FIC/FEM formulation with matrix stabilizing terms for incompressible flows at low and high Reynolds numbers

The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-006-0060-yWe present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.Peer ReviewedPostprint (author's final draft

An advancing front point generation technique

An algorithm to construct boundary‐conforming, isotropic clouds of points with variable density in space is described. The input required consists of a specified mean point distance and an initial triangulation of the surface. Borrowing a key concept from advancing front grid generators, one point at a time is removed and, if possible, surrounded by admissible new points. This operation is repeated until no active points are left. Timings show that the scheme is about an order of magnitude faster than volume grid generators based on the advancing front technique, making it possible to generate large (>106) yet optimal clouds of points in a matter of minutes on a workstation. Several examples are included that demonstrate the capabilities of the technique.&nbsp

An advancing front technique for filling space with arbitrary separated objects

An advancing front technique for filling space with arbitrary, separated objects has been developed. The input required consists of the specification of the desired object type, the mean object size, the distance between objects in space, as well as an initial triangulation of the surface. The objects are assumed to be described by a coarse mesh of tetrahedra. One face at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active faces are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Several examples are included that demonstrate the capabilities of the technique. Copyright © 2009 John Wiley & Sons, Ltd

A general advancing front technique for filling space with arbitrary objects

An advancing front space‐filling technique for arbitrary objects has been developed. The input required consists of the specification of the desired mean point distance in space and an initial triangulation of the surface. One object at a time is removed from the active front, and, if possible, surrounded by admissible new objects. This operation is repeated until no active objects are left. Two techniques to obtain maximum packing are discussed: closest object placement (during generation) and move/enlarge (after generation). Different deposition or layering patterns can be achieved by selecting the order in which objects are eliminated from the active front. Timings show that for simple objects like spheres the scheme is considerably faster than volume mesh generators based on the advancing front technique, making it possible to generate large (> 106) yet optimal clouds of points in a matter of minutes on a PC. For more general objects, the performance may degrade depending on the complexity of the penetration checks. Several examples are included that demonstrate the capabilities of the technique.&nbsp

Advancing front techniques for filling space with arbitrary separated objects

A review is given of advancing front techniques for filling space with arbitrary separated objects. Over the last decade, these techniques have reached a considerable degree of maturity and are being used to generate clouds of points for SPH and FPM simulations, as well as spheres, ellipsoids, objects defined by a collection of spheres or polyhedral objects for DEM simulations. Algorithmic as well as implementational aspects are discussed. Techniques to obtain maximum packing, such as closest object placement (during generation) and move/enlarge (after generation) are also considered. Several examples are included that demonstrate the capabilities developed

A variational formulation for the multilayer perceptron

In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for the multilayer perceptron provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique we use a multilayer perceptron to solve some classical problems in the calculus of variations

Particle finite element method in fluid-mechanics including thermal convection-diffusion

A method is presented for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of the motion. Due to the severe element distortion, a frequent remeshing is performed in an efficient manner. An implicit time integration through a classical fractional step is presented. The non-linearities of the formulation are taken into account and solved with the fixed-point iteration method. The displacement and temperature solutions are coupled through the Boussinesq approximation. The Lagrangian formulation provides an elegant way of solving free-surface problems with thermal convection as the particles are followed during their motion. To illustrate the method, the Rayleigh–Bénard instability with and without free surface in two dimensions has been computed

Fractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEM

The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505–526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS

Incompressible lagrangian fluid flow with thermal coupling

A method is presented for the solution of an incompressible viscous fluid flow with heat transfer and solidification using a fully Lagrangian description of the motion. The originality of this method consists in assembling various concepts and techniques which appear naturally due to the Lagrangian formulation. First of all, the Navier-Stokes equations of motion coupled with the Boussinesq approximation must be reformulated in the Lagrangian framework, whereas they have been mostly derived in an Eulerian context. Secondly, the Lagrangian formulation implies to follow the material particles during their motion, which means to convect the mesh in the case of the Finite Element Method (FEM), the spatial discretisation method chosen in this work. This provokes various difficulties for the mesh generation, mainly in three dimensions, whereas it eliminates the classical numerical difficulty to deal with the convective term, as much in the Navier-Stokes equations as in the energy equation. Even without the discretization of the convective term, an efficient iterative solver, which constitutes the only viable alternative for three dimensional problems, must be designed for the class of Generalized Stokes Problems (GSP), which could be able to behave well independently of the mesh Reynolds number, as it can vary greatly for coupled fluid-thermal analysis. Moreover, it offers a natural framework to treat free-surface problems like wave breaking and rough fluid-structure contact. On one hand, the convection of the mesh during one time step after the resolution of the non-linear system provides explicitly the locus of the domain to be considered. On the other hand, fluid-to-fluid and fluid-to-wall contact, as well as the update of the domain due to the remeshing, must be accurately and efficiently performed. Finally, the solidification of the fluid coupled with its motion through a variable viscosity is considered An efficient overall algorithm must be designed to bring the method effective, particularly in a three dimensional context, which is the ambition of this monograph. Various numerical examples are included to validate and highlight the potential of the method

Analysis of the discharge capacity of radial gated spillways using numerical modelling application to Oliana dam

Current paper focuses on the analysis of radial gated spillways, which are analyzed by the solution of a numerical model. The Oliana Dam study case is considered and the discharge capacity is predicted both by the application of a level-set based free-surface solver and by the use of traditional empirical formulations The results of the analysis are then used in training an Artificial Neural Network so to allow real-time predictions of the discharge in any situation of energy head and gate opening within the operation range of the reservoir. The comparison of the results obtained with the different methods shows that numerical models can be useful as a predictive tool for the analysis of the hydraulic performance of radial-gated spillways, and highlights some drawbacks regarding the application of the empirical formulas