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

On the algebraic independence of periods of abelian varieties and their exponentials

We generalize a result by Vasil'ev on the algebraic independence of periods of abelian varieties to the case when some of these periods are replaced by their exponentials. We eventually derive some applications to values of the beta function at rational points.Comment: 17 page

Improving productivity of an electron beam melting system using Ti – 6Al – 4V

The electron beam melting system is a unique powder bed technology used to manufacture high value components for different applications. Titanium alloys are conventionally used to produce additive manufacturing parts in several industrial sectors due its mechanical and geometrical characteristics. This demonstrates an increasing interest in this system. However, limits on productivity are pushing the market to improve the process of additive manufacturing (AM) parts into real production. The aim of this thesis is to gain a fundamental understanding of the Arcam A2XX system and its characteristics in order to explore new approaches for improving productivity. This thesis explores fundamental studies of Ti - 6Al - 4V alloy manufactured with an electron powder bed fusion (E-PBF) system using a standard configuration, hardware reduction, and advanced methods to decrease the manufacturing time and its impact in production. All the studies include a metallurgical investigation of the parts, mechanical properties and an overall analysis of the components manufactured. A standard build was first investigated to capture the E-PBF A2XX system behaviour and its build characteristics. After a fundamental study investigation, the hardware was modified to better understand the flexibility of the standard system. An “adaptonic chamber” was manufactured to reduce the amount of powder required during the build. This optimised the chamber volume, which generated benefits such as time saving and machine turnaround. Subsequently, two advanced manufacturing techniques called “in-situ shelling” and “hybrid manufacturing” were explored in order to understand whether the production time capturing un-melted powder in a shell to post treat could be reduced, and to include the starting plate as part of the final component respectively. Time and cost were monitored to measure productivity. Further research is recommended to gain deeper insight into the techniques successfully explored in this thesis

On the use of ensemble averaging techniques to accelerate the Uncertainty Quantification of CFD predictions in wind engineering

In this work we focus on reducing the wall clock time required to compute statistical estimators of highly chaotic incompressible flows on high performance computing systems. Our approach consists of replacing a single long-term simulation by an ensemble of multiple independent realizations, which are run in parallel. A failure probability convergence criteria must be satisfied by the statistical estimator of interest to assess convergence. The error analysis 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 needed in order to minimize the initialization bias, as well as techniques to choose the effective time needed to keep the statistical error under control. This is accompanied by strategies to reduce simulation cost. The proposed method is assessed in application to the prediction of the drag force over high rise buildings and specifically in application to the CAARC building, a relevant benchmark for the wind engineering community.The authors thank Prof. Barbara Wohlmuth and Dr. Brendan Keith for their valuable discussions and contributions to the subject. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 800898 and from project RTI2018-096898-B-I00 from the FEDER/Ministerio de Ciencia e Innovación - Agencia Estatal de Investigación. The authors also acknowledge the Severo Ochoa Centre of Excellence (2019–2023), which financially supported this work under the grant CEX2018-000797-S funded by MCIN/AEI/10.13039/501100011033. The authors thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (IM-2020-2-0030). This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ (ID:90140). Dr. Jordi Pons-Prats acknowledges the support of the Serra Hunter programme by the Catalan Government.Peer ReviewedPostprint (published version

Remanufacture of Turbine Blades by Laser Cladding, Machining and In-Process Scanning in a Single Machine

Remanufacturing is one of the most efficient ways of recycling worn parts because it consumes only a fraction of the energy, cost, and material required for new parts. Remanufacture of engineering components typically entails serial labor intensive and operator skill sensitive processes, often requiring parts to move between manufacturers and subcontractors. Unfortunately the logistics and quality assurance measures required for effective remanufacturing currently restrict its implementation primarily to high value components (e.g. turbine blades, blisks, etc.). This research reports progress toward an integrated production system which combines laser cladding, machining and in-process scanning in a single machine for flexible and lean remanufacturing.Mechanical Engineerin

Fast-Gated 16 x 16 SPAD Array With 16 on-Chip 6 ps Time-to-Digital Converters for Non-Line-of-Sight Imaging

We present the design and characterization of a fully-integrated array of 16 x 16 Single-Photon Avalanche Diodes (SPADs) with fast-gating capabilities and 16 on-chip 6 ps time-to-digital converters, which has been embedded in a compact imaging module. Such sensor has been developed for Non-Line-Of-Sight imaging applications, which require: i) a narrow instrument response function, for a centimeter-accurate single-shot precision; ii) fast-gated SPADs, for time-filtering of directly reflected photons; iii) high photon detection probability, for acquiring faint signals undergoing multiple scattering events. Thanks to a novel multiple differential SPAD-SPAD sensing approach, SPAD detectors can be swiftly activated in less than 500 ps and the full-width at half maximum of the instrument response function is always less than 75 ps (60 ps on average). Temporal responses are consistently uniform throughout the gate window, showing just few picoseconds of time dispersion when 30 ns gate pulses are applied, while the differential non-linearity is as low as 250 fs. With a photon detection probability peak of 70% at 490 nm, a fill-factor of 9.6% and up to 1.6 . 10(8) photon time-tagging measurements per second, such sensor fulfills the demand for fully-integrated imaging solutions optimized for non-line-of-sight imaging applications, enabling to cut exposure times while also optimizing size, weight, power and cost, thus paving the way for further scaled architectures

Remanufacture of turbine blades by laser cladding, machining and in-process scanning in a single machine

Remanufacturing is one of the most efficient ways of recycling worn parts because it consumes only a fraction of the energy, cost, and material required for new parts. Remanufacture of engineering components typically entails serial labor intensive and operator skill sensitive processes, often requiring parts to move between manufacturers and subcontractors. Unfortunately the logistics and quality assurance measures required for effective remanufacturing currently restrict its implementation primarily to high value components (e.g. turbine blades, blisks, etc.). This research reports progress toward an integrated production system which combines laser cladding, machining and in-process scanning in a single machine for flexible and lean remanufacturing.This research was undertaken with gracious support of the UK Technology Strategy Board Project No: TP11/ HVM/6/I/AB194F. RECLAIM project contributions are gratefully acknowledged from: Airfoil Technologies International Llc, Cummins Inc, De Montfort University, Delcam plc, Electrox Ltd, Manufacturing Technology Centre Ltd, TWI Ltd, Precision Engineering Technologies Ltd, and Renishaw plc