Advances in global instability computations: from incompressible to hypersonic flow

Esta tesis constituye un gran avance en el conocimiento del estudio y análisis de inestabilidades hidrodinámicas desde un punto de vista físico y teórico, como consecuencia de haber desarrollado innovadoras técnicas para la resolución computacional eficiente y precisa de la parte principal del espectro correspondiente a los problemas de autovalores (EVP) multidimensionales que gobiernan la inestabilidad de flujos con dos o tres direcciones espaciales inhomogéneas, denominados problemas de estabilidad global lineal. En el contexto del trabajo de desarrollo de herramientas computacionales presentado en la tesis, la discretización mediante métodos de diferencias finitas estables de alto orden de los EVP bidimensionales y tridimensionales que se derivan de las ecuaciones de Navier-Stokes linealizadas sobre flujos con dos o tres direcciones espaciales inhomogéneas, ha permitido una aceleración de cuatro órdenes de magnitud en su resolución. Esta mejora de eficiencia numérica se ha conseguido gracias al hecho de que usando estos esquemas de diferencias finitas, técnicas eficientes de resolución de problemas lineales son utilizables, explotando el alto nivel de dispersión o alto número de elementos nulos en las matrices involucradas en los problemas tratados. Como más notable consecuencia cabe destacar que la resolución de EVPs multidimensionales de inestabilidad global, que hasta la fecha necesitaban de superordenadores, se ha podido realizar en ordenadores de sobremesa. Además de la solución de problemas de estabilidad global lineal, el mencionado desarrollo numérico facilitó la extensión de las ecuaciones de estabilidad parabolizadas (PSE) lineales y no lineales para analizar la inestabilidad de flujos que dependen fuertemente en dos direcciones espaciales y suavemente en la tercera con las ecuaciones de estabilidad parabolizadas tridimensionales (PSE-3D). Precisamente la capacidad de extensión del novedoso algoritmo PSE-3D para el estudio de interacciones no lineales de los modos de estabilidad, desarrollado íntegramente en esta tesis, permite la predicción de transición en flujos complejos de gran interés industrial y por lo tanto extiende el concepto clásico de PSE, el cuál ha sido empleado exitosamente durante las pasadas tres décadas en el mismo contexto para problemas de capa límite bidimensional. Típicos ejemplos de flujos incompresibles se han analizado en este trabajo sin la necesidad de recurrir a restrictivas presuposiciones usadas en el pasado. Se han estudiado problemas vorticales como es el caso de un vórtice aislado o sistemas de vórtices simulando la estela de alas, en los que la homogeneidad axial no se impone y así se puede considerar la difusión viscosa del flujo. Además, se ha estudiado el chorro giratorio turbulento, cuya inestabilidad se utiliza para mejorar las características de funcionamiento de combustores. En la tesis se abarcan adicionalmente problemas de flujos compresibles. Se presenta el estudio de inestabilidad de flujos de borde de ataque a diferentes velocidades de vuelo. También se analiza la estela formada por un elemento rugoso aislado en capa límite supersónica e hipersónica, mostrando excelentes comparaciones con resultados obtenidos mediante simulación numérica directa. Finalmente, nuevas inestabilidades se han identificado en el flujo hipersónico a Mach 7 alrededor de un cono elíptico que modela el vehículo de pruebas en vuelo HIFiRE-5. Los resultados comparan favorablemente con experimentos en vuelo, lo que subraya aún más el potencial de las metodologías de análisis de estabilidad desarrolladas en esta tesis. ABSTRACT The present thesis constitutes a step forward in advancing the frontiers of knowledge of fluid flow instability from a physical point of view, as a consequence of having been successful in developing groundbreaking methodologies for the efficient and accurate computation of the leading part of the spectrum pertinent to multi-dimensional eigenvalue problems (EVP) governing instability of flows with two or three inhomogeneous spatial directions. In the context of the numerical work presented in this thesis, the discretization of the spatial operator resulting from linearization of the Navier-Stokes equations around flows with two or three inhomogeneous spatial directions by variable-high-order stable finite-difference methods has permitted a speedup of four orders of magnitude in the solution of the corresponding two- and three-dimensional EVPs. This improvement of numerical performance has been achieved thanks to the high-sparsity level offered by the high-order finite-difference schemes employed for the discretization of the operators. This permitted use of efficient sparse linear algebra techniques without sacrificing accuracy and, consequently, solutions being obtained on typical workstations, as opposed to the previously employed supercomputers. Besides solution of the two- and three-dimensional EVPs of global linear instability, this development paved the way for the extension of the (linear and nonlinear) Parabolized Stability Equations (PSE) to analyze instability of flows which depend in a strongly-coupled inhomogeneous manner on two spatial directions and weakly on the third. Precisely the extensibility of the novel PSE-3D algorithm developed in the framework of the present thesis to study nonlinear flow instability permits transition prediction in flows of industrial interest, thus extending the classic PSE concept which has been successfully employed in the same context to boundary-layer type of flows over the last three decades. Typical examples of incompressible flows, the instability of which was analyzed in the present thesis without the need to resort to the restrictive assumptions used in the past, range from isolated vortices, and systems thereof, in which axial homogeneity is relaxed to consider viscous diffusion, as well as turbulent swirling jets, the instability of which is exploited in order to improve flame-holding properties of combustors. The instability of compressible subsonic and supersonic leading edge flows has been solved, and the wake of an isolated roughness element in a supersonic and hypersonic boundary-layer has also been analyzed with respect to its instability: excellent agreement with direct numerical simulation results has been obtained in all cases. Finally, instability analysis of Mach number 7 ow around an elliptic cone modeling the HIFiRE-5 flight test vehicle has unraveled flow instabilities near the minor-axis centerline, results comparing favorably with flight test predictions.

On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

El plan global frente al riesgo de inundación en la ribera del Júcar

El Plan Global del Júcar frente al riesgo de inundación pretende minimizar los daños causados por las avenidas que periódicamente afectan a la Ribera del Júcar. En el presente artículo se describen y analizan las actuaciones de este Plan, la génesis del mismo, el proceso de elaboración y sus resultados. La problemática es compleja, ya que el riesgo de inundación abarca un territorio muy poblado, con un importante desarrollo industrial y agrícola. Además, la existencia de espacios naturales de elevado valor ambiental, hace que las intervenciones derivadas del Plan consideren al mismo nivel la defensa frente a avenidas y las demandas sociales y ambientales, tras el consenso alcanzado en un proceso de participación pública. El Plan incorpora aspectos innovadores en ingeniería hidráulica, cuyo resultado es una actuación integrada y sostenible, que compatibiliza la protección frente a avenidas con la recuperación y mejora del ámbito fluvial, y su función como corredor vertebrador del territorio.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

The Enlarged European Union and its Eastern Neighbours: Problems and Solutions. OSW Point of View, October 2003

The EU enlargement is scheduled to take place in 2004. After this date, it should be a priority for the EU to develop a coherent and comprehensive policy towards its nearest neighbours, i.e. countries bordering the Member States, which cannot join the EU in the nearest future due to their location or weaknesses of their political and economic systems. There are at least three reasons for this. Firstly, good relations with neighbours will underlie the broadly understood security of the Community. Relations with the nearest neighbours will determine both military security of the EU (including the combating of terrorism) and its ability to prevent other threats such as illegal migration, smuggling, etc. Secondly, good economic relations with neighbours may contribute to the Member States' economic growth in the longer term. And finally, the EU's ability to develop an effective and adequate policy towards its nearest neighbours will demonstrate its competence as a subject of international politics. In other words, the EU will not be recognised as a reliable political player in the global scene until it develops an effective strategy for its neighbourhood.

On the periphery of global jihad. The North Caucasus: the illusion of stabilisation. OSW Point of View Number 45, November 2014

The situation in the North Caucasus has stabilised, in comparison with previous years, mainly as regards the activity of the Islamic military underground. This is an effect of ideological changes among the militants which have led to a dilution of the Caucasian armed struggle and its marginalisation in global jihad, since top priority has been granted to the Middle Eastern front. The factors which have contributed to this stabilisation are the organisational crisis in the Caucasus Emirate and the outflux of militants to the Middle East, as well the successful ‘carrot and stick’ policy adopted by Moscow. However, the partial stabilisation in the Caucasus is inherently precarious, being a contingent outcome of the situation rather than the result of systemic change. The region’s pressing problems remain unresolved; and these problems are generating chronic instability and cauing the Caucasus to drift away from Russia in civilisational terms. An economic or political crisis in the Russian Federation may result in the conflicts in the Caucasus unfreezing, including a reactivation of the idea of Chechen independence as well as the idea of the Caucasus Emirate, which is a part of global jihad.

America’s global defence predicament – Why the Asia ‘rebalancing’ has little significance for European security. Egmont Paper No. 72, December 2014

Summary. This paper argues that the Obama Administration’s Asia ‘pivot’ or ‘rebalancing’ is mainly a rhetorical construct that has very little substantive effect on US security policy. In contrast to the widely held belief that a renewed emphasis on Asia would place meaningful restrictions on America’s willingness and ability to deal with European security problems there is little evidence to support this argument nor is it well-grounded conceptually. Furthermore, undue emphasis on this aspect of American policy has detracted attention from more important developments in Washington’s capacity to effectively project military power.

America's global defence predicament-Why the Asia 'rebalancing' has little significance for European security. Egmont Paper No. 72, December 2014

This paper argues that the Obama Administration’s Asia ‘pivot’ or ‘rebalancing’ is mainly a rhetorical construct that has very little substantive effect on US security policy. In contrast to the widely held belief that a renewed emphasis on Asia would place meaningful restrictions on America’s willingness and ability to deal with European security problems there is little evidence to support this argument nor is it well-grounded conceptually. Furthermore, undue emphasis on this aspect of American policy has detracted attention from more important developments in Washington’s capacity to effectively project military power.

Russia marks the 70th anniversary of the victory over Nazism: What significance does it have in an epoch of global confrontation? OSW Commentary No. 171, 20 May 2015

The Victory Day celebrations held in Russia on 9 May 2015 were special for marking the seventieth anniversary of the end of World War II but the particular international and domestic context they were set in was of yet greater importance. The element which set the celebrations in 2015 apart from those in the preceding years was how the military and moral aspects of Soviet victory over Nazi Germany was made part of the current geopolitical confrontation with the West concerning the Ukrainian crisis. The escalation of the aggressive rhetoric on Europe and the USA and accusations that the West is destabilising the international situation and striving for conflict was accompanied by a display of the increasing military power of the Russian Federation; the display itself was stronger than has been seen in preceding years. This was a clear sign that Moscow is ready to protect its national interests in the area of foreign policy by any means. At the same time, the creation of an atmosphere of threat and stoking patriotic feelings was intended to mobilise the Russian public around the political leadership while the country’s economic problems are deteriorating further.

How to get out of the crisis without reforms? The Belarusian authorities confront growing economic problems. OSW Commentary NUMBER 202/21.03.2016

2015 saw a drop in Belarus’s GDP for the first time in almost 20 years, which is primarily the result of a significant reduction in levels of production and export. As a consequence, there was also a serious depletion of the country’s foreign exchange reserves, as well as a progressive weakening of the Belarusian rouble. The macroeconomic figures from January and February 2016 show that these trends are not only continuing, but they are also becoming even more severe, which confirms that Belarus now finds itself in a prolonged economic crisis. On one hand, the reason for this state of affairs is the protracted economic recession in Russia, which is Belarus’s main economic partner, together with the drastic global decline in prices for fuel, which is a key Belarusian export. On the other hand, meanwhile, an equally important reason for the current crisis is the failure of the Belarusian economic model. President Aleksandr Lukashenko, out of fear that his authoritarian system of government will be dismantled and that public discontent will rise, has categorically rejected the proposals for even partial reforms put forward by some of his entourage, who are aware of the need for the immediate transformation of the country’s anachronistic and very costly economic model, based as it still is on quasi-Soviet management policies.

Essays on coordination problems in economics

No estudo da economia, há diversas situações em que a propensão de um indivíduo a tomar determinada ação é crescente na quantidade de outras pessoas que este indivíduo acredita que tomarão a mesma ação. Esse tipo de complementaridade estratégica geralmente leva à existência de múltiplos equilíbrios. Além disso, o resultado atingido pelas decisões decentralizadas dos agentes pode ser ineficiente, deixando espaço para intervenções de política econômica. Esta tese estuda diferentes ambientes em que a coordenação entre indivíduos é importante. O primeiro capítulo analisa como a manipulação de informação e a divulgação de informação afetam a coordenação entre investidores e o bem-estar em um modelo de corridas bancárias. No modelo, há uma autoridade reguladora que não pode se comprometer a revelar a verdadeira situação do setor bancário. O regulador observa informações idiossincráticas dos bancos (através de um stress test, por exemplo) e escolhe se revela essa informação para o público ou se divulga somente um relatório agregado sobre a saúde do sistema financeiro como um todo. O relatório agregado pode ser distorcido a um custo – um custo mais elevado significa maior credibilidade do regulador. Os investidores estão cientes dos incentivos do regulador a esconder más notícias do mercado, mas a manipulação de informação pode, ainda assim, ser efetiva. Se a credibilidade do regulador não for muito baixa, a política de divulgação de informação é estado-contingente, e existe sempre um conjunto de estados em que há manipulação de informação em equilíbrio. Se a credibilidade for suficientemente baixa, porém, o regulador opta por transparência total dos resultados banco-específicos, caso em que somente os bancos mais sólidos sobrevivem. Uma política de opacidade levaria a uma crise bancária sistêmica, independentemente do estado. O nível de credibilidade que maximiza o bem-estar agregado do ponto de vista ex ante é interior. O segundo e o terceiro capítulos estudam problemas de coordenação dinâmicos. O segundo capítulo analisa o bem-estar em um ambiente em que agentes recebem oportunidades aleatórias para migrar entre duas redes. Os resultados mostram que sempre que a rede de pior qualidade (intrínseca) prevalece, isto é eficiente. Na verdade, um planejador central estaria ainda mais inclinado a escolher a rede de pior qualidade. Em equilíbrio, pode haver mudanças ineficientes que ampliem a rede de qualidade superior. Quando indivíduos escolhem entre dois padrões ou redes com níveis de qualidade diferentes, se todos os indivíduos fizessem escolhas simultâneas, a solução eficiente seria que todos adotassem a rede de melhor qualidade. No entanto, quando há fricções e os agentes tomam decisões escalonadas, a solução eficiente difere ix do senso comum. O terceiro capítulo analisa um problema de coordenação dinâmico com decisões escalonadas em que os agentes são heterogêneos ex ante. No modelo, existe um único equilíbrio, caracterizado por thresholds que determinam as escolhas para cada tipo de agente. Apesar da heterogeneidade nos payoffs, há bastante conformidade nas ações individuais em equilíbrio. Os thresholds de diferentes tipos de agentes coincidem parcialmente contanto que exista um conjunto de crenças arbitrário que justifique esta conformidade. No entanto, as estratégias de equilíbrio de diferentes tipos nunca coincidem totalmente. Além disso, a conformidade não é ineficiente. A solução eficiente apresentaria estratégias ainda mais similares para tipos distintos em comparação com o equilíbrio decentralizado.

Prioritizing global conservation efforts

One of the most pressing issues facing the global conservation community is how to distribute limited resources between regions identified as priorities for biodiversity conservation(1-3). Approaches such as biodiversity hotspots(4), endemic bird areas(5) and ecoregions(6) are used by international organizations to prioritize conservation efforts globally(7). Although identifying priority regions is an important first step in solving this problem, it does not indicate how limited resources should be allocated between regions. Here we formulate how to allocate optimally conservation resources between regions identified as priorities for conservation - the 'conservation resource allocation problem'. Stochastic dynamic programming is used to find the optimal schedule of resource allocation for small problems but is intractable for large problems owing to the curse of dimensionality(8). We identify two easy- to- use and easy- to- interpret heuristics that closely approximate the optimal solution. We also show the importance of both correctly formulating the problem and using information on how investment returns change through time. Our conservation resource allocation approach can be applied at any spatial scale. We demonstrate the approach with an example of optimal resource allocation among five priority regions in Wallacea and Sundaland, the transition zone between Asia and Australasia.

Comparative cost-effectiveness of policy instruments for reducing the global burden of alcohol, tobacco and illicit drug use

Alcohol, tobacco and illicit drug use together pose a formidable challenge to international public health. Building on earlier estimates of the demonstrated burden of alcohol, tobacco and illicit drug use at the global level, this review aims to consider the comparative cost-effectiveness of evidence-based interventions for reducing the global burden of disease from these three risk factors. Although the number of published cost-effectiveness studies in the addictions field is now extensive ( reviewed briefly here) there are a series of practical problems in using them for sector-wide decision making, including methodological heterogeneity, differences in analytical reference point and the specificity of findings to a particular context. In response to these limitations, a more generalised form of cost-effectiveness analysis (CEA) is proposed, which enables like-with-like comparisons of the relative efficiency of preventive or individual-based strategies to be made, not only within but also across diseases or their risk factors. The application of generalised CEA to a range of personal and non-personal interventions for reducing the burden of addictive substances is described. While such a development avoids many of the obstacles that have plagued earlier attempts and in so doing opens up new opportunities to address important policy questions, there remain a number of caveats to population-level analysis of this kind, particularly when conducted at the global level. These issues are the subject of the final section of this review.

A new relaxation method for roll forming problems

Finite element analysis (FEA) of nonlinear problems in solid mechanics is a time consuming process, but it can deal rigorously with the problems of both geometric, contact and material nonlinearity that occur in roll forming. The simulation time limits the application of nonlinear FEA to these problems in industrial practice, so that most applications of nonlinear FEA are in theoretical studies and engineering consulting or troubleshooting. Instead, quick methods based on a global assumption of the deformed shape have been used by the roll-forming industry. These approaches are of limited accuracy. This paper proposes a new form-finding method - a relaxation method to solve the nonlinear problem of predicting the deformed shape due to plastic deformation in roll forming. This method involves applying a small perturbation to each discrete node in order to update the local displacement field, while minimizing plastic work. This is iteratively applied to update the positions of all nodes. As the method assumes a local displacement field, the strain and stress components at each node are calculated explicitly. Continued perturbation of nodes leads to optimisation of the displacement field. Another important feature of this paper is a new approach to consideration of strain history. For a stable and continuous process such as rolling and roll forming, the strain history of a point is represented spatially by the states at a row of nodes leading in the direction of rolling to the current one. Therefore the increment of the strain components and the work-increment of a point can be found without moving the object forward. Using this method we can find the solution for rolling or roll forming in just one step. This method is expected to be faster than commercial finite element packages by eliminating repeated solution of large sets of simultaneous equations and the need to update boundary conditions that represent the rolls.