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Doctoral thesis (Dissertations and theses)
Résolution d'un problème aux limites à frontières libres au moyen d'un algorithme de remaillage adaptatif et anisotrope
Béchet, Eric
2002
 

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Keywords :
mesh generation; finite elements; RTM
Abstract :
[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.
Disciplines :
Mechanical engineering
Author, co-author :
Béchet, Eric ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Conception géométrique assistée par ordinateur
Language :
English
Title :
Résolution d'un problème aux limites à frontières libres au moyen d'un algorithme de remaillage adaptatif et anisotrope
Alternative titles :
[en] Resolution of a free-surface boundary value problem by means of an adaptive anisotropic remeshing algorithm
Defense date :
November 2002
Institution :
École Polytechnique de Montréal, Montréal, Canada
Degree :
Ph.D.
Available on ORBi :
since 14 May 2014

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