplifications in geometric models on simulations of cardiac electrophysiology. Such models consist of a connected mesh of polygonal elements and must often capture complex external and internal boundaries. A conforming mesh contains elements that follow closely the shapes of boundaries; nonconforming meshes fit the boundaries only approximately and are easier to construct but their impact on simulation accuracy has, to our knowledge, remained unknown. We evaluated the impact of this simplification on a set of three different forms of bioelectric field simulations. The third project evaluated the impact of an additional geometric modeling error; positional uncertainty of the heart in simulations of the ECG. We applied a relatively novel and highly efficient statistical approach, the generalized Polynomial Chaos-Stochastic Collocation method (gPC-SC), to a boundary element formulation of the electrocardiographic forward problem to carry out the necessary comprehensive sensitivity analysis. We found variations large enough to mask or to mimic signs of ischemia in the ECG

Towards stochastic methods in CFD for engineering applications

Recent developments of high performance computing capabilities allow solving modern science problems employing sophisticated computational techniques. However, it is necessary to ensure the efficiency of state of the art computational methods to fully take advantage of modern technology capabilities. In this thesis we propose uncertainty quantification and high performance computing strategies to solve fluid dynamics systems characterized by uncertain conditions and unknown parameters. We verify that such techniques allow us to take decisions faster and ensure the reliability of simulation results. Different sources of uncertainties can be relevant in computational fluid dynamics applications. For example, we consider the shape and time variability of boundary conditions, as well as the randomness of external forces acting on the system. From a practical point of view, one has to estimate statistics of the flow, and a failure probability convergence criterion must be satisfied by the statistical estimator of interest to assess reliability. We use hierarchical Monte Carlo methods as uncertainty quantification strategy to solve stochastic systems. Such algorithms present three levels of parallelism: over levels, over realizations per level, and on the solution of each realization. We propose an improvement by adding a new level of parallelism, between batches, where each batch has its independent hierarchy. These new methods are called asynchronous hierarchical Monte Carlo, and we demonstrate that such techniques take full advantage of concurrency capabilities of modern high performance computing environments, while preserving the same reliability of state of the art methods. Moreover, we focus on reducing the wall clock time required to compute statistical estimators of chaotic incompressible flows. Our approach consists in replacing a single long-term simulation with an ensemble of multiple independent realizations, which are run in parallel with different initial conditions. The error analysis of the statistical estimator leads to the identification of two error contributions: the initialization bias and the statistical error. We propose an approach to systematically detect the burn-in time to minimize the initialization bias, accompanied by strategies to reduce the simulation cost. Finally, we propose an integration of Monte Carlo and ensemble averaging methods for reducing the wall clock time required for computing statistical estimators of time-dependent stochastic turbulent flows. A single long-term Monte Carlo realization is replaced by an ensemble of multiple independent realizations, each characterized by the same random event and different initial conditions. We consider different systems, relevant in the computational fluid dynamics engineering field, as realistic wind flowing around high-rise buildings or compressible potential flow problems. By solving such numerical examples, we demonstrate the accuracy, efficiency, and effectiveness of our proposals.Los desarrollos relacionados con la computación de alto rendimiento de las últimas décadas permiten resolver problemas científicos actuales, utilizando métodos computacionales sofisticados. Sin embargo, es necesario asegurarse de la eficiencia de los métodos computacionales modernos, con el fin de explotar al máximo las capacidades tecnológicas. En esta tesis proponemos diferentes métodos, relacionados con la cuantificación de incertidumbres y el cálculo de alto rendimiento, con el fin de minimizar el tiempo de computación necesario para resolver las simulaciones y garantizar una alta fiabilidad. En concreto, resolvemos sistemas de dinámica de fluidos caracterizados por incertidumbres. En el campo de la dinámica de fluidos computacional existen diferentes tipos de incertidumbres. Nosotros consideramos, por ejemplo, la forma y la evolución en el tiempo de las condiciones de frontera, así como la aleatoriedad de las fuerzas externas que actúan sobre el sistema. Desde un punto de vista práctico, es necesario estimar valores estadísticos del flujo del fluido, cumpliendo los criterios de convergencia para garantizar la fiabilidad del método. Para cuantificar el efecto de las incertidumbres utilizamos métodos de Monte Carlo jerárquicos, también llamados hierarchical Monte Carlo methods. Estas estrategias tienen tres niveles de paralelización: entre los niveles de la jerarquía, entre los eventos de cada nivel y durante la resolución del evento. Proponemos agregar un nuevo nivel de paralelización, entre batches, en el cual cada batch es independiente de los demás y tiene su propia jerarquía, compuesta por niveles y eventos distribuidos en diferentes niveles. Definimos estos nuevos algoritmos como métodos de Monte Carlo asíncronos y jerárquicos, cuyos nombres equivalentes en inglés son asynchronous hierarchical Monte Carlo methods. También nos enfocamos en reducir el tiempo de computación necesario para calcular estimadores estadísticos de flujos de fluidos caóticos e incompresibles. Nuestro método consiste en reemplazar una única simulación de dinámica de fluidos, caracterizada por una ventana de tiempo prolongada, por el promedio de un conjunto de simulaciones independientes, caracterizadas por diferentes condiciones iniciales y una ventana de tiempo menor. Este conjunto de simulaciones se puede ejecutar en paralelo en superordenadores, reduciendo el tiempo de computación. El método de promedio de conjuntos se conoce como ensemble averaging. Analizando las diferentes contribuciones del error del estimador estadístico, identificamos dos términos: el error debido a las condiciones iniciales y el error estadístico. En esta tesis proponemos un método que minimiza el error debido a las condiciones iniciales, y en paralelo sugerimos varias estrategias para reducir el coste computacional de la simulación. Finalmente, proponemos una integración del método de Monte Carlo y del método de ensemble averaging, cuyo objetivo es reducir el tiempo de computación requerido para calcular estimadores estadísticos de problemas de dinámica de fluidos dependientes del tiempo, caóticos y estocásticos. Reemplazamos cada realización de Monte Carlo por un conjunto de realizaciones independientes, cada una caracterizada por el mismo evento aleatorio y diferentes condiciones iniciales. Consideramos y resolvemos diferentes sistemas físicos, todos relevantes en el campo de la dinámica de fluidos computacional, como problemas de flujo del viento alrededor de rascacielos o problemas de flujo potencial. Demostramos la precisión, eficiencia y efectividad de nuestras propuestas resolviendo estos ejemplos numéricos.Gli sviluppi del calcolo ad alte prestazioni degli ultimi decenni permettono di risolvere problemi scientifici di grande attualità, utilizzando sofisticati metodi computazionali. È però necessario assicurarsi dell’efficienza di questi metodi, in modo da ottimizzare l’uso delle odierne conoscenze tecnologiche. A tal fine, in questa tesi proponiamo diversi metodi, tutti inerenti ai temi di quantificazione di incertezze e calcolo ad alte prestazioni. L’obiettivo è minimizzare il tempo necessario per risolvere le simulazioni e garantire alta affidabilità. Nello specifico, utilizziamo queste strategie per risolvere sistemi fluidodinamici caratterizzati da incertezze in macchine ad alte prestazioni. Nel campo della fluidodinamica computazionale esistono diverse tipologie di incertezze. In questo lavoro consideriamo, ad esempio, il valore e l’evoluzione temporale delle condizioni di contorno, così come l’aleatorietà delle forze esterne che agiscono sul sistema fisico. Dal punto di vista pratico, è necessario calcolare una stima delle variabili statistiche del flusso del fluido, soddisfacendo criteri di convergenza, i quali garantiscono l’accuratezza del metodo. Per quantificare l’effetto delle incertezze sul sistema utilizziamo metodi gerarchici di Monte Carlo, detti anche hierarchical Monte Carlo methods. Queste strategie presentano tre livelli di parallelizzazione: tra i livelli della gerarchia, tra gli eventi di ciascun livello e durante la risoluzione del singolo evento. Proponiamo di aggiungere un nuovo livello di parallelizzazione, tra gruppi (batches), in cui ogni batch sia indipendente dagli altri ed abbia una propria gerarchia, composta da livelli e da eventi distribuiti su diversi livelli. Definiamo questi nuovi algoritmi come metodi asincroni e gerarchici di Monte Carlo, il cui corrispondente in inglese è asynchronous hierarchical Monte Carlo methods. Ci focalizziamo inoltre sulla riduzione del tempo di calcolo necessario per stimare variabili statistiche di flussi caotici ed incomprimibili. Il nostro metodo consiste nel sostituire un’unica simulazione fluidodinamica, caratterizzata da un lungo arco temporale, con il valore medio di un insieme di simulazioni indipendenti, caratterizzate da diverse condizioni iniziali ed un arco temporale minore. Questo insieme 10 di simulazioni può essere eseguito in parallelo in un supercomputer, riducendo il tempo di calcolo. Questo metodo è noto come media di un insieme o, in inglese, ensemble averaging. Calcolando la stima di variabili statistiche, commettiamo due errori: l’errore dovuto alle condizioni iniziali e l’errore statistico. In questa tesi proponiamo un metodo per minimizzare l’errore dovuto alle condizioni iniziali, ed in parallelo suggeriamo diverse strategie per ridurre il costo computazionale della simulazione. Infine, proponiamo un’integrazione del metodo di Monte Carlo e del metodo di ensemble averaging, il cui obiettivo è ridurre il tempo di calcolo necessario per stimare variabili statistiche di problemi di fluidodinamica dipendenti dal tempo, caotici e stocastici. Ogni realizzazione di Monte Carlo è sostituita da un insieme di simulazioni indipendenti, ciascuna caratterizzata dallo stesso evento casuale, da differenti condizioni iniziali e da un arco temporale minore. Consideriamo e risolviamo differenti sistemi fisici, tutti rilevanti nel campo della fluidodinamica computazionale, come per esempio problemi di flusso del vento attorno a grattacieli, o sistemi di flusso potenziale. Dimostriamo l’accuratezza, l’efficienza e l’efficacia delle nostre proposte, risolvendo questi esempi numerici.Postprint (published version

Large eddy simulation and direct numerical simulation of high speed turbulent reacting flows

The objective of this research is to make use of Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first phase of this research conducted within the past three years have been directed in several issues pertaining to intricate physics of turbulent reacting flows. In our previous 5 semi-annual reports submitted to NASA LaRC, as well as several technical papers in archival journals, the results of our investigations have been fully described. In this progress report which is different in format as compared to our previous documents, we focus only on the issue of LES. The reason for doing so is that LES is the primary issue of interest to our Technical Monitor and that our other findings were needed to support the activities conducted under this prime issue. The outcomes of our related investigations, nevertheless, are included in the appendices accompanying this report. The relevance of the materials in these appendices are, therefore, discussed only briefly within the body of the report. Here, results are presented of a priori and a posterior analyses for validity assessments of assumed Probability Density Function (PDF) methods as potential subgrid scale (SGS) closures for LES of turbulent reacting flows. Simple non-premixed reacting systems involving an isothermal reaction of the type A + B yields Products under both chemical equilibrium and non-equilibrium conditions are considered. A priori analyses are conducted of a homogeneous box flow, and a spatially developing planar mixing layer to investigate the performance of the Pearson Family of PDF's as SGS models. A posteriori analyses are conducted of the mixing layer using a hybrid one-equation Smagorinsky/PDF SGS closure. The Smagorinsky closure augmented by the solution of the subgrid turbulent kinetic energy (TKE) equation is employed to account for hydrodynamic fluctuations, and the PDF is employed for modeling the effects of scalar fluctuations. The implementation of the model requires the knowledge of the local values of the first two SGS moments. These are provided by additional modeled transport equations. In both a priori and a posteriori analyses, the predicted results are appraised by comparison with subgrid averaged results generated by DNS. Based on these results, the paths to be followed in future investigations are identified

2010 program of study : swirling and swimming in turbulence

Swirling and Swimming in Turbulence was the theme at the 2010 GFD Program. Professors Glenn Flierl (M.I.T.), Antonello Provenzale (ISAC-CNR, Turin) and Jean-Luc Thiffeault (University of Wisconsin) were the principal lecturers. Together they navigated an elegant path through topics ranging from mixing protocols and efficiencies to ecological strategies, schooling and genetic development. The first ten chapters of this volume document these lectures, each prepared by pairs of this summer’s GFD fellows. Following on are the written reports of the fellows’ own research projects.Funding was provided by the Office of Naval Research under Contract No. N000-14-09-10844 and the National Science Foundation through Grant No. OCE 082463