Automatic generation of a quadrangular mesh

Whereas the precision of calculations performed by finite element, finite volume or finite difference codes closely depends on the discretization mesh. Mesh quality depends on its geometry and on its adaptation to variations of calculated values. After an overview of peculiarities of Lagrangian meshes, the author reports an analysis of existing methods of automatic mesh generation, and presents a method of automatic generation of a non-structured quadrangular mesh from a triangular mesh. Then, he describes the generation of a triangular mesh adapted to the domain geometry, its modification in order to comply with requirements related to the formation of quadrangles, the generation of the corresponding quadrangular mesh by regrouping triangles two by two, and the smoothing of the so-obtained mesh according to defined criteria and to the calculated solution