391 research outputs found
A CutFEM method for two-phase flow problems
In this article, we present a cut finite element method for two-phase
Navier-Stokes flows. The main feature of the method is the formulation of a
unified continuous interior penalty stabilisation approach for, on the one
hand, stabilising advection and the pressure-velocity coupling and, on the
other hand, stabilising the cut region. The accuracy of the algorithm is
enhanced by the development of extended fictitious domains to guarantee a well
defined velocity from previous time steps in the current geometry. Finally, the
robustness of the moving-interface algorithm is further improved by the
introduction of a curvature smoothing technique that reduces spurious
velocities. The algorithm is shown to perform remarkably well for low capillary
number flows, and is a first step towards flexible and robust CutFEM algorithms
for the simulation of microfluidic devices
Virtual Delamination Testing through Non-Linear Multi-Scale Computational Methods: Some Recent Progress
This paper deals with the parallel simulation of delamination problems at the
meso-scale by means of multi-scale methods, the aim being the Virtual
Delamination Testing of Composite parts. In the non-linear context, Domain
Decomposition Methods are mainly used as a solver for the tangent problem to be
solved at each iteration of a Newton-Raphson algorithm. In case of strongly
nonlinear and heterogeneous problems, this procedure may lead to severe
difficulties. The paper focuses on methods to circumvent these problems, which
can now be expressed using a relatively general framework, even though the
different ingredients of the strategy have emerged separately. We rely here on
the micro-macro framework proposed in (Ladev\`eze, Loiseau, and Dureisseix,
2001). The method proposed in this paper introduces three additional features:
(i) the adaptation of the macro-basis to situations where classical
homogenization does not provide a good preconditioner, (ii) the use of
non-linear relocalization to decrease the number of global problems to be
solved in the case of unevenly distributed non-linearities, (iii) the
adaptation of the approximation of the local Schur complement which governs the
convergence of the proposed iterative technique. Computations of delamination
and delamination-buckling interaction with contact on potentially large
delaminated areas are used to illustrate those aspects
A stable cut finite element method for multiple unilateral contact
International audienceThis paper presents a novel CutFEM-LaTIn algorithm to solve multiple unilateral contact problems over geometries that do not conform with the finite element mesh. We show that our method is (i) stable, independently of the interface locations (ii) optimally convergent with mesh refinement and (iii) efficient from an algorithmic point of view
Statistical extraction of process zones and representative subspaces in fracture of random composite
We propose to identify process zones in heterogeneous materials by tailored
statistical tools. The process zone is redefined as the part of the structure
where the random process cannot be correctly approximated in a low-dimensional
deterministic space. Such a low-dimensional space is obtained by a spectral
analysis performed on pre-computed solution samples. A greedy algorithm is
proposed to identify both process zone and low-dimensional representative
subspace for the solution in the complementary region. In addition to the
novelty of the tools proposed in this paper for the analysis of localised
phenomena, we show that the reduced space generated by the method is a valid
basis for the construction of a reduced order model.Comment: Submitted for publication in International Journal for Multiscale
Computational Engineerin
Concurrent multiscale analysis without meshing: Microscale representation with CutFEM and micro/macro model blending
In this paper, we develop a novel unfitted multiscale framework that combines
two separate scales represented by only one single computational mesh. Our
framework relies on a mixed zooming technique where we zoom at regions of
interest to capture microscale properties and then mix the micro and macroscale
properties in a transition region. Furthermore, we use homogenization
techniques to derive macro model material properties. The microscale features
are discretized using CutFEM. The transition region between the micro and
macroscale is represented by a smooth blending function. To address the issues
with ill-conditioning of the multiscale system matrix due to the arbitrary
intersections in cut elements and the transition region, we add stabilization
terms acting on the jumps of the normal gradient (ghost-penalty stabilization).
We show that our multiscale framework is stable and is capable to reproduce
mechanical responses for heterogeneous structures in a mesh-independent manner.
The efficiency of our methodology is exemplified by 2D and 3D numerical
simulations of linear elasticity problems
A CutFEM method for Stefan-Signorini problems with application in pulsed laser ablation
In this article, we develop a cut finite element method for one-phase Stefan
problems, with applications in laser manufacturing. The geometry of the
workpiece is represented implicitly via a level set function. Material above
the melting/vaporisation temperature is represented by a fictitious gas phase.
The moving interface between the workpiece and the fictitious gas phase may cut
arbitrarily through the elements of the finite element mesh, which remains
fixed throughout the simulation, thereby circumventing the need for cumbersome
re-meshing operations. The primal/dual formulation of the linear one-phase
Stefan problem is recast into a primal non-linear formulation using a
Nitsche-type approach, which avoids the difficulty of constructing inf-sup
stable primal/dual pairs. Through the careful derivation of stabilisation
terms, we show that the proposed Stefan-Signorini-Nitsche CutFEM method remains
stable independently of the cut location. In addition, we obtain optimal
convergence with respect to space and time refinement. Several 2D and 3D
examples are proposed, highlighting the robustness and flexibility of the
algorithm, together with its relevance to the field of micro-manufacturing
Bridging Proper Orthogonal Decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
This article describes a bridge between POD-based model order reduction
techniques and the classical Newton/Krylov solvers. This bridge is used to
derive an efficient algorithm to correct, "on-the-fly", the reduced order
modelling of highly nonlinear problems undergoing strong topological changes.
Damage initiation problems are addressed and tackle via a corrected
hyperreduction method. It is shown that the relevancy of reduced order model
can be significantly improved with reasonable additional costs when using this
algorithm, even when strong topological changes are involved
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