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This monograph develops a numerical tool (the Virtual Wind Tunnel, VWT) for the reso-lution of problems involving fluid flow around structures. Due to the limitations that traditional methods may have in this context, the VWT is based on the use of fixed mesh technologies (CutFEM-type) combined with an implicit representation of the embedded bodies. One of the main contributions of the monograph is the use of such fixed mesh methods to solve lightweight thin-walled structures problems. Hence, two embedded formulations capable of representing the flow around bodies with and without internal volume are proposed. The first one results in a simpler implementation and lower computational effort but can only represent a slip behavior of the wall. The second one gets rid of such limitation by including a Nitsche imposition of the Navier-slip condition, thus allowing modelling any wall behavior as a wall law would do. The applicability range of the VWT includes the fluid–structure i nteraction problem (FSI). To that purpose an improvement for the boundary condition imposition of the FM-ALE algorithm mesh motion problem is also proposed. Moreover, the implementation, which has been conceived to be easily extended to any other coupled problem, is also treated. The validation of the technologies within the VWT includes multiple theoretical test cases as well as feasible industrial applications. Among these, the FSI analysis of a 4-point tent during a strong wind episode deserves to be highlighted as it showcases the achievement of the initial objective of the monograph.

This paper presents a finite element solver for the simulation of steady non-Newtonian flow problems, using a regularized Bingham model, with adaptive mesh refinement capabilities. The solver is based on a stabilized formulation derived from the variational multiscale framework. This choice allows the introduction of an a posteriori error indicator based on the small scale part of the solution, which is used to drive a mesh refinement procedure based on element subdivision. This approach applied to the solution of a series of benchmark examples, which allow us to validate the formulation and assess its capabilities to model 2D and 3D non-Newtonian flows.

En los últimos años el estudio del comportamiento de los materiales a nivel microscópico ha aumentado significativamente en términos de diseño de materiales de altas prestaciones. A pesar de los recientes avances de ordenadores de elevado rendimiento, la aplicación de métodos numéricos multiescala para simular grandes estructuras aún requiere costes computacionales prohibitivos. Éste trabajo presenta un procedimiento capaz de predecir la respuesta mecánica no-lineal de los materiales compuestos con el fin de reducir el coste computacional necesario para el análisis numérico de estructuras complejas. La solución de la estructura macroscópica a través del método multiescala de primer orden (FE2) se sustituirá por un modelo discreto obtenido de un análisis del comportamiento de un Volumen Representativo Elemental (RVE) del material. A través de las definiciones de un parámetro de daño equivalente (deq), función del esfuerzo global en la microescala, se realizarán una serie de ensayos virtuales en control de deformación, almacenando el estado de tensión-deformación alcanzado por ciertos niveles de deqen una base de datos. Analizando la evolución de la fractura en los materiales compuestos se puede observar como el régimen no-lineal se alcanza solo en algunos elementos de la estructura. Es por ello que se plantea un procedimiento, el Discrete Multiscale Threshold Surface (DMTS), en el que el análisis del RVE sirve para obtener la superficie en la que empieza el daño (deq>0). Esta ley permite saber si para un determinado estado tenso-deformacional el material ha dañado, sin necesidad de resolver el micro-modelo. Una vez iniciado el daño, se propone de generar de forma adaptiva un RVE con el que obtener el comportamiento dañado del material. Luego, el método FE2 se utilizará solo en los puntos de integración que hayan dañado. Este trabajo demuestra que el método FE2 puede ser remplazado por un Modelo Discreto Multiescala, representativo del material compuesto, obteniendo mejoras computacionales significativas.

Several comparisons between experiments and computational models are presented in the following pages. The objective is to verify the ability of Particle Finite Elements Methods (PFEM) to reproduce hydraulic phenomena involving large deformation of the fluid domain.

In recent years the technology on embankments dams has developed sensibly due to the advances in soil mechanic, and in all related sciences. Nevertheless their vulnerability to overtopping is still an open theme of discussion. Such an extreme phenomenon can lead to catastrophic consequences with loss of stability and failure of the entire structure. In spite of that, the consequences of an overtopping are still difficult to analyze and to prevent optimally. The possibility to define a numerical instrument to provide support for analyzing the failure of a dam is an important step ahead fororganizing the intervention measures and for optimizing the economic plan. This is the principal reason why the Spanish ministry of Science and Innovation is funding the XPRES project, between the Polytechnic University of Madrid (UPM), the Centre for Hydrographical Studies of CEDEX and the International Centre for Numerical Methods in Engineering (CIMNE). The characterization of the failure process is dealt with by combining new numerical models, developed by CIMNE, with experimental tests on physical models of different sizes and scales carried out by UPM and CEDEX. In the present paper the work carried out by CIMNE is presented. The numerical model is based on combination of Lagrangian Particle Finite Element Method (PFEM) and Eulerian level set techniques in order to optimize the coupling between the dynamic effect of water inside and outside the dam, with the structural deformation and collapse induced on the down stream shoulder. The breaching formation and the consequent beginning of the failure are analyzed with particular interest. The specific features of the adopted method make it appropriate to treat the rockfill material and its large deformations and shape changes. A variable viscosity law and an energetic erosion criterion are used to take into account mass sliding and erosion acting in combined or alternative way

We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations are solved, as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.

The Navier–Stokes equations written in Laplace form are often the starting point of many numerical methods for the simulation of viscous flows. Imposing the natural boundary conditions of the Laplace form or neglecting the viscous contributions on free surfaces are traditionally considered reasonable and harmless assumptions. With these boundary conditions any formulation derived from integral methods (like finite elements or finite volumes) recovers the pure Laplacian aspect of the strong form of the equations. This approach has also the advantage of being convenient in terms of computational effort and, as a consequence, it is used extensively. However, we have recently discovered that these resulting Laplacian formulations violate a basic axiom of continuum mechanics: the principle of objectivity. In the present article we give an accurate account about these topics. We also show that unexpected differences may sometimes arise between Laplace discretizations and divergence discretizations.&nbsp

The solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice‐Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge‐based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection‐diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU‐accelerated OpenCL code consistently outperforms the OpenMP version.

In this work we study the numerical simulation of particle-laden fluids, with an emphasis on Newtonian fluids and spherical, rigid particles. Our general strategy consists in using the discrete element method (DEM) to model the particles and the finite element method (FEM) to discretize the continuous phase, such that the fluid is not resolved around the particles, but rather averaged over them. The effect of the particles on the fluid is taken into account by averaging (filtering) their individual volumes and particle-fluid interaction forces. In the first part of the work we study the Maxey–Riley equation of motion for an isolated particle in a nonuniform flow; the equation used to calculate the trajectory of the DEM particles. In particular, we perform a detailed theoretical study of its range of applicability, reviewing the initial effects of breaking its fundamental hypotheses, such as small Reynolds number, sphericity of the particle, isolation etc. The output of this study is a set of tables containing order-of-magnitude inequalities to assess the validity of the method in practice. The second part of the work deals with the numerical discretization of the MRE and, in particular, the study of different techniques for the treatment of the history-dependent term, which is difficult to calculate efficiently. We provide improvements on an existing method, proposed by van Hinsberg et al. (2011), and demonstrate its accuracy and efficiency in a sequence of tests of increasing complexity. In the final part of the work we give three application examples representative of different regimes that may be encountered in the industry, demonstrating the versatility of our numerical tool. For that, we describe necessary generalizations to the MRE to cover problems outside its range of applicability. Furthermore, we give a detailed account of the stabilized FEM algorithm used to discretize the fluid phase and compare several derivative recovery tools necessary to calculate some of the interphase coupling terms. Finally, we generalize the algorithm to include the backward-coupling effects according to the theory of multicomponent continua, allowing the code to deal with arbitrarily dense flow regimes.

We propose a technique for improving mass‐conservation features of fractional step schemes applied to incompressible flows. The method is illustrated by using a Lagrangian fluid formulation, where the mass loss effects are particularly apparent. However, the methodology is general and could be used for fixed grid approaches. The idea consists in reflecting the incompressibility condition already in the intermediate velocity. This is achieved by predicting the end‐of‐step pressure and using this prediction in the fractional momentum equation. The resulting intermediate velocity field is thus much closer to the final incompressible one than that of the standard fractional step scheme. In turn, the predicted pressure can be used as the boundary condition necessary for the solution of the pressure Poisson equation in case a continuous Laplacian matrix is employed. Using this approximation of the end‐of‐step incompressible pressure as the essential boundary condition considerably improves the conservation of mass, specially for the free surface flows of fluids with low viscosity. The pressure prediction does not require the resolution of any additional equations system. The efficiency of the method is shown in two examples. The first one shows the performance of the method with respect to mass conservation. The second one tests the method in a challenging fluid–structure interaction benchmark, which can be naturally resolved by using the presented approach.

The computational challenge in dealing with membrane systems is closely connected to the lack of bending stiffness that constitutes the main feature of this category of structures. This manifests numerically in badly conditioned or singular systems requiring the use of stabilized solution procedures, in our case of a ‘pseudo‐dynamic’ approach. The absence of the flexural stiffness makes the membrane very prone to local instabilities which manifest physically in the formation of little ‘waves’ in ‘compressed’ areas. Current work presents an efficient, sub‐iteration free ‘explicit’, penalty material based, wrinkling simulation procedure suitable for the solution of ‘static’ problems. The procedure is stabilized by taking full advantage of the pseudo‐dynamic solution strategy, which allows to retain the elemental quadratic convergence properties inside the single solution step. Results are validated by comparison with published results and by setting up ‘numerical experiments’ based on the solution of test cases using dense meshes. Copyright © 2005 John Wiley & Sons, Ltd.&nbsp

Rockfill dams are nowadays often preferred over concrete dams because of their economic advantages, their flexible and thank to the great advance achieved in geosciences and geomechanics. Unfortunately their behavior in case of overtopping is still an open issue. In fact very little is known on this phenomenon that in most cases leads to the complete finite failure o the structure with catastrophic consequences in term of loss of lives and economic damage. The principal aim of the present work is the development of a computational method to simulate the overtopping and the beginning of failure of the downstream shoulder of a rockfill dam. The whole phenomenon is treated in a continuous framework. The fluid free surface problem outside and inside the rockfill slop e is treated using a unique Eulerian fixed mesh formulation. A level set technique is employed to track the evolution of the free surface. The traditional Navier-Stokes equations are modified in order to automatically detect the presence of the porous media. The non-linear seepage is evaluated using a quadratic form of the resistance law for which the Ergun's coefficients have been chosen. &nbsp

In this work, a new modal reanalysis algorithm based on AMLS method is proposed for local, nontop ological,high rank modifications. Instead of using some perturbation technique[44, 85] or using the Kirsch Combined method[223, 226], the proposed reanalysis procedure uses AMLS method to perform the reanalysisexp lo itin g the concept of substructure. The modification affects a particular path on the hierarchical partitiontree, which traces back from the modified nodes to the root node. In our proposed modal reanalysis algorithmonly the modified substructures and affected substructures due to the propagation need to be recalculated. This algorithm can significantly improve the efficiency compared to the full recalculation. Some of the advantages are: 1. Larger substructure size increases moderately the accurate of the AMLS method. For medium substructure size, the efficiency of AMLS method can be improved using a sparse linear solver and sparse eigen solver. 2. If the modified substructures are recalculated using exact method, the reanalysis does not affect the precision of the final results by AMLS method. The eigen-values computed are accurate as the precision of AMLS method is. 3. The amplitude of modification is not limited to small modification change, as being required by approximate method. 4. It is only required to identify the corresponding modified and affected sub-structures for performing the recalculation and save the data of the non-modified sub-structures. In the worst case, the computational cost is no more than the fresh AMLS-solution. 5. It is more suitable for large-scale eigen value problem with local high-rank modifications. &nbsp

We propose a simple technique for improving computationally the efficiency of monolithic velocity–pressure solvers for incompressible flow problems. The idea consists in solving the discrete nonlinear system of governing equations in two steps: introducing ‘artificial’ compressibility first and afterwards correcting the solution by solving the original incompressible system. The speed‐up is obtained because of a better conditioning of the modified discrete system solved at the prediction step. The formulation can be easily implemented into existing monolithic codes requiring minor modification only. The paper concludes with two examples validating the formulation and facilitating the estimation of the obtained speed‐up. For the tests chosen, an average speed‐up is approximately double, suggesting that the method is a feasible approach for incompressible flows' simulation.&nbsp

We present an efficient technique for the solution of free surface flow problems using level set and a parallel edge‐based finite element method. An unstructured semi‐explicit solution scheme is proposed. A custom data structure, obtained by blending node‐based and edge‐based approaches is presented so to allow a good parallel performance. In addition to standard velocity extrapolation (for the convection of the level set function), an explicit extrapolation of the pressure field is performed in order to impose both the pressure boundary condition and the volume conservation. The latter is also improved with a modification of the divergence free constrain. The method is shown to allow an efficient solution of both simple benchmark cases and complex industrial examples

Las conferencias presentadas durante la Jornada Técnica sobre Avances en investigación aplicada en seguridad hidráulica de presas organizada por el Centro de Estudios Hidrográficos del CEDEX y la Universidad Politécnica de Madrid el mes de junio de 2013 versan sobre la mejora de la seguridad hidráulica de las presas, una materia de especial importancia en nuestro país (habida cuenta del elevado número de infraestructuras de regulación en servicio y de su antigüedad media) y constituye una tarea en la que tanto el CEDEX como la Universidad Politécnica de Madrid han trabajado activamente en los últimos años. El Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE) es un centro de investigación dependiente del Gobierno de Cataluña y de la Universidad Politécnica de Cataluña creado en 1987. Su principal actividad es el desarrollo y aplicación de métodos numéricos innovadores para resolver problemas prácticos en diversos campos de la ingeniería, y se desarrolla fundamentalmente en el marco de proyectos de investigación nacionales e internacionales. En los últimos años el centro ha participado en diversos proyectos relacionados con la seguridad de presas, fundamentalmente hidráulica, pero también estructural, en cooperación con diversas empresas y organismos públicos de investigación como el CEDEX y la UPM. La presente comunicación describe brevemente los objetivos principales de los mencionados proyectos, haciendo hincapié en cómo la modelación numérica ha contribuido a alcanzarlos.

In this paper, we propose a computational algorithm for the solution of thermally coupled flows in subsonic regime. The formulation is based upon the compressible Navier–Stokes equations, written in nonconservation form. An efficient modular implementation is obtained by solving the energy equation separately and then using the computed temperature as a known value in the momentum-continuity system. If an explicit single-step time integration scheme for the energy equation is used, the decoupling results to be natural. Integration of the momentum-continuity system is carried out using a semi-explicit method, combining Runge–Kutta and Backward Euler schemes for the momentum and continuity equations, respectively. Implicit treatment of pressure leads to favorable time step estimates even in the low Mach number (Ma ≪ 1) regimes. The numerical dissipation introduced by the Backward Euler scheme ensures absence of the spurious high frequencies in the numerical solution. The key point of the method is the assumption of linear variation of the temperature within a time step. Combined with a fractional splitting of the momentum-continuity system, it allows to solve the continuity only once per time step. Omitting the necessity of solving for the pressure at every intermediate step of the Runge–Kutta scheme minimizes the computational cost associated to the implicit step and leads to an efficiency close to that of a purely explicit scheme. The method is tested using two benchmark examples.

A new computational procedure for analysis of the melting and flame spread of polymers under fire conditions is presented. The method, termed Particle Finite Element Method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved as in the standard FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including loss of mass by gasification, is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting and flame spread of polymers under different fire conditions are described. Numerical results are compared with experimental data provided by NIST.

The field of fluid-structure interaction (FSI) has important applications ranging from the bio-medical to the civil and aeronautical engineering fields. Despite the different approaches developed over recent years the general solution of FSI problems remains however far from being closed. This paper addresses the theoretical analysis of a several partitioned solution schemes for FSI. This is achieved by choosing a simple but representative model problem which allows to obtain analytical results. A loose coupling partitioned procedure is presented first. An iterative version of the same algorithm is presented next together with an analysis of its convergence properties and a brief discussion of a possible acceleration strategy. Finally a new iterative strategy based on solving a modified equation is described. Some examples of application of the partitioned algorithms considered are presented including the aeroelastic analysis of a bridge.

In this paper, the so‐called added‐mass effect is investigated from a different point of view of previous publications. The monolithic fluid–structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid–structure interaction problems, which has good convergent characteristics even for biomechanical application, where the added‐mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods. Copyright © 2009 John Wiley & Sons, Ltd.

This diploma thesis deals with the implementation of a fluid solver for incompressible and compressible flows within the multi-physics framework Kratos. The presentation of this environment based on the finite element method (FEM) and an introduction to multidisciplinary problems in general are the starting point of this work and help understanding the following steps more easily. Originating from the basic conservation equations for mass, momentum and energy, the Euler equations for inviscid flow are derived. In this context some approximations are presented that avoid the solution of the energy equation and allow the use of a general approach for the simulation of incompressible, slightly compressible and barotropic flow. The implementation of the incompressible case is outlined step-by-step: Having discretized the continuous problem, a fractional step scheme is presented in order to uncouple pressure and velocity components by a split of the momentum equation. Emphasis is placed on the nodal implementation using an edge-based data structure. Moreover, the orthogonal subscale stabilization - necessary because of the finite element discretization - is explained very briefly. Subsequently, the solver is extended to compressible regime mentioning the respective modifications. For validation purposes numerical examples of incompressible and compressible flows in two and three dimensions round of this first part. In a second step, the implemented flow solver is prepared for the fluid-structure coupling. After presenting solving procedures for multi-disciplinary problems, the arbitrary Lagrangian Eulerian (ALE) formulation is introduced and the conservation equations are modified accordingly. Some preliminary tests are performed, particularly with regard to mesh motion and adjustment of the boundary conditions. Finally, expectations for the envisaged fluid-structure coupling are brought forward.