Mixing Snapshots and Fast Time Integration of PDEs

A local proper orthogonal decomposition (POD) plus Galerkin projection method was recently developed to accelerate time dependent numerical solvers of PDEs. This method is based on the combined use of a numerical code (NC) and a Galerkin sys- tem (GS) in a sequence of interspersed time intervals, INC and IGS, respectively. POD is performed on some sets of snapshots calculated by the numerical solver in the INC inter- vals. The governing equations are Galerkin projected onto the most energetic POD modes and the resulting GS is time integrated in the next IGS interval. The major computa- tional e®ort is associated with the snapshots calculation in the ¯rst INC interval, where the POD manifold needs to be completely constructed (it is only updated in subsequent INC intervals, which can thus be quite small). As the POD manifold depends only weakly on the particular values of the parameters of the problem, a suitable library can be con- structed adapting the snapshots calculated in other runs to drastically reduce the size of the ¯rst INC interval and thus the involved computational cost. The strategy is success- fully tested in (i) the one-dimensional complex Ginzburg-Landau equation, including the case in which it exhibits transient chaos, and (ii) the two-dimensional unsteady lid-driven cavity problem

Aerodynamic Optimization of High-Speed Trains Nose using a Genetic Algorithm and Artificial Neural Network

An aerodynamic optimization of the train aerodynamic characteristics in term of front wind action sensitivity is carried out in this paper. In particular, a genetic algorithm (GA) is used to perform a shape optimization study of a high-speed train nose. The nose is parametrically defined via Bézier Curves, including a wider range of geometries in the design space as possible optimal solutions. Using a GA, the main disadvantage to deal with is the large number of evaluations need before finding such optimal. Here it is proposed the use of metamodels to replace Navier-Stokes solver. Among all the posibilities, Rsponse Surface Models and Artificial Neural Networks (ANN) are considered. Best results of prediction and generalization are obtained with ANN and those are applied in GA code. The paper shows the feasibility of using GA in combination with ANN for this problem, and solutions achieved are included.

Independence in CLP Languages

Studying independence of goals has proven very useful in the context of logic programming. In particular, it has provided a formal basis for powerful automatic parallelization tools, since independence ensures that two goals may be evaluated in parallel while preserving correctness and eciency. We extend the concept of independence to constraint logic programs (CLP) and prove that it also ensures the correctness and eciency of the parallel evaluation of independent goals. Independence for CLP languages is more complex than for logic programming as search space preservation is necessary but no longer sucient for ensuring correctness and eciency. Two additional issues arise. The rst is that the cost of constraint solving may depend upon the order constraints are encountered. The second is the need to handle dynamic scheduling. We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow dierent optimizations, from parallelism to intelligent backtracking. Sucient conditions for independence which can be evaluated \a priori" at run-time are also proposed. Our study also yields new insights into independence in logic programming languages. In particular, we show that search space preservation is not only a sucient but also a necessary condition for ensuring correctness and eciency of parallel execution.

Independence in constraint logic programs

Studying independence of literals, variables, and substitutions has proven very useful in the context of logic programming (LP). Here we study independence in the broader context of constraint logic programming (CLP). We show that a naive extrapolation of the LP definitions of independence to CLP is unsatisfactory (in fact, wrong) for two reasons. First, because interaction between variables through constraints is more complex than in the case of logic programming. Second, in order to ensure the efUciency of several optimizations not only must independence of the search space be considered, but also an orthogonal issue - "independence of constraint solving." We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow different independence-related optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a-priori" at run-time are also proposed. Our results suggest that independence, provided a suitable definition is chosen, is even more useful in CLP than in LP.

Towards resource usage analysis of miniZinc models

We present a method for the static resource usage analysis of MiniZinc models. The analysis can infer upper bounds on the usage that a MiniZinc model will make of some resources such as the number of constraints of a given type (equality, disequality, global constraints, etc.), the number of variables (search variables or temporary variables), or the size of the expressions before calling the solver. These bounds are obtained from the models independently of the concrete input data (the instance data) and are in general functions of sizes of such data. In our approach, MiniZinc models are translated into Ciao programs which are then analysed by the CiaoPP system. CiaoPP includes a parametric analysis framework for resource usage in which the user can define resources and express the resource usage of library procedures (and certain program construets) by means of a language of assertions. We present the approach and report on a preliminary implementation, which shows the feasibility of the approach, and provides encouraging results.

Accelerating CFD via local POD plus Galerkin projections

Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

Coupled model of initiation and propagation of corrosion in reinforced concrete

Corrosion of reinforcing steel in concrete due to chloride ingress is one of the main causes of the deterioration of reinforced concrete structures. Structures most affected by such a corrosion are marine zone buildings and structures exposed to de-icing salts like highways and bridges. Such process is accompanied by an increase in volume of the corrosión products on the rebarsconcrete interface. Depending on the level of oxidation, iron can expand as much as six times its original volume. This increase in volume exerts tensile stresses in the surrounding concrete which result in cracking and spalling of the concrete cover if the concrete tensile strength is exceeded. The mechanism by which steel embedded in concrete corrodes in presence of chloride is the local breakdown of the passive layer formed in the highly alkaline condition of the concrete. It is assumed that corrosion initiates when a critical chloride content reaches the rebar surface. The mathematical formulation idealized the corrosion sequence as a two-stage process: an initiation stage, during which chloride ions penetrate to the reinforcing steel surface and depassivate it, and a propagation stage, in which active corrosion takes place until cracking of the concrete cover has occurred. The aim of this research is to develop computer tools to evaluate the duration of the service life of reinforced concrete structures, considering both the initiation and propagation periods. Such tools must offer a friendly interface to facilitate its use by the researchers even though their background is not in numerical simulation. For the evaluation of the initiation period different tools have been developed: Program TavProbabilidade: provides means to carry out a probability analysis of a chloride ingress model. Such a tool is necessary due to the lack of data and general uncertainties associated with the phenomenon of the chloride diffusion. It differs from the deterministic approach because it computes not just a chloride profile at a certain age, but a range of chloride profiles for each probability or occurrence. Program TavProbabilidade_Fiabilidade: carries out reliability analyses of the initiation period. It takes into account the critical value of the chloride concentration on the steel that causes breakdown of the passive layer and the beginning of the propagation stage. It differs from the deterministic analysis in that it does not predict if the corrosion is going to begin or not, but to quantifies the probability of corrosion initiation. Program TavDif_1D: was created to do a one dimension deterministic analysis of the chloride diffusion process by the finite element method (FEM) which numerically solves Fick’second Law. Despite of the different FEM solver already developed in one dimension, the decision to create a new code (TavDif_1D) was taken because of the need to have a solver with friendly interface for pre- and post-process according to the need of IETCC. An innovative tool was also developed with a systematic method devised to compare the ability of the different 1D models to predict the actual evolution of chloride ingress based on experimental measurements, and also to quantify the degree of agreement of the models with each others. For the evaluation of the entire service life of the structure: a computer program has been developed using finite elements method to do the coupling of both service life periods: initiation and propagation. The program for 2D (TavDif_2D) allows the complementary use of two external programs in a unique friendly interface: • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. This program (TavDif_2D) is responsible to decide in each time step when and where to start applying the boundary conditions of fracture mechanics module in function of the amount of chloride concentration and corrosion parameters (Icorr, etc). This program is also responsible to verify the presence and the degree of fracture in each element to send the Information of diffusion coefficient variation with the crack width. • GMSH - an finite element mesh generator and post-processing viewer • OOFEM – a finite element solver. The advantages of the FEM with the interface provided by the tool are: • the flexibility to input the data such as material property and boundary conditions as time dependent function. • the flexibility to predict the chloride concentration profile for different geometries. • the possibility to couple chloride diffusion (initiation stage) with chemical and mechanical behavior (propagation stage). The OOFEM code had to be modified to accept temperature, humidity and the time dependent values for the material properties, which is necessary to adequately describe the environmental variations. A 3-D simulation has been performed to simulate the behavior of the beam on both, action of the external load and the internal load caused by the corrosion products, using elements of imbedded fracture in order to plot the curve of the deflection of the central region of the beam versus the external load to compare with the experimental data.

The Ciao clp(FD) library. A modular CLP extension for Prolog

We present a new free library for Constraint Logic Programming over Finite Domains, included with the Ciao Prolog system. The library is entirely written in Prolog, leveraging on Ciao's module system and code transformation capabilities in order to achieve a highly modular design without compromising performance. We describe the interface, implementation, and design rationale of each modular component. The library meets several design goals: a high level of modularity, allowing the individual components to be replaced by different versions; highefficiency, being competitive with other TT> implementations; a glass-box approach, so the user can specify new constraints at different levels; and a Prolog implementation, in order to ease the integration with Ciao's code analysis components. The core is built upon two small libraries which implement integer ranges and closures. On top of that, a finite domain variable datatype is defined, taking care of constraint reexecution depending on range changes. These three libraries form what we call the TT> kernel of the library. This TT> kernel is used in turn to implement several higher-level finite domain constraints, specified using indexicals. Together with a labeling module this layer forms what we name the TT> solver. A final level integrates the CLP (J7©) paradigm with our TT> solver. This is achieved using attributed variables and a compiler from the CLP (J7©) language to the set of constraints provided by the solver. It should be noted that the user of the library is encouraged to work in any of those levels as seen convenient: from writing a new range module to enriching the set of TT> constraints by writing new indexicals.

Reduced order modeling of three dimensional external aerodynamic flows

A method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computational domain, including the boundary layer attached to the aircraft surface and the wake. Thus, the method is both robust and computationally efficient, which is checked considering the aerodynamic flow around a horizontal tail plane, in the transonic range 0.4?Mach number?0.8, ?3°?angle of attack?3°.

Computational Fluid Dynamics Expert System using Artificial Neural Networks

The design of a modern aircraft is based on three pillars: theoretical results, experimental test and computational simulations. As a results of this, Computational Fluid Dynamic (CFD) solvers are widely used in the aeronautical field. These solvers require the correct selection of many parameters in order to obtain successful results. Besides, the computational time spent in the simulation depends on the proper choice of these parameters. In this paper we create an expert system capable of making an accurate prediction of the number of iterations and time required for the convergence of a computational fluid dynamic (CFD) solver. Artificial neural network (ANN) has been used to design the expert system. It is shown that the developed expert system is capable of making an accurate prediction the number of iterations and time required for the convergence of a CFD solver.

SVis: A computational steering visualization environment for surface structure determination

The arrangement of atoms at the surface of a solid accounts for many of its properties: Hardness, chemical activity, corrosion, etc. are dictated by the precise surface structure. Hence, finding it, has a broad range of technical and industrial applications. The ability to solve this problem opens the possibility of designing by computer materials with properties tailored to specific applications. Since the search space grows exponentially with the number of atoms, its solution cannot be achieved for arbitrarily large structures. Presently, a trial and error procedure is used: an expert proposes an structure as a candidate solution and tries a local optimization procedure on it. The solution relaxes to the local minimum in the attractor basin corresponding to the initial point, that might be the one corresponding to the global minimum or not. This procedure is very time consuming and, for reasonably sized surfaces, can take many iterations and much effort from the expert. Here we report on a visualization environment designed to steer this process in an attempt to solve bigger structures and reduce the time needed. The idea is to use an immersive environment to interact with the computation. It has immediate feedback to assess the quality of the proposed structure in order to let the expert explore the space of candidate solutions. The visualization environment is also able to communicate with the de facto local solver used for this problem. The user is then able to send trial structures to the local minimizer and track its progress as they approach the minimum. This allows for simultaneous testing of candidate structures. The system has also proved very useful as an educational tool for the field.

Aerodynamic optimization of the ICE2 high-speed train nose using a genetic algorithm and metamodels

An aerodynamic optimization of the ICE 2 high-speed train nose in term of front wind action sensitivity is carried out in this paper. The nose is parametrically defined by Be?zier Curves, and a three-dimensional representation of the nose is obtained using thirty one design variables. This implies a more complete parametrization, allowing the representation of a real model. In order to perform this study a genetic algorithm (GA) is used. Using a GA involves a large number of evaluations before finding such optimal. Hence it is proposed the use of metamodels or surrogate models to replace Navier-Stokes solver and speed up the optimization process. Adaptive sampling is considered to optimize surrogate model fitting and minimize computational cost when dealing with a very large number of design parameters. The paper introduces the feasi- bility of using GA in combination with metamodels for real high-speed train geometry optimization.

Benchmarking of COBAYA3 pin-by-pin for VVER

This paper presents results of the benchmarking of COBAYA3 pin-by-pin for VVER-1000 obtained in the frame of the EU NURISP project. The 3D lattice solver in COBAYA3 uses transport corrected multi-group diffusion approximation with side-dependent interface discontinuity factors of GET or Selengut Black Box type. The objective of this study is to test the few-group calculation scheme when using structur ed and unstructured spatial meshes. Unstructured mesh is necessary to model the water gaps between the hexagonal assemblies. The benchmark problems include pin-by-pin calculations of 2D subsets of the core and comparison with APOLLO2 and TR IPOLI4 transport reference solutions. COBAYA3 solutions in 2, 4 and 8 energy groups have been tested. The results show excellent agreement with the reference on es when using side-dependent interface discontinuity factors.

Finite Element Analysis Model of a Contactless Transformer for Battery Chargers in Electric Vehicles

A contactless transformer model is proposed in this paper using Finite Element Analysis (FEA). This model can be used to simulate Inductive Coupling Power Transfer (ICPT) systems with good accuracy of the transformer and reduce the fabrication time of these systems. The model not only takes into account the geometry of the windings but also the frequency effects in them. As the transformer does not have a magnetic core, it is complicated to model because the flux is expanded in the area around the windings. In order to obtain a very accurate model, it is necessary to use a 2D/3D field solver.

CFD modelling of wind farms in complex terrain

Modelling of entire wind farms in flat and complex terrain using a full 3D Navier–Stokes solver for incompressible flow is presented in this paper. Numerical integration of the governing equations is performed using an implicit pressure correction scheme, where the wind turbines (W/Ts) are modelled as momentum absorbers through their thrust coefficient. The k–ω turbulence model, suitably modified for atmospheric flows, is employed for closure. A correction is introduced to account for the underestimation of the near wake deficit, in which the turbulence time scale is bounded using a general “realizability” constraint for the fluctuating velocities. The second modelling issue that is discussed in this paper is related to the determination of the reference wind speed for the thrust calculation of the machines. Dealing with large wind farms and wind farms in complex terrain, determining the reference wind speed is not obvious when a W/T operates in the wake of another WT and/or in complex terrain. Two alternatives are compared: using the wind speed value at hub height one diameter upstream of the W/T and adopting an induction factor-based concept to overcome the utilization of a wind speed at a certain distance upwind of the rotor. Application is made in two wind farms, a five-machine one located in flat terrain and a 43-machine one located in complex terrain.