Reference : Résolution d'un problème aux limites à frontières libres au moyen d'un algorithme de ...
Dissertations and theses : Doctoral thesis
Engineering, computing & technology : Mechanical engineering
http://hdl.handle.net/2268/167480
Résolution d'un problème aux limites à frontières libres au moyen d'un algorithme de remaillage adaptatif et anisotrope
English
[en] Resolution of a free-surface boundary value problem by means of an adaptive anisotropic remeshing algorithm
Béchet, Eric mailto [Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur >]
Nov-2002
École Polytechnique de Montréal, ​Montréal, ​​Canada
Ph.D.
[en] mesh generation ; finite elements ; RTM
[en] This thesis focuses on the study and development of remeshing algorithms for the
simulation of free surface flows in porous medium. This kind of flow is coming up with
the mould filling phase when manufacturing composite parts with the RTM process
(Resin Transfer Moulding), for which the majority of the applications of this research
have been done. Remeshing methods presented here are based on the Delaunay criterion
for triangulations. An adaptation for curved surfaces is proposed here. This adaptation
avoid to keep the link with an exact representation of the CAD surface, and allows the
use of a simple tessellation, instead. In fact, the ability to generate anisotropic surface
meshes without keeping the link with the tool used to model those surfaces allows to
interface finite element solvers with ease. A first publication has been made, based on
this part. For practical problems arising in RTM, the ideas coming from the first part
have been adapted to the goal of generating anisotropic elements. Thus, the Delaunay
criterion considered here is anisoptropic. In fact, the remeshing method presented in this
thesis allows a better simulation of the advancing flow front by using anisotropic
elements flattened in the direction of the flow. Thus, the resolution of the flow front is
high an shows a smooth and regular front. This was not the case with simulations made
on a fixed and isotropic mesh, with the same number of degree of freedom. For the
evolution of the free surface in time, a level-set approach was originally combined with
the remeshing algorithm in order to control the time step independently to the mesh. A
second publication has been based on this part. An adaptation of the remeshing
algorithm is proposed for thermal problems in the third part of this thesis. In fact, the
remeshing allows a better control of the numerical (artificial) diffusion that arise while
solving a transport phenomenon. This diffusion is related to the spatial discretisation
step. In the case of RTM it happens frequently, in the vicinity of the flow front and
when temperature differ notably to the temperature of the mould and the fibres, that the
numerical diffusion is an obstacle preventing to achieve a precise simulation of the
thermal behaviour in the mould. Transport equations require also a condition on the
time step to stabilize the numerical scheme when solved on an Eulerian grid. A variable
time-stepping for the sole calculation of transport phenomenon is proposed. A study
aimed to prove the possibility of generating a fixed mesh for the whole simulation is
proposed for planar geometries. An error estimator based on the Hessian matrix in
pressure is used to generate a mesh that will make the interpolation error uniform in the
domain. At the same time, an heuristic is built to stretch elements in function of the
successive positions of the mesh, determined a priori. This is improving the approximation of the front that is made during the simulation. Finally, an analytical study of a injection case is done, showing the difficulty to generate a mesh satisfying two conditions : uniformity of the interpolation error, and uniformity of the Courant number (which is shown to minimize the numerical diffusion in transport equations).
This work was published in a third article. The last part of this thesis focuses on the
application of the error estimator to curved surfaces. The surfaces considered here are
discrete, it is necessary to separate the interpolation error from the geometrical error.
This is done to avoid useless refinement of the mesh near angles in the geometry. An
sample case from industry is studied. This part composes the fourth article. Finally, a
discussion on the whole research made in this thesis is presented.
http://hdl.handle.net/2268/167480

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