Automatic construction of non-obtuse boundary and/or interface Delaunay triangulations for control volume methods

A Delaunay mesh without triangles having obtuse angles opposite to boundary and interface edges (obtuse boundary=interface triangles) is the basic requirement for problems solved using the control volume method. In this paper we discuss postprocess algorithms that allow the elimination of obtuse boundary=interface triangles of any constrained Delaunay triangulation with minimum angle . This is performed by the Delaunay insertion of a nite number of boundary and=or interface points. Techniques for the elimination of two kinds of obtuse boundary=interface triangles are discussed in detail: 1-edge obtuse triangles, which have a boundary=interface (constrained) longest edge; and 2-edge obtuse triangles, which have both their longest and second longest edge over the boundary=interface. More complex patterns of obtuse boundary=interface triangles, namely chains of 2-edge constrained triangles forming a saw diagram and clusters of triangles that have constrained edges sharing a common vertex are managed by using a generalization of the above techniques. Examples of the use of these techniques for semiconductor device applications and a discussion on their generalization to 3-dimensions (3D) are also included