Efficient adaptive methods based on adjoint equations and truncation error estimation for unstructured grids

El propósito de esta tesis es la implementación de métodos eficientes de adaptación de mallas basados en ecuaciones adjuntas en el marco de discretizaciones de volúmenes finitos para mallas no estructuradas. La metodología basada en ecuaciones adjuntas optimiza la malla refinándola adecuadamente con el objetivo de mejorar la precisión de cálculo de un funcional de salida dado. El funcional suele ser una magnitud escalar de interés ingenieril obtenida por post-proceso de la solución, como por ejemplo, la resistencia o la sustentación aerodinámica. Usualmente, el método de adaptación adjunta está basado en una estimación a posteriori del error del funcional de salida mediante un promediado del residuo numérico con las variables adjuntas, “Dual Weighted Residual method” (DWR). Estas variables se obtienen de la solución del problema adjunto para el funcional seleccionado. El procedimiento habitual para introducir este método en códigos basados en discretizaciones de volúmenes finitos involucra la utilización de una malla auxiliar embebida obtenida por refinamiento uniforme de la malla inicial. El uso de esta malla implica un aumento significativo de los recursos computacionales (por ejemplo, en casos 3D el aumento de memoria requerida respecto a la que necesita el problema fluido inicial puede llegar a ser de un orden de magnitud). En esta tesis se propone un método alternativo basado en reformular la estimación del error del funcional en una malla auxiliar más basta y utilizar una técnica de estimación del error de truncación, denominada _ -estimation, para estimar los residuos que intervienen en el método DWR. Utilizando esta estimación del error se diseña un algoritmo de adaptación de mallas que conserva los ingredientes básicos de la adaptación adjunta estándar pero con un coste computacional asociado sensiblemente menor. La metodología de adaptación adjunta estándar y la propuesta en la tesis han sido introducidas en un código de volúmenes finitos utilizado habitualmente en la industria aeronáutica Europea. Se ha investigado la influencia de distintos parámetros numéricos que intervienen en el algoritmo. Finalmente, el método propuesto se compara con otras metodologías de adaptación de mallas y su eficiencia computacional se demuestra en una serie de casos representativos de interés aeronáutico. ABSTRACT The purpose of this thesis is the implementation of efficient grid adaptation methods based on the adjoint equations within the framework of finite volume methods (FVM) for unstructured grid solvers. The adjoint-based methodology aims at adapting grids to improve the accuracy of a functional output of interest, as for example, the aerodynamic drag or lift. The adjoint methodology is based on the a posteriori functional error estimation using the adjoint/dual-weighted residual method (DWR). In this method the error in a functional output can be directly related to local residual errors of the primal solution through the adjoint variables. These variables are obtained by solving the corresponding adjoint problem for the chosen functional. The common approach to introduce the DWR method within the FVM framework involves the use of an auxiliary embedded grid. The storage of this mesh demands high computational resources, i.e. over one order of magnitude increase in memory relative to the initial problem for 3D cases. In this thesis, an alternative methodology for adapting the grid is proposed. Specifically, the DWR approach for error estimation is re-formulated on a coarser mesh level using the _ -estimation method to approximate the truncation error. Then, an output-based adaptive algorithm is designed in such way that the basic ingredients of the standard adjoint method are retained but the computational cost is significantly reduced. The standard and the new proposed adjoint-based adaptive methodologies have been incorporated into a flow solver commonly used in the EU aeronautical industry. The influence of different numerical settings has been investigated. The proposed method has been compared against different grid adaptation approaches and the computational efficiency of the new method has been demonstrated on some representative aeronautical test cases.

Mesh traversal and sorting for efficient memory usage in scientific codes

Applications that operate on meshes are very popular in High Performance Computing (HPC) environments. In the past, many techniques have been developed in order to optimize the memory accesses for these datasets. Different loop transformations and domain decompositions are com- monly used for structured meshes. However, unstructured grids are more challenging. The memory accesses, based on the mesh connectivity, do not map well to the usual lin- ear memory model. This work presents a method to improve the memory performance which is suitable for HPC codes that operate on meshes. We develop a method to adjust the sequence in which the data are used inside the algorithm, by means of traversing and sorting the mesh. This sorted mesh can be transferred sequentially to the lower memory levels and allows for minimum data transfer requirements. The method also reduces the lower memory requirements dra- matically: up to 63% of the L1 cache misses are removed in a traditional cache system. We have obtained speedups of up to 2.58 on memory operations as measured in a general- purpose CPU. An improvement is also observed with se- quential access memories, where we have observed reduc- tions of up to 99% in the required low-level memory size.

NURBS-Based Geometry Parameterization for Aerodynamic Shape Optimization

La motivación de esta tesis es el desarrollo de una herramienta de optimización automática para la mejora del rendimiento de formas aerodinámicas enfocado en la industria aeronáutica. Este trabajo cubre varios aspectos esenciales, desde el empleo de Non-Uniform Rational B-Splines (NURBS), al cálculo de gradientes utilizando la metodología del adjunto continuo, el uso de b-splines volumétricas como parámetros de diseño, el tratamiento de la malla en las intersecciones, y no menos importante, la adaptación de los algoritmos de la dinámica de fluidos computacional (CFD) en arquitecturas hardware de alto paralelismo, como las tarjetas gráficas, para acelerar el proceso de optimización. La metodología adjunta ha posibilitado que los métodos de optimización basados en gradientes sean una alternativa prometedora para la mejora de la eficiencia aerodinámica de los aviones. La formulación del adjunto permite calcular los gradientes de una función de coste, como la resistencia aerodinámica o la sustentación, independientemente del número de variables de diseño, a un coste computacional equivalente a una simulación CFD. Sin embargo, existen problemas prácticos que han imposibilitado su aplicación en la industria, que se pueden resumir en: integrabilidad, rendimiento computacional y robustez de la solución adjunta. Este trabajo aborda estas contrariedades y las analiza en casos prácticos. Como resumen, las contribuciones de esta tesis son: • El uso de NURBS como variables de diseño en un bucle de automático de optimización, aplicado a la mejora del rendimiento aerodinámico de alas en régimen transónico. • El desarrollo de algoritmos de inversión de punto, para calcular las coordenadas paramétricas de las coordenadas espaciales, para ligar los vértices de malla a las NURBS. • El uso y validación de la formulación adjunta para el calculo de los gradientes, a partir de las sensibilidades de la solución adjunta, comparado con diferencias finitas. • Se ofrece una estrategia para utilizar la geometría CAD, en forma de parches NURBS, para tratar las intersecciones, como el ala-fuselaje. • No existen muchas alternativas de librerías NURBS viables. En este trabajo se ha desarrollado una librería, DOMINO NURBS, y se ofrece a la comunidad como código libre y abierto. • También se ha implementado un código CFD en tarjeta gráfica, para realizar una valoración de cómo se puede adaptar un código sobre malla no estructurada a arquitecturas paralelas. • Finalmente, se propone una metodología, basada en la función de Green, como una forma eficiente de paralelizar simulaciones numéricas. Esta tesis ha sido apoyada por las actividades realizadas por el Área de Dinámica da Fluidos del Instituto Nacional de Técnica Aeroespacial (INTA), a través de numerosos proyectos de financiación nacional: DOMINO, SIMUMAT, y CORESFMULAERO. También ha estado en consonancia con las actividades realizadas por el departamento de Métodos y Herramientas de Airbus España y con el grupo Investigación y Tecnología Aeronáutica Europeo (GARTEUR), AG/52. ABSTRACT The motivation of this work is the development of an automatic optimization strategy for large scale shape optimization problems that arise in the aeronautics industry to improve the aerodynamic performance; covering several aspects from the use of Non-Uniform Rational B-Splines (NURBS), the calculation of the gradients with the continuous adjoint formulation, the development of volumetric b-splines parameterization, mesh adaptation and intersection handling, to the adaptation of Computational Fluid Dynamics (CFD) algorithms to take advantage of highly parallel architectures in order to speed up the optimization process. With the development of the adjoint formulation, gradient-based methods for aerodynamic optimization become a promising approach to improve the aerodynamic performance of aircraft designs. The adjoint methodology allows the evaluation the gradients to all design variables of a cost function, such as drag or lift, at the equivalent cost of more or less one CFD simulation. However, some practical problems have been delaying its full implementation to the industry, which can be summarized as: integrability, computer performance, and adjoint robustness. This work tackles some of these issues and analyse them in well-known test cases. As summary, the contributions comprises: • The employment of NURBS as design variables in an automatic optimization loop for the improvement of the aerodynamic performance of aircraft wings in transonic regimen. • The development of point inversion algorithms to calculate the NURBS parametric coordinates from the space coordinates, to link with the computational grid vertex. • The use and validation of the adjoint formulation to calculate the gradients from the surface sensitivities in an automatic optimization loop and evaluate its reliability, compared with finite differences. • This work proposes some algorithms that take advantage of the underlying CAD geometry description, in the form of NURBS patches, to handle intersections and mesh adaptations. • There are not many usable libraries for NURBS available. In this work an open source library DOMINO NURBS has been developed and is offered to the community as free, open source code. • The implementation of a transonic CFD solver from scratch in a graphic card, for an assessment of the implementability of conventional CFD solvers for unstructured grids to highly parallel architectures. • Finally, this research proposes the use of the Green's function as an efficient paralellization scheme of numerical solvers. The presented work has been supported by the activities carried out at the Fluid Dynamics branch of the National Institute for Aerospace Technology (INTA) through national founding research projects: DOMINO, SIMUMAT, and CORESIMULAERO; in line with the activities carried out by the Methods and Tools and Flight Physics department at Airbus and the Group for Aeronautical Research and Technology in Europe (GARTEUR) action group AG/52.

Self-adaptive grids for noise mapping refinement

Noise maps are usually represented as contour or isolines maps describing the sound levels in a region. Using this kind of representation the user can easily find the noise level assigned to every location in the map. But the acoustic calculations behind the map are not performed for every single location on it; they are only performed in a grid of receivers. The results in this calculation grid are interpolated to draw the isolines or contours. Therefore, the resolution of the calculation grid and the way it was created (rectangular, triangulated, random…) have an effect on the resulting map. In this paper we describe a smart iterative procedure to optimize the quality of the map at a really low additional computational cost, using self-adaptive grids for the acoustic calculations. These self-adaptive grids add new receivers to the sampling grid in those locations where they are expected to be more useful, so that the performance at the output of the interpolator is enhanced. Self-adaptive sampling grids can be used for minimizing the overall error of the map (improving its quality), or for reducing calculation times, and can be also applied selectively to target areas or contour lines. This can be done by the user customizing the maximum number of iterations, the number of new receivers for each iteration, the target isolines, the target quality…

The estimation of truncation error by tau-estimation revisited

The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the @t-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.

Simulation of AC, DC, and AC-DC coupled mini-grids. In search of the most efficient system

Renewable energy hybrid systems and mini-grids for electrification of rural areas are known to be reliable and more cost efficient than grid extension or only-diesel based systems. However, there is still some uncertainty in some areas, for example, which is the most efficient way of coupling hybrid systems: AC, DC or AC-DC? With the use of Matlab/Simulink a mini-grid that connects a school, a small hospital and an ecotourism hostel has been modelled. This same mini grid has been coupled in the different possible ways and the system’s efficiency has been studied. In addition, while keeping the consumption constant, the generation sources and the consumption profile have been modified and the effect on the efficiency under each configuration has also been analysed. Finally different weather profiles have been introduced and, again, the effect on the efficiency of each system has been observed.

Large-Scale smart grids as system of systems

Smart Grids are advanced power networks that introduce intelligent management, control, and operation systems to address the new challenges generated by the growing energy demand and the appearance of renewal energies. In the literature, Smart Grids are presented as an exemplar SoS: systems composed of large heterogeneous and independent systems that leverage emergent behavior from their interaction. Smart Grids are currently scaling up the electricity service to millions of customers. These Smart Grids are known as Large-Scale Smart Grids. From the experience in several projects about Large-Scale Smart Grids, this paper defines Large-Scale Smart Grids as a SoS that integrate a set of SoS and conceptualizes the properties of this SoS. In addition, the paper defines the architectural framework for deploying the software architectures of Large-Scale Smart Grid SoS.

Designing and simulating smart grids

Growing energy demands and the increased use of renewal energies have changed the landscape of power networks leading to new challenges. Smart Grids have emerged to cope with these challenges by facilitating the integration of traditional and renewable energy resources in distributed, open, and self-managed ways. Innovative models are needed to design energy infrastructures that can enable self-management of the power grid. Software architectures smoothly integrate the software that provides self-management to Smart Grids and their hardware infrastructures. We present a framework to design the software architectures of autonomous Smart Grids in an intuitive domain-oriented way and to simulate their execution by automatically generating the code from the designed autonomous smart grid architectures.

AVR adjustment of Synchronous Generators in Weak Grids under Faulty Conditions.

In weak grids, an important problem with voltage stability and protections coordination of power plants exists. This problem appears because all the generation groups are connected to the same bus bar. As a result, if a fault occurs in any of the generation groups, or in the bus bar that connect them, the system voltage will have large oscillations. Hence, in weak grids the correct adjustment of AVR (Automatic Voltage Regulator) is critical. In this work an experimental study of differents AVR adjustments against fault in weak grids is described.

Evaluación del dispositivo Raspberry Pi como elemento de despliegue de servicios en el marco de las Smart Grids

La tendencia actual de las redes de telecomunicaciones conduce a pensar en un futuro basado en el concepto emergente de las Smart Cities¸ que tienen como objetivo el desarrollo urbano basado en un modelo de sostenibilidad que responda a las necesidades crecientes de las ciudades. Dentro de las Smart Cities podemos incluir el concepto de Smart Grid, el cual está referido a sistemas de administración y producción de energía eficientes, que permitan un sistema energético sostenible, y que den cabida a las fuentes de energía renovables. Sistemas de este tipo se muestran a los usuarios como un conjunto de servicios con los que interactuar sin ser tan sólo un mero cliente, sino un agente más del entorno energético. Por otro lado, los sistemas de software distribuidos son cada vez más comunes en una infraestructura de telecomunicaciones cada vez más extensa y con más capacidades. Dentro de este ámbito tecnológico, las arquitecturas orientadas a servicios han crecido exponencialmente sobre todo en el sector empresarial. Con sistemas basados en estas arquitecturas, se pueden ofrecer a empresas y usuarios sistemas software basados en el concepto de servicio. Con la progresión del hardware actual, la miniaturización de los equipos es cada vez mayor, sin renunciar por ello a la potencia que podemos encontrar en sistemas de mayor tamaño. Un ejemplo es el dispositivo Raspberry Pi, que contiene un ordenador plenamente funcional contenido en el tamaño de una cajetilla de tabaco, y con un coste muy reducido. En este proyecto se pretenden aunar los tres conceptos expuestos. De esta forma, se busca utilizar el dispositivo Raspberry Pi como elemento de despliegue integrado en una arquitectura de Smart Grid orientada a servicios. En los trabajos realizados se ha utilizado la propuesta definida por el proyecto de I+D europeo e-GOTHAM, con cuya infraestructura se ha tenido ocasión de realizar diferentes pruebas de las descritas en esta memoria. Aunque esta arquitectura está orientada a la creación de una Smart Grid, lo experimentado en este PFG podría encajar en otro tipo de aplicaciones. Dentro del estudio sobre las soluciones software actuales, se ha trabajado en la evaluación de la posibilidad de instalar un Enterprise Service Bus en el Raspberry Pi y en la optimización de la citada instalación. Una vez conseguida una instalación operativa, se ha desarrollado un controlador de un dispositivo físico (sensor/actuador), denominado Dispositivo Lógico, a modo de prueba de la viabilidad del uso del Raspberry Pi para actuar como elemento en el que instalar aplicaciones en entornos de Smart Grid o Smart Home. El éxito logrado con esta experimentación refuerza la idea de considerar al Raspberry Pi, como un importante elemento a tener en cuenta para el despliegue de servicios de Smart Cities o incluso en otros ámbitos tecnológicos. ABSTRACT. The current trend of telecommunication networks lead to think in a future based on the emerging concept of Smart Cities, whose objective is to ensure the urban development based on a sustainable model to respond the new necessities of the cities. Within the Smart cites we can include the concept of Smart Grid, which is based on management systems and efficient energy production, allowing a sustainable energy producing system, and that includes renewable energy sources. Systems of this type are shown to users as a set of services that allow users to interact with the system not only as a single customer, but also as other energy environment agent. Furthermore, distributed software systems are increasingly common in a telecommunications infrastructure more extensive and with more capabilities. Within this area of technology, service-oriented architectures have grown exponentially especially in the business sector. With systems based on these architectures, can be offered to businesses and users software systems based on the concept of service. With the progression of the actual hardware, the miniaturization of computers is increasing, without sacrificing the power of larger systems. An example is the Raspberry Pi, which contains a fully functional computer contained in the size of a pack of cigarettes, and with a very low cost. This PFG (Proyecto Fin de Grado) tries to combine the three concepts presented. Thus, it is intended to use the Raspberry Pi device as a deployment element integrated into a service oriented Smart Grid architecture. In this PFG, the one proposed in the European R&D e-GOTHAM project has been observed. In addition several tests described herein have been carried out using the infrastructure of that project. Although this architecture is oriented to the creation of a Smart Grid, the experiences reported in this document could fit into other applications. Within the study on current software solutions, it have been working on assessing the possibility of installing an Enterprise Service Bus in the Raspberry Pi and optimizing that facility. Having achieved an operating installation, it has been developed a driver for a physical device (sensor / actuator), called logical device, for testing the feasibility of using the Raspberry Pi to act as an element in which to install applications in Smart Grid and Smart Home Environments. The success of this experiment reinforces the idea of considering the Raspberry Pi as an important element to take into account in the deployment of Smart Cities services or even in other technological fields.

Uso de DES y RANS no estacionario para la simulación del flujo alrededor de una carena Wigley - Use of Unsteady RANS and DES to simulate flows around a Wigley Hull)

Computer Fluid Dynamics tools have already become a valuable instrument for Naval Architects during the ship design process, thanks to their accuracy and the available computer power. Unfortunately, the development of RANSE codes, generally used when viscous effects play a major role in the flow, has not reached a mature stage, being the accuracy of the turbulence models and the free surface representation the most important sources of uncertainty. Another level of uncertainty is added when the simulations are carried out for unsteady flows, as those generally studied in seakeeping and maneuvering analysis and URANS equations solvers are used. Present work shows the applicability and the benefits derived from the use of new approaches for the turbulence modeling (Detached Eddy Simulation) and the free surface representation (Level Set) on the URANS equations solver CFDSHIP-Iowa. Compared to URANS, DES is expected to predict much broader frequency contents and behave better in flows where boundary layer separation plays a major role. Level Set methods are able to capture very complex free surface geometries, including breaking and overturning waves. The performance of these improvements is tested in set of fairly complex flows, generated by a Wigley hull at pure drift motion, with drift angle ranging from 10 to 60 degrees and at several Froude numbers to study the impact of its variation. Quantitative verification and validation are performed with the obtained results to guarantee their accuracy. The results show the capability of the CFDSHIP-Iowa code to carry out time-accurate simulations of complex flows of extreme unsteady ship maneuvers. The Level Set method is able to capture very complex geometries of the free surface and the use of DES in unsteady simulations highly improves the results obtained. Vortical structures and instabilities as a function of the drift angle and Fr are qualitatively identified. Overall analysis of the flow pattern shows a strong correlation between the vortical structures and free surface wave pattern. Karman-like vortex shedding is identified and the scaled St agrees well with the universal St value. Tip vortices are identified and the associated helical instabilities are analyzed. St using the hull length decreases with the increase of the distance along the vortex core (x), which is similar to results from other simulations. However, St scaled using distance along the vortex cores shows strong oscillations compared to almost constants for those previous simulations. The difference may be caused by the effect of the free-surface, grid resolution, and interaction between the tip vortex and other vortical structures, which needs further investigations. This study is exploratory in the sense that finer grids are desirable and experimental data is lacking for large α, especially for the local flow. More recently, high performance computational capability of CFDSHIP-Iowa V4 has been improved such that large scale computations are possible. DES for DTMB 5415 with bilge keels at α = 20º were conducted using three grids with 10M, 48M and 250M points. DES analysis for flows around KVLCC2 at α = 30º is analyzed using a 13M grid and compared with the results of DES on the 1.6M grid by. Both studies are consistent with what was concluded on grid resolution herein since dominant frequencies for shear-layer, Karman-like, horse-shoe and helical instabilities only show marginal variation on grid refinement. The penalties of using coarse grids are smaller frequency amplitude and less resolved TKE. Therefore finer grids should be used to improve V&V for resolving most of the active turbulent scales for all different Fr and α, which hopefully can be compared with additional EFD data for large α when it becomes available.

Using Clouds to Scale Grid Resources: An Economic Model

Infrastructure as a Service clouds are a flexible and fast way to obtain (virtual) resources as demand varies. Grids, on the other hand, are middleware platforms able to combine resources from different administrative domains for task execution. Clouds can be used by grids as providers of devices such as virtual machines, so they only use the resources they need. But this requires grids to be able to decide when to allocate and release those resources. Here we introduce and analyze by simulations an economic mechanism (a) to set resource prices and (b) resolve when to scale resources depending on the users’ demand. This system has a strong emphasis on fairness, so no user hinders the execution of other users’ tasks by getting too many resources. Our simulator is based on the well-known GridSim software for grid simulation, which we expand to simulate infrastructure clouds. The results show how the proposed system can successfully adapt the amount of allocated resources to the demand, while at the same time ensuring that resources are fairly shared among users.

Field analysis of solar PV-based collective systems for rural electrification.

This article analyses the long-term performance of collective off-grid photovoltaic (PV) systems in rural areas. The use of collective PV systems for the electrification of small medium-size villages in developing countries has increased in the recent years. They are basically set up as stand-alone installations (diesel hybrid or pure PV) with no connection with other electrical grids. Their particular conditions (isolated) and usual installation places (far from commercial/industrial centers) require an autonomous and reliable technology. Different but related factors affect their performance and the energy supply; some of them are strictly technical but others depend on external issues like the solar energy resource and users’ energy and power consumption. The work presented is based on field operation of twelve collective PV installations supplying the electricity to off-grid villages located in the province of Jujuy, Argentina. Five of them have PV generators as unique power source while other seven include the support of diesel groups. Load demand evolution, energy productivity and fuel consumption are analyzed. Besides, energy generation strategies (PV/diesel) are also discussed.

Dealing with Semantic Heterogeneity Issues on the Web

The Semantic Web is an extension of the traditional Web in which meaning of information is well defined, thus allowing a better interaction between people and computers. To accomplish its goals, mechanisms are required to make explicit the semantics of Web resources, to be automatically processed by software agents (this semantics being described by means of online ontologies). Nevertheless, issues arise caused by the semantic heterogeneity that naturally happens on the Web, namely redundancy and ambiguity. For tackling these issues, we present an approach to discover and represent, in a non-redundant way, the intended meaning of words in Web applications, while taking into account the (often unstructured) context in which they appear. To that end, we have developed novel ontology matching, clustering, and disambiguation techniques. Our work is intended to help bridge the gap between syntax and semantics for the Semantic Web construction

Identifying Moderator Variables Through Requirements Elicitation Experiments Limitations

Interviews are the most widely used elicitation technique in Requirements Engineering (RE). Despite its importance, research in interviews is quite limited, in particular from an experimental perspective. We have performed a series of experiments exploring the relative effectiveness of structured and unstructured interviews. This line of research has been active in Information Systems in the past years, so that our experiments can be aggregated together with existing ones to obtain guidelines for practice. Experimental aggregation is a demanding task. It requires not only a large number of experiments, but also considering the influence of the existing moderators. However, in the current state of the practice in RE, those moderators are unknown. We believe that analyzing the threats to validity in interviewing experiments may give insight about how to improve further replications and the corresponding aggregations. It is likely that this strategy may be applied in other Software Engineering areas as well.