Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

Empirical studies in industrial location: an assessment of their methods and results

This paper surveys recent evidence on the determinants of (national and/or foreign) industrial location. We find that the basic analytical framework has remained essentially unaltered since the early contributions of the early 1980's while, in contrast, there have been significant advances in the quality of the data and, to a lesser extent, the econometric modelling. We also identify certain determinants (neoclassical and institutional factors) that tend to provide largely consistent results across the reviewed studies. In light of this evidence, we finally suggest future lines of research.

Assessing the assignation of public subsidies: Do the experts choose the most efficient R&D projects?

The implementation of public programs to support business R&D projects requires the establishment of a selection process. This selection process faces various difficulties, which include the measurement of the impact of the R&D projects as well as selection process optimization among projects with multiple, and sometimes incomparable, performance indicators. To this end, public agencies generally use the peer review method, which, while presenting some advantages, also demonstrates significant drawbacks. Private firms, on the other hand, tend toward more quantitative methods, such as Data Envelopment Analysis (DEA), in their pursuit of R&D investment optimization. In this paper, the performance of a public agency peer review method of project selection is compared with an alternative DEA method.

The Black Box of Business Dynamics

Research in business dynamics has been advancing rapidly in the last years but the translation of the new knowledge to industrial policy design is slow. One striking aspect in the policy area is that although research and analysis do not identify the existence of an specific optimal rate of business creation and business exit, governments everywhere have adopted business start-up support programs with the implicit principle that the more the better. The purpose of this article is to contribute to understand the implications of the available research for policy design. Economic analysis has identified firm heterogeneity as being the most salient characteristic of industrial dynamics, and so a better knowledge of the different types of entrepreneur, their behavior and their specific contribution to innovation and growth would enable us to see into the ‘black box’ of business dynamics and improve the design of appropriate public policies. The empirical analysis performed here shows that not all new business have the same impact on relevant economic variables, and that self-employment is of quite a different economic nature to that of firms with employees. It is argued that public programs should not promote indiscriminate entry but rather give priority to able entrants with survival capacities. Survival of entrants is positively related to their size at birth. Innovation and investment improve the likelihood of survival of new manufacturing start-ups. Investment in R&D increases the risk of failure in new firms, although it improves the competitiveness of incumbents.

Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

We construct a new family of semi-discrete numerical schemes for the approximation of the one-dimensional periodic Vlasov-Poisson system. The methods are based on the coupling of discontinuous Galerkin approximation to the Vlasov equation and several finite element (conforming, non-conforming and mixed) approximations for the Poisson problem. We show optimal error estimates for the all proposed methods in the case of smooth compactly supported initial data. The issue of energy conservation is also analyzed for some of the methods.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

Aproximació a la figura dels Business Angels

Els business angels són persones físiques que inverteixen una part dels seus diners en empreses joves, tot just acabades de crear, en alguns casos fins i tot ajuden a crear-les. El nom d’àngels té el seu origen en els rics filantrops de Nova York que finançaven les obres que s’estrenaven a Broadway. Aquests filantrops invertien els seus diners en una obra de teatre, pel plaer de contribuir a la cultura, molt sovint no arribaven a recuperar mai aquests diners. Els business angels, no són filantrops, inverteixen esperant guanyar diners, però al igual que els àngels de Broadway, els mou alguna cosa més que els diners, ja que està àmpliament documentat que darrera d’aquestes inversions hi ha també raons no financeres, com ara fomentar l’esperit emprenedor o fins i tot la cerca de diversió. Podríem dir que el terme “business angel” es va encunyar a principis dels 80 als EUA, per tant aviat farà 30 anys, no obstant, encara avui, la majoria de catalans no coneixen el significat d’aquest terme. A Catalunya i Espanya anem terriblement retardats en l’estudi i la promoció d’aquesta figura en relació a països com els EUA i el Regne Unit, però també massa enrera en relació a països com Finlàndia, Suècia, Noruega i Alemanya. L’objectiu d’aquest treball és doncs oferir una complerta aproximació a aquesta figura del business angel, una figura que entenem clau en el desenvolupament empresarial i per tant una figura que cal potenciar a tots els nivells. Per tal de contextualitzar aquesta important figura, el treball parteix de l’anàlisi de la relació existent entre emprenedoria i creixement econòmic, s’endinsa després en el capital risc, per presentar finalment qui és i que fa el business angel. El treball intenta també mostrar l’abús d’usos i la inconsistència de les definicions que es donen del terme “business angel” i per tant la gran confusió que tot això genera.

Stabilized Petrov-Galerkin methods for the convection-diffusion-reaction and the Helmholtz equations

We present two new stabilized high-resolution numerical methods for the convection–diffusion–reaction (CDR) and the Helmholtz equations respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e.g. M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not feasible when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the 1D CDR problem. The problem is studied from a fresh point of view, including practical implications on the formulation of the maximum principle, M-Matrices theory, monotonicity and total variation diminishing (TVD) finite volume schemes. The current method is next in line to earlier methods that may be viewed as an upwinding plus a discontinuity-capturing operator. Finally, some remarks are made on the extension of the HRPG method to multidimensions. Next, we present a new numerical scheme for the Helmholtz equation resulting in quasi-exact solutions. The focus is on the approximation of the solution to the Helmholtz equation in the interior of the domain using compact stencils. Piecewise linear/bilinear polynomial interpolation are considered on a structured mesh/grid. The only a priori requirement is to provide a mesh/grid resolution of at least eight elements per wavelength. No stabilization parameters are involved in the definition of the scheme. The scheme consists of taking the average of the equation stencils obtained by the standard Galerkin finite element method and the classical finite difference method. Dispersion analysis in 1D and 2D illustrate the quasi-exact properties of this scheme. Finally, some remarks are made on the extension of the scheme to unstructured meshes by designing a method within the Petrov–Galerkin framework.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines? decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines ?networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub.

Discontinuous Galerkin methods for the Multi-dimensional Vlasov-Poisson problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov-Poisson system. The schemes are constructed by combing a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

Did the cooperative start life as a Joint-Stock company? business law and cooperatives in Spain, 1869–1931

Studies of Spanish cooperatives date their spread from the Law on Agrarian Syndicates of 1906. But the first legislative appearance of cooperatives is an 1869 measure that permitted general incorporation for lending companies. The 1931 general law on cooperatives, which was the first act permitting the formation of cooperatives in any activity, reflects the gradual disappearance of the cooperative’s "business" characteristics. In this paper we trace the Spanish cooperative’s legal roots in business law and its connections to broader questions of the freedom of association, the formation of joint-stock enterprises, and the liability of investors in business and cooperative entities. Our account underscores the similarities of the organizational problems approach by cooperatives and business firms, while at the same time respecting the distinctive purposes cooperatives served.

Business plan: PARQUETS, S.A.

Aquest Treball Final de Carrera pretén desenvolupar un Pla de Viabilitat, que garanteixi una millora en la rendibilitat de PARQUETS S.A., una empresa amb més de 40 anys d’existència en el sector de la instal-lació de paviments per al terra. A partir de la realització inicial d’un estudi del mercat, s’ha elaborat un complet anàlisi sobre els punts principals que componen qualsevol Pla de Negoci: el Pla de Marketing, el Pla d’Operacions, el Pla d’Organització i el Pla Econòmic-Financer. A més, amb la realització d’aquest estudi, hem pogut verificar que al mercat hi ha importants economies d’escala que cal aprofitar, i que intervindrien amb èxit amb l’expansió geogràfica, organitzativa i operativa de l’empresa.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines' decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines' networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub. Keywords: regional jet technology; low-cost business model; point-to-point network; hub-and-spoke network JEL Classi…fication Numbers: L13; L2; L93

Cronyism in Business, Public Sector and Politics

This paper contrasts the incentives for cronyism in business, the public sector and politics within an agency problem model with moral hazard. The analysis is focused on the institutional differences between private, public and political organizations. In business, when facing a residual claimant contract, a chief manager ends up with a relatively moderate …rst-best level of cronyism within a …firm. The institutional framework of the public sector does not allow explicit contracting, which leads to a more severe cronyism problem within public organizations. Finally, it is shown that the nature of political appointments (such that the subordinate's reappointment is conditioned on the chief's re-election) together with implicit contracting makes political cronyism the most extreme case. JEL classifi…cation: D72, D73, D86. Keywords: Cronyism; Meritocracy; Manager; Bureaucrat; Politician.