159,866 research outputs found
Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection
This work presents the application of density-based topology optimisation to
the design of three-dimensional heat sinks cooled by natural convection. The
governing equations are the steady-state incompressible Navier-Stokes equations
coupled to the thermal convection-diffusion equation through the Bousinessq
approximation. The fully coupled non-linear multiphysics system is solved using
stabilised trilinear equal-order finite elements in a parallel framework
allowing for the optimisation of large scale problems with order of 40-330
million state degrees of freedom. The flow is assumed to be laminar and several
optimised designs are presented for Grashof numbers between and .
Interestingly, it is observed that the number of branches in the optimised
design increases with increasing Grashof numbers, which is opposite to
two-dimensional optimised designs.Comment: Submitted (18th of August 2015
Cut Finite Elements for Convection in Fractured Domains
We develop a cut finite element method (CutFEM) for the convection problem in
a so called fractured domain which is a union of manifolds of different
dimensions such that a dimensional component always resides on the boundary
of a dimensional component. This type of domain can for instance be used
to model porous media with embedded fractures that may intersect. The
convection problem can be formulated in a compact form suitable for analysis
using natural abstract directional derivative and divergence operators. The cut
finite element method is based on using a fixed background mesh that covers the
domain and the manifolds are allowed to cut through a fixed background mesh in
an arbitrary way. We consider a simple method based on continuous piecewise
linear elements together with weak enforcement of the coupling conditions and
stabilization. We prove a priori error estimates and present illustrating
numerical examples
A monolithic fluid-structure interaction formulation for solid and liquid membranes including free-surface contact
A unified fluid-structure interaction (FSI) formulation is presented for
solid, liquid and mixed membranes. Nonlinear finite elements (FE) and the
generalized-alpha scheme are used for the spatial and temporal discretization.
The membrane discretization is based on curvilinear surface elements that can
describe large deformations and rotations, and also provide a straightforward
description for contact. The fluid is described by the incompressible
Navier-Stokes equations, and its discretization is based on stabilized
Petrov-Galerkin FE. The coupling between fluid and structure uses a conforming
sharp interface discretization, and the resulting non-linear FE equations are
solved monolithically within the Newton-Raphson scheme. An arbitrary
Lagrangian-Eulerian formulation is used for the fluid in order to account for
the mesh motion around the structure. The formulation is very general and
admits diverse applications that include contact at free surfaces. This is
demonstrated by two analytical and three numerical examples exhibiting strong
coupling between fluid and structure. The examples include balloon inflation,
droplet rolling and flapping flags. They span a Reynolds-number range from
0.001 to 2000. One of the examples considers the extension to rotation-free
shells using isogeometric FE.Comment: 38 pages, 17 figure
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study
It is well known that the solution of topology optimization problems may be
affected both by the geometric properties of the computational mesh, which can
steer the minimization process towards local (and non-physical) minima, and by
the accuracy of the method employed to discretize the underlying differential
problem, which may not be able to correctly capture the physics of the problem.
In light of the above remarks, in this paper we consider polygonal meshes and
employ the virtual element method (VEM) to solve two classes of paradigmatic
topology optimization problems, one governed by nearly-incompressible and
compressible linear elasticity and the other by Stokes equations. Several
numerical results show the virtues of our polygonal VEM based approach with
respect to more standard methods
Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and devise the hybridizable discontinuous Galerkin (HDG) method. Exact geometry described by non-uniform rational B-splines (NURBS) is integrated into HDG using the framework of the NURBS-enhanced finite element method (NEFEM). Moreover, optimal convergence and superconvergence properties of HDG-Voigt formulation in presence of symmetric second-order tensors are exploited to construct inexpensive error indicators and drive degree adaptive procedures. Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows are presented. Moreover, this is done for both high-order HDG approximations and the lowest-order framework of face-centered finite volumes (FCFV).Peer ReviewedPostprint (author's final draft
An adaptive fixed-mesh ALE method for free surface flows
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version
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