Unsteady flowfields are integral to high-speed applications, demanding precise modelling to characterize their unsteady features accurately. The simulation of unsteady supersonic and hypersonic flows is inherently computationally expensive, requiring a highly refined mesh to capture these unsteady effects. While anisotropic metric-based adaptive mesh refinement has proven effective in achieving accuracy with much less complexity, current algorithms are primarily tailored for steady flow fields. This thesis presents a novel approach to address the challenges of anisotropic grid adaptation of unsteady flows by leveraging a data-driven technique called Dynamic Mode Decomposition (DMD). DMD has proven to be a powerful tool to model complex nonlinear flows, given its links to the Koopman operator, and also its easy mathematical implementation. This research proposes the integration of DMD into the process of anisotropic grid adaptation to dynamically adjust the mesh in response to evolving flow features. The effectiveness of the proposed approach is demonstrated through numerical experiments on representative unsteady flow configurations, such as a cylinder in a subsonic flow and a cylinder in a supersonic channel flow. Results indicate that the incorporation of DMD enables an accurate representation of unsteady flow dynamics. Overall, this thesis contributes to making advances in the adaptation of unsteady flows. The novel framework proposed makes it computationally tractable to track the evolution of the main coherent features of the flowfield without losing out on accuracy by using a data-driven method. / Master of Science / Simulating unsteady, high-speed fluid flows around objects like aircraft and rockets poses a significant computational challenge. These flows exhibit rapidly evolving, intricate pattern structures that demand highly refined computational meshes to capture accurately. However, using a statically refined mesh for the entire simulation is computationally prohibitive. This research proposes a novel data-driven approach to enable efficient anisotropic mesh adaptation for such unsteady flow simulations. It leverages a technique called Dynamic Mode Decomposition (DMD) to model the dominant coherent structures and their evolution from snapshot flow field data. DMD has shown powerful capabilities in identifying the most energetic flow features and their time dynamics from numerical or experimental data. By integrating DMD into the anisotropic mesh adaptation process, the computational mesh can be dynamically refined anisotropically just in regions containing critical time-varying flow structures. The efficacy of this DMD-driven anisotropic adaptation framework is demonstrated in representative test cases - an unsteady subsonic flow over a circular cylinder and a supersonic channel flow over a cylinder. Results indicate that it enables accurate tracking and resolution of the key unsteady flow phenomena like vortex shedding using far fewer computational cells compared to static mesh simulations. In summary, this work makes anisotropic mesh adaptation computationally tractable for unsteady flow simulations by leveraging data-driven DMD modelling of the evolving coherent structures. The developed techniques pave the way for more accurate yet efficient unsteady CFD simulations.

Compuesta por tres capítulos: El primero es un estudio sobre la implementación the Sparse Grid métodos para es el estudio de modelos económicos con muchas dimensiones. Llevado a cabo mediante aplicaciones noveles del método de Smolyak con el objetivo de favorecer la tratabilidad y obtener resultados preciso. Los resultados muestran mejoras en la eficiencia de la implementación de modelos con múltiples agentes. El segundo capítulo introduce una nueva metodología para la evaluación de políticas económicas, llamada Synthetic Control with Statistical Learning, todo ello aplicado a políticas particulares: a) reducción del número de horas laborales en Portugal en 1996 y b) reducción del coste del despido en España en 2010. La metodología funciona y se erige como alternativa a previos métodos. En términos empíricos se muestra que tras la implementación de la política se produjo una reducción efectiva del desempleo y en el caso de España un incremento del mismo. El tercer capítulo utiliza la metodología utiliza en el segundo capítulo y la aplica para evaluar la implementación del Tercer Programa Europeo para la Seguridad Vial (Third European Road Safety Action Program) entre otras metodologías. Los resultados muestran que la coordinación a nivel europeo de la seguridad vial a supuesto una ayuda complementaria. En el año 2010 se estima una reducción de víctimas mortales de entre 13900 y 19400 personal en toda Europa.