Génération de maillages tridimensionnels pour la simulation des phénomènes physiques en géosciences

François Lepage. ( 2003 )
INPL, Nancy, France

Abstract

Three-dimensional meshes are widely used in Geosciences for discretizing the geological objects of the problem domain, thus providing a support for the numerical simulation of various processes depending on physical properties, such as balanced unfolding, raytracing, or fluid flow modelling in porous and permeable rock bodies. However, to ensure accuracy, efficiency, and stability, mesh elements must meet several requirements, especially on their shape and size. This work tackles some problems related to the generation of three-dimensional meshes that are expected be tailored to the applications they are dedicated to: First of all, starting from a structural madel, that is to say a set of interconnected surfaces representing the boundaries of the problem domain, a macro-model, called Soft Frame Madel, is defined for integrating the produced meshes and ensuring the geometrical and topological validity of their contacts. Then, solutions are proposed for the automatic generation of constrained triangulations for the three-dimensional surfaces of the structural model. The presented algorithms are guaranteed to terminate, ensure a minimum quality of the triangles, and allow a precise control of their size, depending on various constraints. As an application, a robust method is described for building sealed geological models. Finally, this work presents new algorithms for meshing volumes with tetrahedra or arbitrary polyhedra, and providing an efficient control on their shape and size. Their compatibility with existing numerical schemes is shown through some examples of simulations on real cases.

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BibTeX Reference

@PHDTHESIS{Lepage03These,
    author = { Lepage, François },
     title = { Génération de maillages tridimensionnels pour la simulation des phénomènes physiques en géosciences },
   chapter = { 0 },
      year = { 2003 },
    school = { INPL, Nancy, France },
  abstract = { Three-dimensional meshes are widely used in Geosciences for discretizing the geological
objects of the problem domain, thus providing a support for the numerical simulation
of various processes depending on physical properties, such as balanced unfolding, raytracing,
or fluid flow modelling in porous and permeable rock bodies. However, to ensure
accuracy, efficiency, and stability, mesh elements must meet several requirements, especially
on their shape and size.
This work tackles some problems related to the generation of three-dimensional meshes
that are expected be tailored to the applications they are dedicated to:
First of all, starting from a structural madel, that is to say a set of interconnected
surfaces representing the boundaries of the problem domain, a macro-model, called Soft
Frame Madel, is defined for integrating the produced meshes and ensuring the geometrical
and topological validity of their contacts. Then, solutions are proposed for the automatic
generation of constrained triangulations for the three-dimensional surfaces of the structural
model. The presented algorithms are guaranteed to terminate, ensure a minimum
quality of the triangles, and allow a precise control of their size, depending on various
constraints. As an application, a robust method is described for building sealed geological
models. Finally, this work presents new algorithms for meshing volumes with tetrahedra
or arbitrary polyhedra, and providing an efficient control on their shape and size.
Their compatibility with existing numerical schemes is shown through some examples of
simulations on real cases. }
}