A simple quality triangulation algorithm for complex geometries

This paper presents a simple algorithm for quality triangulation in domains with complex geometries. Based on the fact that the equilateral triangles (regular meshes) are ideal for numerical computations in computational fluids dynamics (CFD) analysis, the proposed algorithm starts with an initial equilateral triangle mesh covering the whole domain. Nodes close to the boundary edges satisfy the so-called non-encroaching criterion, the distance from any inserted node to any boundary vertices and the midpoints of any boundary edge is greater than a given characteristic length. Both nearly uniform and non-uniform triangle meshes can be generated using a mesh size reduction technique. Local refinement is achieved by using transition layers. More regular meshes can be generated in the interior of the domain and all angles of the triangle mesh produced by this algorithm are proven to be bounded in a reasonable range (19.5-141 degrees). Copyright (C) 2010 John Wiley & Sons, Ltd.