Comparison of mapping operators for unstructured meshes

In this paper, two PDE-based mapping operators for the generation of unstructured meshes are compared. While the Winslow operator allows the construction of valid meshes for most configurations, the functional-based operators based on area, length, orthogonality and their combinations provide a finer control on the resulting meshes. Two distinct discretization methods of the operators are also compared. An original approach using a finite difference scheme on unstructured meshes is implemented and compared to a finite volume formulation. While more complex to implement and control, mainly because of the cross-derivative terms which must be carefully discretized, the finite volume method yields a more robust and stable formulation that allows dealing with sharp curvature variations of the boundaries. Finally, a criterion for the mesh smoothness which has a global definition is presented in order to compare the smoothness of the resulting mesh obtained by different operators.