Parallel Algorithms for FE-BE Coupling

When non linear physical systems of infinite extent are modelled, such as tunnels and perforations, it is necessary to simulate suitably the solution in the infinite as well as the non linearity. The finite element method (FEM) is a well known procedure for simulating the non linear behavior. However, the treatment of the infinite field with domain truncations is often questionable. On the other hand, the boundary element method (BEM) is suitable to simulate the infinite behavior without truncations. Because of this, by the combination of both methods, suitable use of the advantages of each one may be obtained. Several possibilities of FEM-BEM coupling and their performance in some practical cases are discussed in this paper. Parallelizable coupling algorithms based on domain decomposition are developed and compared with the most traditional coupling methods.

Pulsatile flow in coronary bifurcations for different stenting techniques

The objective of this work is to analyze the local hem odynamic changes caused in a coronary bifurcation by three different stenting techniques: simple stenting of the main vessel, simple stenting of the main vessel with kissing balloon in the side branch and culotte. To carry out this study an idealized geometry of a coronary bifurcation is used, and two bifurcation angles, 45º and 90º, are chosen as representative of the wide variety of re al configurations. In order to quantify the influence of the stenting technique on the local blood flow, both numeri- cal simulations and experimental measurements are performed. First, steady simulations are carried out with the commercial code ANSYS-Fluent, and then, experimental measurements with PIV (Particle Image Velocimetry) obtained in the laboratory are used to validate the numerical simulation. The steady computational simulations show a good overall agreement with the experimental data. Second, pulsatile flow is considered to take into account the tran- sient effects. The time averaged wall shear stress, scillatory shear index and pressure drop obtained numerically are used to compare the behavior of the stenting techniques.

Simulación en tiempo real de vehículos industriales con modelos multicuerpo de gran complejidad

El objetivo de esta Tesis ha sido la consecución de simulaciones en tiempo real de vehículos industriales modelizados como sistemas multicuerpo complejos formados por sólidos rígidos. Para el desarrollo de un programa de simulación deben considerarse cuatro aspectos fundamentales: la modelización del sistema multicuerpo (tipos de coordenadas, pares ideales o impuestos mediante fuerzas), la formulación a utilizar para plantear las ecuaciones diferenciales del movimiento (coordenadas dependientes o independientes, métodos globales o topológicos, forma de imponer las ecuaciones de restricción), el método de integración numérica para resolver estas ecuaciones en el tiempo (integradores explícitos o implícitos) y finalmente los detalles de la implementación realizada (lenguaje de programación, librerías matemáticas, técnicas de paralelización). Estas cuatro etapas están interrelacionadas entre sí y todas han formado parte de este trabajo. Desde la generación de modelos de una furgoneta y de camión con semirremolque, el uso de tres formulaciones dinámicas diferentes, la integración de las ecuaciones diferenciales del movimiento mediante métodos explícitos e implícitos, hasta el uso de funciones BLAS, de técnicas de matrices sparse y la introducción de paralelización para utilizar los distintos núcleos del procesador. El trabajo presentado en esta Tesis ha sido organizado en 8 capítulos, dedicándose el primero de ellos a la Introducción. En el Capítulo 2 se presentan dos formulaciones semirrecursivas diferentes, de las cuales la primera está basada en una doble transformación de velocidades, obteniéndose las ecuaciones diferenciales del movimiento en función de las aceleraciones relativas independientes. La integración numérica de estas ecuaciones se ha realizado con el método de Runge-Kutta explícito de cuarto orden. La segunda formulación está basada en coordenadas relativas dependientes, imponiendo las restricciones por medio de penalizadores en posición y corrigiendo las velocidades y aceleraciones mediante métodos de proyección. En este segundo caso la integración de las ecuaciones del movimiento se ha llevado a cabo mediante el integrador implícito HHT (Hilber, Hughes and Taylor), perteneciente a la familia de integradores estructurales de Newmark. En el Capítulo 3 se introduce la tercera formulación utilizada en esta Tesis. En este caso las uniones entre los sólidos del sistema se ha realizado mediante uniones flexibles, lo que obliga a imponer los pares por medio de fuerzas. Este tipo de uniones impide trabajar con coordenadas relativas, por lo que la posición del sistema y el planteamiento de las ecuaciones del movimiento se ha realizado utilizando coordenadas Cartesianas y parámetros de Euler. En esta formulación global se introducen las restricciones mediante fuerzas (con un planteamiento similar al de los penalizadores) y la estabilización del proceso de integración numérica se realiza también mediante proyecciones de velocidades y aceleraciones. En el Capítulo 4 se presenta una revisión de las principales herramientas y estrategias utilizadas para aumentar la eficiencia de las implementaciones de los distintos algoritmos. En primer lugar se incluye una serie de consideraciones básicas para aumentar la eficiencia numérica de las implementaciones. A continuación se mencionan las principales características de los analizadores de códigos utilizados y también las librerías matemáticas utilizadas para resolver los problemas de álgebra lineal tanto con matrices densas como sparse. Por último se desarrolla con un cierto detalle el tema de la paralelización en los actuales procesadores de varios núcleos, describiendo para ello el patrón empleado y las características más importantes de las dos herramientas propuestas, OpenMP y las TBB de Intel. Hay que señalar que las características de los sistemas multicuerpo problemas de pequeño tamaño, frecuente uso de la recursividad, y repetición intensiva en el tiempo de los cálculos con fuerte dependencia de los resultados anteriores dificultan extraordinariamente el uso de técnicas de paralelización frente a otras áreas de la mecánica computacional, tales como por ejemplo el cálculo por elementos finitos. Basándose en los conceptos mencionados en el Capítulo 4, el Capítulo 5 está dividido en tres secciones, una para cada formulación propuesta en esta Tesis. En cada una de estas secciones se describen los detalles de cómo se han realizado las distintas implementaciones propuestas para cada algoritmo y qué herramientas se han utilizado para ello. En la primera sección se muestra el uso de librerías numéricas para matrices densas y sparse en la formulación topológica semirrecursiva basada en la doble transformación de velocidades. En la segunda se describe la utilización de paralelización mediante OpenMP y TBB en la formulación semirrecursiva con penalizadores y proyecciones. Por último, se describe el uso de técnicas de matrices sparse y paralelización en la formulación global con uniones flexibles y parámetros de Euler. El Capítulo 6 describe los resultados alcanzados mediante las formulaciones e implementaciones descritas previamente. Este capítulo comienza con una descripción de la modelización y topología de los dos vehículos estudiados. El primer modelo es un vehículo de dos ejes del tipo chasis-cabina o furgoneta, perteneciente a la gama de vehículos de carga medianos. El segundo es un vehículo de cinco ejes que responde al modelo de un camión o cabina con semirremolque, perteneciente a la categoría de vehículos industriales pesados. En este capítulo además se realiza un estudio comparativo entre las simulaciones de estos vehículos con cada una de las formulaciones utilizadas y se presentan de modo cuantitativo los efectos de las mejoras alcanzadas con las distintas estrategias propuestas en esta Tesis. Con objeto de extraer conclusiones más fácilmente y para evaluar de un modo más objetivo las mejoras introducidas en la Tesis, todos los resultados de este capítulo se han obtenido con el mismo computador, que era el top de la gama Intel Xeon en 2007, pero que hoy día está ya algo obsoleto. Por último los Capítulos 7 y 8 están dedicados a las conclusiones finales y las futuras líneas de investigación que pueden derivar del trabajo realizado en esta Tesis. Los objetivos de realizar simulaciones en tiempo real de vehículos industriales de gran complejidad han sido alcanzados con varias de las formulaciones e implementaciones desarrolladas. ABSTRACT The objective of this Dissertation has been the achievement of real time simulations of industrial vehicles modeled as complex multibody systems made up by rigid bodies. For the development of a simulation program, four main aspects must be considered: the modeling of the multibody system (types of coordinates, ideal joints or imposed by means of forces), the formulation to be used to set the differential equations of motion (dependent or independent coordinates, global or topological methods, ways to impose constraints equations), the method of numerical integration to solve these equations in time (explicit or implicit integrators) and the details of the implementation carried out (programming language, mathematical libraries, parallelization techniques). These four stages are interrelated and all of them are part of this work. They involve the generation of models for a van and a semitrailer truck, the use of three different dynamic formulations, the integration of differential equations of motion through explicit and implicit methods, the use of BLAS functions and sparse matrix techniques, and the introduction of parallelization to use the different processor cores. The work presented in this Dissertation has been structured in eight chapters, the first of them being the Introduction. In Chapter 2, two different semi-recursive formulations are shown, of which the first one is based on a double velocity transformation, thus getting the differential equations of motion as a function of the independent relative accelerations. The numerical integration of these equations has been made with the Runge-Kutta explicit method of fourth order. The second formulation is based on dependent relative coordinates, imposing the constraints by means of position penalty coefficients and correcting the velocities and accelerations by projection methods. In this second case, the integration of the motion equations has been carried out by means of the HHT implicit integrator (Hilber, Hughes and Taylor), which belongs to the Newmark structural integrators family. In Chapter 3, the third formulation used in this Dissertation is presented. In this case, the joints between the bodies of the system have been considered as flexible joints, with forces used to impose the joint conditions. This kind of union hinders to work with relative coordinates, so the position of the system bodies and the setting of the equations of motion have been carried out using Cartesian coordinates and Euler parameters. In this global formulation, constraints are introduced through forces (with a similar approach to the penalty coefficients) are presented. The stabilization of the numerical integration is carried out also by velocity and accelerations projections. In Chapter 4, a revision of the main computer tools and strategies used to increase the efficiency of the implementations of the algorithms is presented. First of all, some basic considerations to increase the numerical efficiency of the implementations are included. Then the main characteristics of the code’ analyzers used and also the mathematical libraries used to solve linear algebra problems (both with dense and sparse matrices) are mentioned. Finally, the topic of parallelization in current multicore processors is developed thoroughly. For that, the pattern used and the most important characteristics of the tools proposed, OpenMP and Intel TBB, are described. It needs to be highlighted that the characteristics of multibody systems small size problems, frequent recursion use and intensive repetition along the time of the calculation with high dependencies of the previous results complicate extraordinarily the use of parallelization techniques against other computational mechanics areas, as the finite elements computation. Based on the concepts mentioned in Chapter 4, Chapter 5 is divided into three sections, one for each formulation proposed in this Dissertation. In each one of these sections, the details of how these different proposed implementations have been made for each algorithm and which tools have been used are described. In the first section, it is shown the use of numerical libraries for dense and sparse matrices in the semirecursive topological formulation based in the double velocity transformation. In the second one, the use of parallelization by means OpenMP and TBB is depicted in the semi-recursive formulation with penalization and projections. Lastly, the use of sparse matrices and parallelization techniques is described in the global formulation with flexible joints and Euler parameters. Chapter 6 depicts the achieved results through the formulations and implementations previously described. This chapter starts with a description of the modeling and topology of the two vehicles studied. The first model is a two-axle chassis-cabin or van like vehicle, which belongs to the range of medium charge vehicles. The second one is a five-axle vehicle belonging to the truck or cabin semi-trailer model, belonging to the heavy industrial vehicles category. In this chapter, a comparative study is done between the simulations of these vehicles with each one of the formulations used and the improvements achieved are presented in a quantitative way with the different strategies proposed in this Dissertation. With the aim of deducing the conclusions more easily and to evaluate in a more objective way the improvements introduced in the Dissertation, all the results of this chapter have been obtained with the same computer, which was the top one among the Intel Xeon range in 2007, but which is rather obsolete today. Finally, Chapters 7 and 8 are dedicated to the final conclusions and the future research projects that can be derived from the work presented in this Dissertation. The objectives of doing real time simulations in high complex industrial vehicles have been achieved with the formulations and implementations developed.

Numerical characterization of particle dispersion in the turbulent recirculation zones of sudden expansion pipe flows

The dispersion of solid particles in the turbulent recirculation zones of sudden expansion pipes can be characterized by different Stokes numbers and mean drift parameter and its study is important because this kind of flows appears in many technological applications.

Bifurcation diagrams for polymer blends with diffuse interfaces in confined and adaptive geometries

Dynamics of binary mixtures such as polymer blends, and fluids near the critical point, is described by the model-H, which couples momentum transport and diffusion of the components [1]. We present an extended version of the model-H that allows to study the combined effect of phase separation in a polymer blend and surface structuring of the film itself [2]. We apply it to analyze the stability of vertically stratified base states on extended films of polymer blends and show that convective transport leads to new mechanisms of instability as compared to the simpler diffusive case described by the Cahn- Hilliard model [3, 4]. We carry out this analysis for realistic parameters of polymer blends used in experimental setups such as PS/PVME. However, geometrically more complicated states involving lateral structuring, strong deflections of the free surface, oblique diffuse interfaces, checkerboard modes, or droplets of a component above of the other are possible at critical composition solving the Cahn Hilliard equation in the static limit for rectangular domains [5, 6] or with deformable free surfaces [6]. We extend these results for off-critical compositions, since balanced overall composition in experiments are unusual. In particular, we study steady nonlinear solutions of the Cahn-Hilliard equation for bidimensional layers with fixed geometry and deformable free surface. Furthermore we distinguished the cases with and without energetic bias at the free surface. We present bifurcation diagrams for off-critical films of polymer blends with free surfaces, showing their free energy, and the L2-norms of surface deflection and the concentration field, as a function of lateral domain size and mean composition. Simultaneously, we look at spatial dependent profiles of the height and concentration. To treat the problem of films with arbitrary surface deflections our calculations are based on minimizing the free energy functional at given composition and geometric constraints using a variational approach based on the Cahn-Hilliard equation. The problem is solved numerically using the finite element method (FEM).

A gradient-enhanced continuum damage model with application to fibre-reinforced tissues at finite strains

A non-local gradient-based damage formulation within a geometrically non-linear set- ting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy function which is additively composed by an isotropic neo-Hookean matrix and by an anisotropic fibre-reinforced material based on the model proposed by T. Gasser, R. Ogden, and G. Holzapfel.

A simple torsion-free nonlinear beam element for multibody dynamics

We propose in this work a very simple torsion-free beam element capable of capturing geometrical nonlinearities. The simple formulation is objective and unconditionally con- vergent for geometrically nonlinear models with large displacements, in the traditional sense that guarantees more precise numerical solutions for finer discretizations. The formulation does not employ rotational degrees of freedom, can be applied to two and three-dimensional problems, and it is computationally very efficient.

Simulating the remote handling of the blanket segments in DEMO fusion reactor with thermo-mechanical meshfree multibody dynamics

The present study shows a first approach to the simulation of the remote handling oper- ation which takes into account the thermal and flexible behavior of the blanket segments and its implications on the remote handling equipment, in order to validate and improve its design.

Energy-consistent time integration for nonlinear viscoelasticity

This work is concerned with the numerical solution of the evolution equations of thermomechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided

Surrogate-based optimization of the nose shape of a train subjected to crosswind

Optimización multi-objetivo frente a varias direcciones del viento incidente del testero de un tren de alta velocidad

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differenti- ated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specif- ically, the direct relations between brain and spinal cord tis- sue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic- based damage criteria, simulated function-based damage cri- teria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus provid- ing a link between mechanical trauma and subsequent func- tional deficits.

A computational model coupling mechanics and electrophysiology in spinal cord injury

Traumatic brain injury and spinal cord injury have recently been put under the spotlight as major causes of death and disability in the developed world. Despite the important ongoing experimental and modeling campaigns aimed at understanding the mechanics of tissue and cell damage typically observed in such events, the differentiated roles of strain, stress and their corresponding loading rates on the damage level itself remain unclear. More specifically, the direct relations between brain and spinal cord tissue or cell damage, and electrophysiological functions are still to be unraveled. Whereas mechanical modeling efforts are focusing mainly on stress distribution and mechanistic-based damage criteria, simulated function-based damage criteria are still missing. Here, we propose a new multiscale model of myelinated axon associating electrophysiological impairment to structural damage as a function of strain and strain rate. This multiscale approach provides a new framework for damage evaluation directly relating neuron mechanics and electrophysiological properties, thus providing a link between mechanical trauma and subsequent functional deficits

Computational model for local damage assesment of structures

In the last years many studies have been developed to analyze the seismic behavior throug the damage concept. In fact, the evaluation of the structural damage is important in order to quantify the safety of new and existing structures and, also, to establish a framework for seismic retrofitting decision making of structures. Most proposed models are based on a post-earthquake evaluation in such a way they uncouple the computation of the structural response from that of damage. However, there are other models which include explicity the existing coupling between the degradation and the structural mechanical beaviour. Those models are closer to the physical reality and its formulation is based on the principles of Continuum Damage Mechanics. In the present work, a coupled model is formulated using a simplified application of the Continuum Damage Mechanics to the analysis of frames and allows its representation in standard finite element programs. This work is part of the activities developed by the Structural Mechanics Department (UPM) within ICONS (European Research Project on Innovative Seismic Design Concepts for New and Existing Structures).

Statistical mechanics approaches to granular media: between micromechanics and macromechanics

The mechanical behavior of granular materials has been traditionally approached through two theoretical and computational frameworks: macromechanics and micromechanics. Macromechanics focuses on continuum based models. In consequence it is assumed that the matter in the granular material is homogeneous and continuously distributed over its volume so that the smallest element cut from the body possesses the same physical properties as the body. In particular, it has some equivalent mechanical properties, represented by complex and non-linear constitutive relationships. Engineering problems are usually solved using computational methods such as FEM or FDM. On the other hand, micromechanics is the analysis of heterogeneous materials on the level of their individual constituents. In granular materials, if the properties of particles are known, a micromechanical approach can lead to a predictive response of the whole heterogeneous material. Two classes of numerical techniques can be differentiated: computational micromechanics, which consists on applying continuum mechanics on each of the phases of a representative volume element and then solving numerically the equations, and atomistic methods (DEM), which consist on applying rigid body dynamics together with interaction potentials to the particles. Statistical mechanics approaches arise between micro and macromechanics. It tries to state which the expected macroscopic properties of a granular system are, by starting from a micromechanical analysis of the features of the particles and the interactions. The main objective of this paper is to introduce this approach.

Linear global instability of non-orthogonal incompressible swept attachment-line boundary layer flow

Instability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.