Search results for "Finite element method"
showing 10 items of 746 documents
The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media
2009
A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection-diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations sy…
Numerical Study of Two Sparse AMG-methods
2003
A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.
Controllability method for the Helmholtz equation with higher-order discretizations
2007
We consider a controllability technique for the numerical solution of the Helmholtz equation. The original time-harmonic equation is represented as an exact controllability problem for the time-dependent wave equation. This problem is then formulated as a least-squares optimization problem, which is solved by the conjugate gradient method. Such an approach was first suggested and developed in the 1990s by French researchers and we introduce some improvements to its practical realization. We use higher-order spectral elements for spatial discretization, which leads to high accuracy and lumped mass matrices. Higher-order approximation reduces the pollution effect associated with finite elemen…
Monotonic solution of heterogeneous anisotropic diffusion problems
2013
Anisotropic problems arise in various areas of science and engineering, for example groundwater transport and petroleum reservoir simulations. The pure diffusive anisotropic time-dependent transport problem is solved on a finite number of nodes, that are selected inside and on the boundary of the given domain, along with possible internal boundaries connecting some of the nodes. An unstructured triangular mesh, that attains the Generalized Anisotropic Delaunay condition for all the triangle sides, is automatically generated by properly connecting all the nodes, starting from an arbitrary initial one. The control volume of each node is the closed polygon given by the union of the midpoint of…
The MAST-edge centred lumped scheme for the flow simulation in variably saturated heterogeneous porous media
2012
A novel methodology is proposed for the solution of the flow equation in a variably saturated heterogeneous porous medium. The computational domain is descretized using triangular meshes and the governing PDEs are discretized using a lumped in the edge centres numerical technique. The dependent unknown variable of the problem is the piezometric head. A fractional time step methodology is applied for the solution of the original system, solving consecutively a prediction and a correction problem. A scalar potential of the flow field exists and in the prediction step a MArching in Space and Time (MAST) formulation is applied for the sequential solution of the Ordinary Differential Equation of…
Fictitious Domain Methods for the Numerical Solution of Two-Dimensional Scattering Problems
1998
Fictitious domain methods for the numerical solution of two-dimensional scattering problems are considered. The original exterior boundary value problem is approximated by truncating the unbounded domain and by imposing a nonreflecting boundary condition on the artificial boundary. First-order, second-order, and exact nonreflecting boundary conditions are tested on rectangular and circular boundaries. The finite element discretizations of the corresponding approximate boundary value problems are performed using locally fitted meshes, and the discrete equations are solved with fictitious domain methods. A special finite element method using nonmatching meshes is considered. This method uses …
Non-reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow
2011
We consider a time-harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non-reflecting boundary condition on the artificial boundary by means of a Dirichlet-to-Neumann (DtN) map based on a modal decomposition. Compared with the hard-walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a …
Analysis of infilled frames using A coupled finite element and boundary element solution scheme
1988
The behaviour of infilled frames subjected to horizontal loads is analysed by an iterative numerical procedure. The stiffness of the structural system is determined with variations in geometrical and mechanical characteristics. The analysis is carried out utilizing the boundary element method (BEM) for the infill and opportunely dividing the frame into finite elements, so as to transform the mutual interactions of the two subsystems into stresses distributed along the boundary for the infill and into nodal actions for the frame. This makes it possible to take into account the separation arising between the two substructures when mutual tensile stresses are involved. At first, infills withou…
Structural Safety Assessment of Marine Operations From a Long-Term Perspective: A Case Study of Offshore Wind Turbine Blade Installation
2019
Abstract A marine operation is a complex non-routine activity of limited duration carried out in offshore environment. Due to safety reasons, these operations are normally performed within specific sea state limits, which are derived from numerical modelling and analysis of hazardous events. In view of the uncertainties in the assessment of structural responses under stochastic environmental conditions, these limiting curves correspond to a target structural failure probability recommended in offshore standards (for example, 10−4 per operation as specified by DNV-GL). However, one of the main limitations is that these curves do not reflect site-specific safety assessment. The current paper …
Transparent boundary condition for acoustic propagation in lined guide with mean flow
2008
A finite element analysis of acoustic radiation in an infinite lined guide with mean flow is studied. In order to bound the domain, transparent boundary conditions are introduced by means of a Dirichlet to Neumann (DtN) operator based on a modal decomposition. This decomposition is easy to carry out in a hard‐walled guide. With absorbant lining, many difficulties occur even without mean flow. Since the eigenvalue problem is no longer selfadjoint, acoustic modes are not orthogonal with respect to the L2‐scalar product. However, an orthogonality relation exists which permits writing the modal decomposition. For a lined guide with uniform mean flow, modes are no longer orthogonal but a new sca…